The John Marshall Law Review
Volume 47 | Issue 4
Article 8
Summer 2014
Does the Prisoner's Dilemma Refute the Coase
Theorem?, 47 J. Marshall L. Rev. 1289 (2014)
Enrique Guerra-Pujol
Orlando Martínez-García
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Enrique Guerra-Pujol & Orlando Martínez-García, Does the Prisoner's Dilemma Refute the Coase Theorem?, 47 J. Marshall L. Rev.
1289 (2014)
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DOES THE PRISONER’S DILEMMA REFUTE
THE COASE THEOREM?
ENRIQUE GUERRA-PUJOL 1
ORLANDO I. MARTÍNEZ-GARCÍA 2
1290
I.Introduction ........................................................................... 1291
1291
II. Standard Versions of the Prisoner’s Dilemma ....................... 1292
1291
A. Numerical Form ...................................................... 1292
1295
B. Algebraic or Logical Form ........................................ 1296
III. Coasean Version of the Dilemma (with Strategic and Non1297
Strategic Bargaining) ..................................................... 1298
A. A Tale of Two Parables: Parable of the Rancher
1298
and the Farmer and Parable of the Prisoners .......... 1298
1300
B. The Three Conditions of the Coase Theorem ............ 1301
1300
1. Reciprocal Nature of the Prisoner’s Dilemma ..... 1301
2. Well-Defined Property Rights............................. 1301
1301
3. Zero Transaction Costs, Strategic Behavior,
1302
and Non-Strategic Bargaining ............................ 1301
4. Strategic Bargaining, Threats and Promises in
1303
the Prisoner’s Dilemm a ...................................... 1301
5. Non-Strategic Coasean Bargaining..................... 1304
1303
IV. The Role of Uncertainty, Exponential Discounting, and
Elasticity in the Coasean Version of the Prisoner’s
1306
Dilemm a ........................................................................ 1307
A. Uncertainty ............................................................. 1307
1306
B. Exponential Discounting ......................................... 1308
1307
C. Price Elasticity of Demand ...................................... 1310
1309
Exam ple #1 ............................................................. 1312
1313
Exam ple #2 ............................................................. 1312
1313
Exam ple #3 ............................................................. 1313
1314
D. Lessons and Discussion ........................................... 1313
1314
V.A Brief Digression Regarding the Role of Third Parties in
the Prisoner’s Dilemm a .................................................. 1315
1314
VI. Some Closing Thoughts on the Complexity of the
Prisoner’s Dilemma ........................................................ 1317
1316
1317
VII. Conclusion ......................................................................... 1318
1 Lecturer, University of Central Florida, Dixon School of Accounting.
College of Business Administration. J.D., Yale Law School. B.A., UCSB.
Enrique Guerra-Pujol presented a previous draft of this paper on the morning
of December 7, 2013 at the 2013 Northeast People of Color Legal Scholarship
Conference held at the University of Puerto School of Law and wishes to thank
Taja-Nia Y. Henderson, Orlando Martinez-Garcia, Adys Ann Guerra, Sydjia
Robinson, Hamed G. Santaella, Carlitos del Valle, and Judge Jenny Rivera for
attending my talk and for their helpful comments and suggestions.
2 Visiting Professor, Interamerican University of Puerto Rico Law School.
Adjunct, University of Puerto Rico, Arecibo Campus, Department of Social
Science. LL.M., University of Pennsylvania. J.D., Interamerican University of
Puerto Rico Law School. B.A.,The American University.
1290
1289
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different from its predecessors, particularly since it had the benefit
of two years of planning.
Like the shift in conference scheduling, other changes have
taken place within the LatCrit entity, including concerted efforts
to continue a process of institutionalization. In recent years, there
has been a growing focus on how to capitalize on its critical niche,
continue cultivating the next generation of critical scholars, and
ensure that the baton of outsider jurisprudence is passed along.
Internally, the organization has shifted, including a gradual
changing of the guard in leadership,
so to speak, as well as a
3
downsizing in administration. For example, from 2008 to the
present, the Board of Directors was intentionally downsized, with
a growing number of Board seats being occupied by junior law
I. INTRODUCTION
professors. 6
Another major development is LatCrit’s acquisition of a
Building upon the main theme of this year’s LatCrit
physical space for the organization. The property, Campo Sano
Conference, Resistance Rising: Theorizing and Building Cross(Spanish for “Camp Healthy,” or more literally, “Camp Sanity”), is
Sector Movements, 4 this paper (i.e., our contribution
to this larger
a ten-acre parcel of land located in Central Florida. 7 Purchased by
critical conversation) challenges one of the dominant paradigms in
LatCrit in 2011, the space is home to 5The Living Justice Center
economics and law: the Coase Theorem. Specifically, we present a
and the LatCrit Community Campus. 8 The physical facility serves
thought-experiment, what we shall call the “pure Coasean version”
as a means “to level the playing field and 6give LatCrit activists a
of the famous Prisoner’s Dilemma game. In brief, what if the
fighting chance to be heard.” 9 The space is intended
prisoners in this game-theory parable were allowed to
communicate and bargain with each other instead of being held in
to serve as the hub of their educational, research,
separate cells, as in the standard version of the dilemma? Would
advocacy and activism to remedy the imbalance and
our prisoners strike a mutually-beneficial and collectively-optimal
deficiencies of the current legal system. Having an
Coasean bargain, as the Coase Theorem predicts? 7 Or, as
independent physical base has become critical as
predicted in the standard one-shot version of the Prisoner’s
universities and law schools increasingly are even less
Dilemma in which bargaining is not allowed, 8 would they still end
3 A.W.
Naming
and
Tucker,
Launching
A Two-Person
a New Discourse
Dilemma: The
of Critical
Prisoner’s
Legal
Dilemma
Scholarship,
(1950), as
2
H
ARV . LATINO
L. REV
(1997). Jr., The Mathematics of Tucker: A Sampler, 14
reprinted
in Philip
D.. 1Straffin,
-YEAR
C. M
ATHEMATICS
J. 228Conferences,
(1983).
also
LatCrit
Biennial
LATCRIT: LATINA & LATINO
TWOSee
4 Latina
CRITICAL
LEGAL
& Latino
THEORY
Critical
, INC.,Legal
http://latcrit.org/content/conferences/latcritTheory, Inc., 2013 Biennial LatCrit
Conference
biennial-conferences/
Program (last
Schedule
visited (and
July 5,Related
2013) (providing
Events), (2013),
a list of available
the previous
at
http://latcrit.org/media/medialibrary/2013/10/LatCrit2013_Conference_Progra
conferences, and providing direct links to view symposia articles for some
m_FinalR.pdf.
years (found by following the respective year’s link to its corresponding
5 The Coase Theorem is named after the late Ronald Coase. Ronald H.
webpage).
1, 1–44
(1960). George
Coase,
The Problem
of Social
Cost, 3 aJ.L.
& ECON.body
Additionally,
LatCrit
has developed
substantial
of scholarship
from
Stigler, other
however,
was the symposia:
economistinter
who alia
first the
presented
the idea
now known
several
stand-alone
South-North
Exchange,
the
EORGE J. STIGLER
, THE THEORY
OF PRICE
113
as
the Space
Coase Series,
Theorem.
Study
the G
International
and Comparative
Colloquia.
LatCrit
ATCed.
RIT:1966).
LATCGeorge
RIT: LATINA
& stated
LATINOCoase’s
CRITICAL
EGAL
THEORY,
(MacMillan,
Stigler
idea Las
a “theorem”
Symposia, L3d
INC.,coined
http://latcrit.org/content/publications/latcrit-symposium/
(last
visited
and
the term “Coase Theorem.” Id.
generally WILLIAM POUNDSTONE , PRISONER’S DILEMMA (Anchor
July6 5,See
2014).
6 These
Professors
Marc-Tizoc
González,
AndreaofFreeman,
and
Books
1993) include
(providing
an overview
and history
of the origins
the dilemma);
César
Cuahtémoc
García Hernández.
SeeofAbout
LatCrit, supra
note 21,
3 (listing
see also
F. E. Guerra-Pujol,
The Parable
the Prisoners,
5–9 (June
2013)
the
professorsGuerra-Pujol,
on the LatCrit
of Directors
their respective
law
[hereinafter
TheBoard
Parable
of the and
Prisoners]
(unpublished
schools).
manuscript)
(on
file
with
author),
available
at
7 Campo Sano, LATCRIT: LATINA AND LATINO CRITICAL (explaining
LEGAL THEORY
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2281593,
the,
INC, http://www.latcrit.org/content/campo-sano/
(last visited July 5, 2014).
prisoner’s
parable).
7 Id.
8
8 See
9
Id. infra Part I.B.
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up defecting?
Before proceeding, it is worth noting that few scholars have
explored the possible relation between the Coase Theorem and the
Prisoner’s Dilemma. One important exception is Wayne Eastman,
a professor at Rutgers Business School, who established a formal
identity between the Coase Theorem and the Prisoner’s Dilemma. 9
3
Instead of following Eastman’s approach (i.e., relating the Coase
Theorem to the Prisoner’s Dilemma), 10 we do the opposite. We
relate the Prisoner’s Dilemma to the Coase Theorem by
I. INTRODUCTION
constructing a pure Coasean
version of the dilemma.
The remainder of this paper is organized as follows: Part II
Building
the main by
theme
of this year’s
LatCrit
provides
someuponbackground
presenting
the standard
Conference, Resistance
Rising: Dilemma
Theorizing
and Building
Crossformulations
of the Prisoner’s
in numerical
as well
as
4 this paper (i.e., our contribution to this larger
Sector Movements,
algebraic
terms. Next,
Part III presents our thought-experiment:
critical
challenges
the Theorem,
dominant we
paradigms
in
orderconversation)
to test the true
value of one
the of
Coase
considerin
a
5 Specifically, we present a
economics
and law:
the Coase
Theorem.
“pure
Coasean
version”
of the
Prisoner’s
Dilemma in which
thought-experiment,
we shalland
calltransactions
the “pure Coasean
version”
property
rights are what
well-defined
costs are
zero
6 In brief, what if the
of the
Prisoner’s
Dilemma
game.
(i.e.,
thefamous
prisoners
are allowed
to openly
communicate
and bargain
prisoners with
in each
this other).
game-theory
allowedof (i)
to
directly
Part IV parable
explores were
the effects
communicate (ii)
andexponential
bargain with
each otherand
instead
of being held
in
uncertainty,
discounting,
(iii) elasticity
on the
separate cells,
in the standard
version version
of the dilemma?
Would
behavior
of theasprisoners
in the Coasean
of the dilemma.
our prisoners
strike
mutually-beneficial
and (and
collectively-optimal
Part
V considers
thea role
of the prosecutor
third parties,
7 Or, as
Coasean bargain,
as the Dilemma
Coase Theorem
predicts?
generally)
in the Prisoner’s
and the overall
complexity
of
predicted
in Lastly,
the standard
the which
Prisoner’s
the
dilemma.
Part VI one-shot
identifies version
conditionsof under
the
8 would they still end
Dilemma inDilemma
which bargaining
is not
allowed,
Prisoner’s
refutes the
Coase
Theorem,
while Part VII
concludes.
3 A.W. Tucker, A Two-Person Dilemma: The Prisoner’s Dilemma (1950), as
II. STANDARD VERSIONS OF THE PRISONER’S DILEMMA
reprinted in Philip D. Straffin, Jr., The Mathematics of Tucker: A Sampler, 14
TWO-YEAR C. MATHEMATICS J. 228 (1983).
4 By
way&ofLatino
background,
we begin
thisInc.,
paper
by Biennial
presenting
the
Latina
Critical Legal
Theory,
2013
LatCrit
Conference or
Program
Schedule
(and Related
Events),
(2013), Dilemma
available at
standard
“canonical”
formulation
of the
Prisoner’s
–
http://latcrit.org/media/medialibrary/2013/10/LatCrit2013_Conference_Progra
by
far the most famous story or parable in all of game theory –
m_FinalR.pdf.
both
in numerical and algebraic form. 11 Readers who are already
5 The Coase Theorem is named after the late Ronald Coase. Ronald H.
familiar
the of
details
the 3Prisoner’s
Dilemma
skip
this
. 1, 1–44may
(1960).
George
Coase, Thewith
Problem
SocialofCost,
J.L. & ECON
part
and
proceed
to
Part
III.
Stigler, however, was the economist who first presented the idea now known
as the Coase Theorem. G EORGE J. STIGLER, THE THEORY OF PRICE 113
(MacMillan, 3d ed. 1966). George
Stigler stated
Coase’s idea as a “theorem”
A. Numerical
Form
and coined the term “Coase Theorem.” Id.
6 See generally W ILLIAM POUNDSTONE , PRISONER’S DILEMMA (Anchor
of history
the dilemma
is of
attributed
to
BooksThe
1993)original
(providingformulation
an overview and
of the origins
the dilemma);
see also F. E. Guerra-Pujol, The Parable of the Prisoners, 5–9 (June 21, 2013)
[hereinafter Guerra-Pujol, The Parable of the Prisoners] (unpublished
9 See Wayne (on
Eastman,fileHow Coasean
Bargaining
a Prisoners’
manuscript)
with
author), Entails
available
at
a formal
Dilemma,
72 NOTRE DAME L. REV . 89, 95–98 (1964) (establishing
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2281593,
(explaining
the
identity
between
the Coase Theorem and the Prisoner’s Dilemma).
prisoner’s
parable).
10Id.
7
Id. at 90 n.7.
11See
8
Seeinfra
sources
Partcited
I.B.supra note 6 and accompanying text.
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Professor from
different
Albert
itsTucker,
predecessors,
a mathematician
particularlyatsince
Princeton
it had University,
the benefit
who
of
twopresented
years of planning.
the parable of the prisoners during a guest lecture
Professor
at Stanford
Like the University
shift in conference
in May scheduling,
1950. 12 Specifically,
other changes
have
Tuckerplace
posedwithin
the following
hypothetical
scenarioconcerted
in a one-page
taken
the LatCrit
entity, including
efforts
mimeograph
A of
Two-Person
Dilemma In
that
he prepared
for
to
continue atitled
process
institutionalization.
recent
years, there
his guest
has
been lecture:
a growing focus on how to capitalize on its critical niche,
continue cultivating the next generation of critical scholars, and
Two
men,
charged
a joint violation
of law,isare
held along.
ensure
that
the
baton with
of outsider
jurisprudence
passed
separately
the police. Each
told thatincluding a gradual
Internally,
the byorganization
has isshifted,
(1) if of
onethe
confesses
the other does
not,speak,
the former
willasbe a
changing
guard and
in leadership,
so to
as well
given
reward of one unit
the latter
will2008
be fined
downsizing
in a administration.
Forand
example,
from
to two
the
present, units,
the Board of Directors was intentionally downsized, with
(2) if both
confess,
each will
be fined
unit. by junior law
a growing
number
of Board
seats
beingone
occupied
At the6 same time each has reason to believe that
professors.
Another
major
development
(3) if neither
confesses
both willisgoLatCrit’s
clear. 13 acquisition of a
physical space for the organization. The property, Campo Sano
In addition,
Professor
Tucker
included
the“Camp
following
“payoff
(Spanish
for “Camp
Healthy,”
or more
literally,
Sanity”),
is
table”
in his
mimeo
illustrate
parable: Florida. 7 Purchased by
a
ten-acre
parcel
of to
land
located his
in Central
LatCrit in 2011, the space is home to The Living Justice Center
and the LatCrit Community Campus. 8 The physical facility serves
as a means “to level the playing field and give LatCrit activists a
fighting chance to be heard.” 9 The space is intended
to serve as the hub of their educational, research,
14
advocacy and activism to remedy the imbalance and
deficiencies of the current legal system. Having an
Although Professor Tucker does not use the terms “Prisoner’s
independent physical base has become critical as
Dilemma” or “Prisoners’ Dilemma” in his original mimeo, he does
universities and law schools increasingly are even less
refer to the prisoners’ predicament as “a two-person dilemma” in
the title of the mimeo. 15 More importantly, in Tucker’s original
telling of his tale, we see all the elements associated with the
Naming and
Launching
New Discourse
of Critical
16
Legal Scholarship, 2
standard
version
of thea Prisoner’s
Dilemma:
HARV . LATINO L. REV . 1 (1997).
-Two Suspects: I and II are held in separate rooms and thus
See also LatCrit Biennial Conferences, LATCRIT: LATINA & LATINO
unable
or bargain with each other;
CRITICALtoLcommunicate
EGAL THEORY, INC., http://latcrit.org/content/conferences/latcrit-Two Choices: (last
confess
orJuly
not 5,
confess;
biennial-conferences/
visited
2013) (providing a list of the previous
conferences,
and providing
direct links
view symposia
articles
for some
-Interdependent
Payoffs:
the topayoffs
associated
with
each
years (found
following
the respective
year’s
to its corresponding
choice
dependbyupon
the choices
made by
bothlink
suspects;
webpage).
-Payoff Table: a visual presentation of the parable, or stated
Additionally, LatCrit has developed a substantial body of scholarship from
formally,
a reduction
the dilemma
to “normal
form.” Exchange, the
several other
stand-aloneofsymposia:
inter alia
the South-North
published
account and
of Comparative
the Prisoner’s
Dilemma,
StudyThe
Spacefirst
Series,
the International
Colloquia.
LatCrit
ATCRITnot
: LATappear
CRIT: LATINA
LATINO years
CRITICALlater,
LEGALwhen
THEORY
Symposia,
however, Ldoes
until &several
R.,
IDuncan
NC.,
http://latcrit.org/content/publications/latcrit-symposium/
(last gamevisited
Luce and Howard Raiffa’s published their classic
July 5, 2014).
6 These include Professors Marc-Tizoc González, Andrea Freeman, and
12 Cuahtémoc
SYLVIA NASAR
, A Hernández.
BEAUTIFUL See
MIND
: A BLatCrit,
IOGRAPHY
OF J
OHN 3F(listing
ORBES
César
García
About
supra
note
NASHprofessors
, JR. 118 (1998);
, supra
6 at, 117–18.
the
on thePOUNDSTONE
LatCrit Board
of note
Directors
and their respective law
13 See Tucker, supra note 3 (presenting the parable of the prisoner).
schools).
14 Tucker,
7
Campo supra
Sano, note
LATC3.RIT: LATINA AND LATINO CRITICAL LEGAL THEORY,
INC,15http://www.latcrit.org/content/campo-sano/
Id.
(last visited July 5, 2014).
16Id.
8
See id. (presenting all of the essential elements of the standard versions
9 Id.
of the
Prisoner’s Dilemma model).
129447:4
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47 JO HN
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theory treatise, Games and Decisions: Introduction and Critical
Survey: 17
The following interpretation [of a two-person, non-zerosum game], known as the prisoner’s dilemma, is popular:
Two suspects are taken into custody and separated. The
3
district attorney is certain that they are guilty of a
specific crime, but does not have adequate evidence to
convict them at trial. He points out to each prisoner that
I. INTRODUCTION
each has two alternatives:
to confess to the crime the
police are sure that they have done, or not to confess. If
Building
main
of this
year’sstates
LatCrit
they both upon
do not the
confess,
thentheme
the district
attorney
Conference,
Theorizing
and Building
Crosshe will Resistance
book themRising:
on some
very minor
trumped-up
Sector
Movements,
(i.e.,and
ourillegal
contribution
to this
larger
charge
such as4 this
pettypaper
larceny
possession
of a
critical
conversation)
of the
dominant
paradigms
weapon,
and theychallenges
will both one
receive
minor
punishment;
if in
5 Specifically, we present a
economics
and law:
the they
Coasewill
Theorem.
they both
confess
both be
prosecuted, but he
thought-experiment,
“puresentence;
Coasean but
version”
will recommendwhat
less we
thanshall
the call
mostthe
severe
6 In brief, what if the
of the
Prisoner’s
game.
if famous
one confesses
andDilemma
the other
does
not, then the
prisoners
in will
this receive
game-theory
allowed to
confessor
lenient parable
treatmentwere
for turning
communicate
and bargain
with the
eachlatter
other will
instead
being
held in
state’s evidence
whereas
get of
“the
book”
separate
cells,at as
in18the standard version of the dilemma? Would
slapped
him.
our prisoners strike a mutually-beneficial and collectively-optimal
as
Coasean
bargain, Luce
as the
Theorem the
predicts?
In addition,
and Coase
Raiffa express
payoffs7 ofOr,their
predicted in
the in
standard
one-shot
version
of the ofPrisoner’s
prisoners’
parable
numerical
form (i.e.,
in terms
years in
would they
still end
Dilemmainina which
is not
allowed,
prison)
payoff bargaining
table, stating
that
“the 8strategic
problem”
in
this particular parable “might reduce to” the following set of
payoffs:
3 A.W. Tucker, A Two-Person Dilemma: The Prisoner’s Dilemma (1950), as
reprinted in Philip D. Straffin, Jr., The Mathematics of Tucker: A Sampler, 14
TWO-YEAR C. MATHEMATICS J. 228 (1983).
4 Latina & Latino Critical Legal Theory, Inc., 2013 Biennial LatCrit
Conference Program Schedule (and Related Events), (2013), available at
http://latcrit.org/media/medialibrary/2013/10/LatCrit2013_Conference_Progra
m_FinalR.pdf.
5 The Coase Theorem is named after the late Ronald Coase. Ronald H.
Coase, The Problem of Social Cost, 3 J.L. & ECON. 1, 1–44 (1960). George
Stigler, however, was the economist who first presented the idea now known
19
as the Coase Theorem. G EORGE J. STIGLER, THE THEORY OF PRICE 113
(MacMillan, 3d ed. 1966). George Stigler stated Coase’s idea as a “theorem”
It is the
worth
that Luce
and coined
term noting
“Coase Theorem.”
Id. and Raiffa specifically included
6 See generally
ILLIAM POUNDSTONE
, PRISONER
’S DILEMMA
(Anchor
Professor
Tucker’sWstrategic
game and
their own
corresponding
Books 1993)
(providing
an overview
historyto
of the
origins of theNon-Zerodilemma);
payoff
matrix
in the
chapter and
devoted
“Two-Person
see also F. E. Guerra-Pujol, The Parable of the Prisoners, 5–9 (June 21, 2013)
[hereinafter Guerra-Pujol, The Parable of the Prisoners] (unpublished
manuscript)
(on
file
with
author),
available
at
17
R. DUNCAN LUCE & HOWARD RAIFFA, G AMES (explaining
AND DECISIONS
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2281593,
the:
INTRODUCTION
AND CRITICAL SURVEY (Dover Publications 2012) (1957).
prisoner’s
parable).
18Id.
7
Id. at 95.
19See
8
Id. infra Part I.B.
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20 In so doing,
Sum Non-Cooperative
different
from its predecessors,
Games.”particularly
since Luce
it had and
the benefit
Raiffa
of
present
two years
the of
Prisoner’s
planning.Dilemma parable in order to illustrate a
particular
Like the
model
shift
of strategic
in conference
behavior
scheduling,
– what game
other theorists
changes have
refer
This
taken
to as aplace
“two-person,
within the
non-zero-sum,
LatCrit entity,
non-cooperative
including concerted
game.” 21efforts
standard
version
of the
Dilemma In
thus
encompasses
all
to
continue
a process
of Prisoner’s
institutionalization.
recent
years, there
the been
elements
essential
non-zero-sum,
nonhas
a growing
focustoonsuch
how two-person,
to capitalize on
its critical niche,
cooperative
games: the next generation of critical scholars, and
continue
cultivating
-First
Prisoner’s
Dilemma is apassed
simplealong.
twoensure
thatand
theforemost,
baton of the
outsider
jurisprudence
person model
game; there has
are only
two prisoners.
is an
Internally,
theor organization
shifted,
including This
a gradual
important of
simplifying
assumption,
sincesothere
could just
as well
changing
the guard
in leadership,
to speak,
as well
as be
a
three, four, in
or nadministration.
number of suspects.
By reducing
number
of
downsizing
For example,
from the
2008
to the
players in
parable
to justwas
twointentionally
suspects, itdownsized,
simplifies with
the
present,
the this
Board
of Directors
underlying
situation.
a
growing strategic
number of
Board seats being occupied by junior law
6
-Second,
the Prisoner’s Dilemma is a non-zero-sum game
professors.
Another
development
LatCrit’s
acquisition
a
insofar
as bothmajor
suspects
can receive islight
sentences
if both are ofable
physical
the organization.
Campo
Sano
to remainspace
silentforinstead
of snitching.The
In property,
a zero-sum
game,
by
(Spanish
more literally,
Sanity”),
is
contrast, for
the “Camp
gain ofHealthy,”
one playeroralways
comes at “Camp
the expense
of the
by
a
ten-acre
parcel
of land located
in Central Florida.
other
player.
Moreover,
in a non-zero-sum
game,7 Purchased
such as the
LatCrit
in Dilemma,
2011, the aspace
is home
to TheisLiving
Justice
Prisoner’s
“win-win”
outcome
possible,
but Center
only if
8 The
physical facility serves
and
LatCrit
Community
Campus.
both the
players
agree
to cooperate
with each
other.
as a -Next,
means the
“to level
the playing
field story
and give
a
prisoners
in this
areLatCrit
playingactivists
a non9 The space
is intended
fighting
chance
to beThe
heard.”
cooperative
game.
prisoners
are incommunicado
insofar as
they are held in separate cells to prevent them from bargaining
to serve
the hub
of theira non-cooperative
educational, research,
with each
other.asStrictly
speaking,
game rules
advocacy
and activism
to remedy
the Coasean
imbalancebargaining
and
out the
possibility
of mutually
beneficial
the our
current
legal
Having
amongdeficiencies
the players.of(For
part, we
shallsystem.
later modify
thisan
aspect
physical when
base we
haspresent
becomeourcritical
as
of theindependent
Prisoner’s Dilemma
pure Coasean
universities
and law
schools
version
of the dilemma
in part
two.) increasingly are even less
-Last, but not least, the Prisoner’s Dilemma is a one-shot
game: the prisoners have only one opportunity to play the game.
Although this requirement is not stated explicitly in Luce and
Naming and Launching a New Discourse of Critical Legal Scholarship, 2
Raiffa’s
interpretation
of the parable, subsequent research has
H
ARV . LATINO
L. REV . 1 (1997).
LATINA
LATINO
See that
also LatCrit
Biennial
Conferences, possible
LATCRIT: when
shown
cooperation
is theoretically
the&game
is
C
RITICALmany
LEGALtimes
THEORY
, INC., http://latcrit.org/content/conferences/latcritplayed
(iteration)
and when the occurrence of the last
biennial-conferences/
visited July 5, 2013) (providing a list of the previous
22
round is uncertain.(last
conferences, and providing direct links to view symposia articles for some
years (found by following the respective year’s link to its corresponding
webpage).
20
Id. at 94–97.
Additionally,
LatCrit has developed a substantial body of scholarship from
21 See
generally,
Johnsymposia:
F. Nash, inter
Non-Cooperative
Games, 54
ANNALS the
OF
several
other
stand-alone
alia the South-North
Exchange,
M
ATHEMATICS
286 (1951).
and Raiffa,
were Colloquia.
one of the LatCrit
first to
Study
Space Series,
the Luce
International
andhowever,
Comparative
CRIT: LAT
CRITof
: L
ATINAin&the
LATINO
CRITICAL
LEGAL Dilemma.
THEORY,
express thisLAT
particular
type
game
form of
the Prisoner’s
Symposia,
ILNC
UCE
., &http://latcrit.org/content/publications/latcrit-symposium/
RAIFFA, supra note 17. As a further aside, John von (last
Neuman
visited
and
Oskar
July 5, Morgenstern
2014).
also presented non-zero-sum games in their foundational
6 These
Marc-Tizoc
González,
Freeman,
and
game
theory include
treatise,Professors
but the focus
of their work
is on Andrea
cooperative
games (i.e.
César
García Hernández.
supra note
games Cuahtémoc
in which bargaining
among See
the About
playersLatCrit,
is allowed),
not 3on(listing
nonVON
NEUMANNlaw
&
the
professors
on the
of Directors
their
respective
cooperative
games,
suchLatCrit
as the Board
Prisoner’s
Dilemma.and
JOHN
O SKAR MORGENSTERN, THEORY OF G AMES AND ECONOMIC BEHAVIOR 504–86
schools).
7 Campo
Sano,
LAT3d
CRIT
LATINA AND LATINO CRITICAL LEGAL THEORY,
(Princeton
Univ.
Press,
ed.: 1953).
INC,22http://www.latcrit.org/content/campo-sano/
See generally ROBERT AXELROD, THE EVOLUTION
(last visited
OFJuly
COOPERATION
5, 2014). 11
8 Id.Books rev. ed. 2006) (1984) (exploring various resolutions to the
(Basic
9 Id.
Prisoner’s
Dilemma when one player in this two-person game plays the game
129647:4
Vol.
Prisoner’s
47 JO HN
Dilemma
M ARS HALL
andL.
CoRase
EV .Theorem
1296
Vol.1295
1291
47:4
In addition, Luce and Raiffa attribute this standard
interpretation of the Prisoner’s Dilemma to A.W. Tucker and also
note that this example “has received considerable attention by
game theorists.” 23 That this particular parable was already
“popular” by the mid-1950s – and sufficiently well-known among
mathematicians to be included in Luce and Raiffa’s treatise on
3
game theory – is itself telling. But why did this parable become so
popular so quickly? One possible reason is the realism of the
Prisoner’s Dilemma.
NTRODUCTION
I. IRaiffa’s
Simply put, Luce and
version of this parable seems to
capture the legal system “in action,” or, more specifically, how the
Building
upon
the actually
main theme
this the
year’s
LatCrit
criminal
justice
system
operatesof when
prosecution
Conference,
Resistance
andmuch
Building
Crossdoes
not have
sufficient Rising:
evidence Theorizing
to go to trial,
less convict
4 this paper (i.e., our contribution to this larger
Sector
Movements,
24 Briefly,
when he is stymied by a lack of evidence,
an
individual.
critical
conversation)
the dominant
in
the
prosecutor
mustchallenges
adjust one
his ofstrategy,
for paradigms
without the
5 Specifically, we present a
economics and
law:
theone
Coase
Theorem.
cooperation
of at
least
of the
prisoners,
he will only be able to
thought-experiment,
what
we“minor
shall call
the “purecharge”
Coasean
secure
a conviction on
some
trumped-up
(toversion”
borrow
brief, come
what as
if the
of
the and
famous
Prisoner’s
Dilemma
Luce
Raiffa’s
phrasing).
And game.
thus 6it Inshould
no
prisoners
in the
this tactics
game-theory
parable
weretreatment”
allowed for
to
surprise that
of offering
“lenient
communicate
and bargain
each other
in
cooperation (i.e.,
getting with
a suspect
to instead
“flip” orof being
turn held
State’s
separate
the standard
version
of the dilemma?
Would
evidence) cells,
and asof infiling
“trumped-up
charges”
(what criminal
our
prisoners
strike refer
a mutually-beneficial
and collectively-optimal
defense
attorneys
to as “overcharging”)
are common
25
Coasean
as the Coase
Theorem predicts? 7 Or, as
strategies bargain,
used by prosecutors.
predicted in the standard one-shot version of the Prisoner’s
8 would they still end
Dilemma in whichB.bargaining
allowed,
Algebraicisornot
Logical
Form
Thus far, we have presented the standard Prisoner’s Dilemma
3 A.W. Tucker, A Two-Person Dilemma: The Prisoner’s Dilemma (1950), as
in numerical
form, but the payoffs in this model can also be
reprinted in Philip D. Straffin, Jr., The Mathematics of Tucker: A Sampler, 14
presented
in
algebraic
form. Consider, for example, the
228 (1983).
TWO-YEAR C. MATHEMATICSorJ. logical
4 Latina
following
payoff
table,
which
presents
theInc.,
Prisoner’s
Dilemma
in
& Latino Critical Legal Theory,
2013 Biennial
LatCrit
Conference
Program
Related Events), (2013), available at
both
numerical
andSchedule
algebraic(and
form:
http://latcrit.org/media/medialibrary/2013/10/LatCrit2013_Conference_Progra
m_FinalR.pdf.
5 The Coase Theorem is named after the late Ronald Coase. Ronald H.
Coase, The Problem of Social Cost, 3 J.L. & ECON. 1, 1–44 (1960). George
Stigler, however, was the economist who first presented the idea now known
as the Coase Theorem. G EORGE J. STIGLER, THE THEORY OF PRICE 113
(MacMillan, 3d ed. 1966). George Stigler stated Coase’s idea as a “theorem”
and coined the term “Coase Theorem.” Id.
6 See generally W ILLIAM POUNDSTONE , PRISONER’S DILEMMA (Anchor
with many
“with
an indefinite
number
of interactions,
Books
1993)iterations
(providing– an
overview
and history
of the
origins of thecooperation
dilemma);
can also
emerge”);
see also Robert
Axelrod
& of
William
D. Hamilton,
The Evolution
see
F. E. Guerra-Pujol,
The
Parable
the Prisoners,
5–9 (June
21, 2013)
1390, Parable
1391–92 of
(1981)
model based
of Cooperation,
241 SCIENCE The
[hereinafter
Guerra-Pujol,
the (presenting
Prisoners] a (unpublished
on the concept of
stable strategy
context of the
manuscript)
(onan evolutionarily
file
with
author), in theavailable
at
Prisoner's Dilemma game).
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2281593,
(explaining the
23 LUCEparable).
& RAIFFA, supra note 17, at 94.
prisoner’s
24Id.
7
Id. at 94–97.
25See
8
Id. infra
at 95.Part I.B.
1296
Vol. 47:4
1168
1296
Prisoner’s
47 JO HN
Dilemma
M ARS HALL
andL.
CoRase
EV .Theorem
1168
Vol. 1297
47:4
different from its predecessors, particularly since it had the benefit
of two years of planning.
Like the shift in conference scheduling, other changes have
taken place within the LatCrit entity, including concerted efforts
to continue a process of institutionalization. In recent years, there
has been a growing focus on how to capitalize on its critical niche,
continue cultivating the next generation of critical scholars, and
ensure that the baton of outsider jurisprudence is passed along.
Internally, the organization has shifted, including a gradual
changing of the guard in leadership, so to speak, as well as a
downsizing in administration. For example, from 2008 to the
present, the Board of Directors was intentionally downsized, with
a growing number of Board seats being occupied by junior26law
professors. 6
Another
development
is LatCrit’s
a
Here, we major
shall focus
on the descriptive
labels acquisition
C and D andofthe
physical
organization.
The the
property,
Campo
Sano
algebraic space
labels for
R, the
S, T,
and P. First,
players’
choices
or
(Spanish
“Camp
Healthy,”
literally,
“Camp
Sanity”),
is
“strategy for
sets”
of the
players or
in more
this matrix
now
appear
in more
7 Purchased
by
a
ten-acre
parcel“cooperation”
of land located
Central
Florida.(“D”)
general
terms:
(“C”)inand
“defection”
correspond
LatCrit
in 2011,
is home
to The Living
Justice
Center
to
“confess”
and the
“notspace
confess,”
respectively,
in the
traditional
8 The physical
27 Likewise,
facilityare
serves
and the ofLatCrit
Community
Campus.
the payoffs
now
version
the Prisoner’s
Dilemma.
as
a means in
“to level
the playing
give LatCrit
activists
a
designated
general
terms. field
For and
example,
“Reward”
(“R”)
9 The space
is intended
fighting
chance
to be heard.”
represents
the payoff
for mutual
cooperation,
“Punishment” (“P”)
represents the payoff for mutual defection, and “Temptation
serveandas“Sucker’s
the hubpayoff”
of their
research,
payoff”to (“T”)
(“S”)educational,
represent the
remaining
28
advocacy
and activism to remedy the imbalance and
two payoffs.
deficiencies
of (i.e.,
the in
current
system.
Having
an to
Stated
formally
generallegal
algebraic
terms
as opposed
independent
physicala base
hasa Prisoner’s
become critical
specific
numerical values),
game is
Dilemmaaswhen
universities
and payoffs
law schools
even less
the values
of the
are increasingly
ranked in are
ordinal
fashion:
T>R>P>S. 29 Moreover, regardless of whether the Prisoner’s
Dilemma is presented in numerical or algebraic form, the outcome
and logic
this game
remain
the same:
defection
is always a2
Naming
andofLaunching
a New
Discourse
of Critical
Legal Scholarship,
30 in the one-shot
dominant
strategy,
or
“Nash
equilibrium,”
HARV . LATINO L. REV . 1 (1997).
See also
version
of theLatCrit
game. Biennial Conferences, LATCRIT: LATINA & LATINO
CRITICAL
LEGAL
THEORY
, INC
., http://latcrit.org/content/conferences/latcritIf the
other
player
cooperates,
there is a choice between
biennial-conferences/ (last visited July 5, 2013) (providing a list of the previous
cooperation
which yields R (the reward for mutual cooperation) or
conferences, and providing direct links to view symposia articles for some
defection
which
yields T the
(therespective
temptation
to defect).
assumption,
years (found
by following
year’s
link to By
its corresponding
T
>
R,
so
that
it
pays
to
defect
if
the
other
cooperates.
On
the other
webpage).
Additionally,
developed
a substantial
bodya ofchoice
scholarship
from
hand,
if the LatCrit
other has
player
defects,
there is
between
several other which
stand-alone
symposia:
alia the
South-North
Exchange,
the
cooperation
yields
S (theinter
sucker’s
payoff)
or defection
which
Study Space Series, the International and Comparative Colloquia. LatCrit
Symposia, LATCRIT: LATCRIT: LATINA & LATINO CRITICAL LEGAL THEORY,
INC.,26 Axelrod
http://latcrit.org/content/publications/latcrit-symposium/
& Hamilton, supra note 22, at 1392.
(last
visited
at 1391–92.
July275,Id.2014).
28 These
6
Id. Forinclude
our part,
Professors
we shallMarc-Tizoc
follow this González,
conventionAndrea
and thus
Freeman,
continueand
to
refer
César toCuahtémoc
the payoffs
García
in theHernández.
Prisoner’s Dilemma
See Aboutusing
LatCrit,
these
supra
standard
note 3labels
(listing
in
these
the professors
algebraic or
ongeneral
the LatCrit
terms. Board of Directors and their respective law
29 See Axelrod & Hamilton, supra note 22, at 1392, Figure 1 (identifying
schools).
Campo
Sano,
LATCRIT
ATINA with
AND illustrative
LATINO CRITICAL
LEGAL
THEORY
that7 the
“payoff
to Player
A :is Lshown
numerical
values[,
and],
INC, http://www.latcrit.org/content/campo-sano/
(last visited July 5, 2014).
[t]he
game is defined by T>R>P>S and R>(S+T)/2”).
30Id.
8
See, e.g., SYLVIA NASAR, A BEAUTIFUL MIND: A BIOGRAPHY OF JOHN
9 Id. NASH, JR. 15, 20 (1998).
FORBES
129847:4
Vol.
Prisoner’s
47 JO HN
Dilemma
M ARS HALL
andL.
CoRase
EV .Theorem
1298
Vol.1297
1291
47:4
yields P (the punishment for mutual defection). By assumption P >
S, so it pays to defect if the other player defects. Thus, no matter
what the other player does, it pays to defect. But, if both defect,
both get P rather than the larger value of R that both could have
gotten had both cooperated. Hence, the dilemma.
With two individuals destined to never meet again, the only
3
strategy that can be called a solution to the game is to defect
always despite the seeming paradoxical outcome that both do
worse than they could have had they cooperated. 31
Therefore, whetherI. theINTRODUCTION
parable is presented in numerical or
algebraic form, the central lesson of the standard one-shot version
upon
the main
year’s is LatCrit
of theBuilding
Prisoner’s
Dilemma
is that theme
defectionofor this
“snitching”
always
Conference,
Resistance ofRising:
Theorizing
and
Building
Crossthe Nash equilibrium
the game.
Moreover,
from
an individual
4 this paper (i.e., our contribution to this larger
Sector
Movements,
perspective,
both prisoners
are always better off by defecting,
critical conversation)
of theFor
dominant
paradigms
in
regardless
of the otherchallenges
prisoner’sone
actions.
example,
if the other
5 Specifically, we present a
economics(“Player
and law:B”)thesnitches,
Coase Theorem.
prisoner
Player A
might as well snitch to
thought-experiment,
what
we shall
call even
the “pure
version”
avoid
S, the sucker’s
payoff.
In fact,
if theCoasean
other prisoner
6 In brief, what if the
of the quiet,
famous
Prisoner’s
Dilemma
game.
keeps
Player
A is still
better off
snitching
insofar as T, the
prisoners
in this
game-theory
parable
were allowed to
temptation payoff,
is always
greater than
R.
communicate
bargain
withare
each
of being
held
in
But whatand
if the
prisoners
notother
held instead
in separate
rooms
(i.e.,
separate
as in the standard
version
the dilemma?
Would
they are cells,
not incommunicado)?
What
if the of
prisoners
could actually
our
prisoners
strikeother
a mutually-beneficial
andtocollectively-optimal
bargain
with each
and had the ability
make enforceable
Or,shall
as
Coasean
bargain,
as threats?
the Coase
Theorem
predicts?
promises and
credible
Would
they still
defect?7 We
predicted
in the
standard
version
of the version”
Prisoner’s
consider these
questions
next one-shot
by presenting
a “Coasean
of
8 would they still end
Dilemma
in which
bargaining
not allowed,
the Prisoner’s
Dilemma,
one iniswhich
the prisoners
are allowed to
communicate and bargain with each other.
A.W. Tucker, A Two-Person Dilemma: The Prisoner’s Dilemma (1950), as
VERSION OF THE DILEMMA (WITH STRATEGIC AND N ONIII. COASEAN
reprinted in Philip D. Straffin, Jr., The Mathematics of Tucker: A Sampler, 14
BARGAINING )
STRATEGIC
J. 228 (1983).
TWO-YEAR C. MATHEMATICS
3
4 Latina & Latino Critical Legal Theory, Inc., 2013 Biennial LatCrit
Conference
Program Schedule
(and Related
(2013),
available
at
The previous
section discussed
the Events),
standard
version
of the
http://latcrit.org/media/medialibrary/2013/10/LatCrit2013_Conference_Progra
Prisoner’s Dilemma, in which both players are separated with no
m_FinalR.pdf.
means
to communicate with each other. This section, however,
5 The Coase Theorem is named after the late Ronald Coase. Ronald H.
removes
element
of separation
and
a theoretical
test
(1960). George
Coase, Thethe
Problem
of Social
Cost, 3 J.L.
& presents
ECON. 1, 1–44
of
the
Coase
Theorem
through
a
novel
thought-experiment
–
a
Stigler, however, was the economist who first presented the idea now known
STIGLER, Dilemma,
THE THEORYone
OF in
PRICE
113
as the Coasean
Coase Theorem.
pure
version GofEORGE
the J.
Prisoner’s
which
(MacMillan, 3d
ed. communication
1966). George Stigler
stated Coase’s
idea the
as aprisoners.
“theorem”
bargaining
and
are allowed
between
and coined the term “Coase Theorem.” Id.
First,
we
compare
the
standard
version
of
the
Prisoner’s
Dilemma
6 See generally W ILLIAM POUNDSTONE , PRISONER’S DILEMMA (Anchor
with
Theorem,
identifying
theof main
conditions
of the
Books the
1993)Coase
(providing
an overview
and history
the origins
of the dilemma);
theorem:
(i)
the
existence
of
a
“reciprocal”
conflict
between
two
see also F. E. Guerra-Pujol, The Parable of the Prisoners, 5–9 (June 21, 2013)
[hereinafter
The Parable
of the
(unpublished
parties;
(ii) Guerra-Pujol,
well-defined property
rights;
and Prisoners]
(iii) zero transaction
manuscript)
(onexplain
file how with
available of the
at
costs.
Next, we
our pureauthor),
Coasean version
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2281593, (explaining the
prisoner’s parable).
7 Id.
31See
8
Axelrod
infra &
Part
Hamilton,
I.B.
supra note 22, at 1391.
1298
Vol. 47:4
1168
1298
Prisoner’s
47 JO HN
Dilemma
M ARS HALL
andL.
CoRase
EV .Theorem
1168
Vol. 1299
47:4
Prisoner’sfromDilemma
different
its predecessors,
satisfiesparticularly
these conditions,
since it had specifically
the benefit
considering
of
two years the
of planning.
application of strategic as well as non-strategic
bargaining
Like the
in shift
the Coasean
in conference
or zeroscheduling,
transaction other
cost version
changesofhave
the
taken
dilemma.
place within the LatCrit entity, including concerted efforts
to continue a process of institutionalization. In recent years, there
has A.
beenA aTale
growing
of Twofocus
Parables:
on how
Parable
to capitalize
of the Rancher
on its critical
and the
niche,
continue cultivating
Farmer
the and
nextParable
generation
of theofPrisoners
critical scholars, and
ensure that the baton of outsider jurisprudence is passed along.
Internally,
Broadly the
speaking,
organization
two of
has the
shifted,
most including
important a ideas
gradual
in
changing
economics ofand
thelaw
guard
are inthe
leadership,
Coase Theorem
so to speak,
and the
as well
Prisoner’s
as a
downsizing
Dilemma, and
in each
administration.
has generated
Fora example,
vast technical
from literature
2008 to –the
a
32 And yet,
each of these
present,
scholarly the
seaBoard
of Borgesian
of Directors
proportions.
was intentionally
downsized,
with
profoundly
based
on a simple
parable:
a
growing influential
number of contributions
Board seats is
being
occupied
by junior
law
6
Ronald Coase’s
“Parable of the Rancher and the Farmer” 33 and the
professors.
34 In summary,
game-theoretic
Another major
“Parable
development
of the Prisoners.”
is LatCrit’s
acquisitionCoase’s
of a
parable concerns
neighbors,
cattle rancher
a
physical
space fortwo
thepastoral
organization.
The aproperty,
Campo and
Sano
whileHealthy,”
Tucker’s or
tale
involves
two “Camp
criminal
suspects
crop farmer,
(Spanish
for 35
“Camp
more
literally,
Sanity”),
is
36 Although
7 Purchased
these
memorable
parables
by
apprehended
by the
police.
a ten-acre parcel
of land
located
in Central
Florida.
evoke
LatCritwildly
in 2011,
different
the space
and divergent
is home worlds
to The(i.e.,
Living
a bucolic
Justiceworld
Center
of
Thehand
physical
facility
serves
neighboring
and the LatCrit
farms
Community
and ranches
Campus.
on the8 one
versus
a film
noir
as a means
“to and
level robbers
the playing
give from
LatCrit
a
world
of cops
on field
the and
other),
an activists
economic
9 The space
is intended
fighting chance
to besimple
heard.” stories
perspective,
these
share
an essential facet in
common. In brief, both parables depict rational actors whose
to serve
of their
educational,
interests
collide.asIn the
the hub
one case,
the conflict
arisesresearch,
out of cattle
advocacy
and
activismcattle
to remedy
and in
trespass
(i.e., the
rancher’s
trampledthe
theimbalance
farmer’s crops);
deficiencies
of the must
current
legal
system.
Having
the other,
each prisoner
decide
whether
to betray
or an
remain
independent
loyal to
the other. 37 physical base has become critical as
Nevertheless,
although
both parables
portray
parties
universities and
law schools
increasingly
arerational
even less
with opposing or conflicting interests, these stories diverge in one
Naming and Launching a New Discourse of Critical Legal Scholarship, 2
32 .At
HARV
LATINO
last count
L. REV
(July
. 1 (1997).
25, 2014), for example, an electronic search for the
ATCRIT:SCHOLAR
LATINA, & LATINO
term
See
“Coase
also theorem”
LatCrit generates
Biennial 25,200
Conferences,
results. G
LOOGLE
CRITICAL LEGAL THEORY, INC., http://latcrit.org/content/conferences/latcrithttp://scholar.google.com/scholar?q=%22coase+theorem%22&btnG=&hl=en&as
biennial-conferences/
(last July
visited
5, 2013)
(providing
list of
the previous
_sdt=0%2C14
(last visited
25,July
2014).
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for the aterm
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conferences,
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to times
view symposia
articles(107,000).
for some
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at (found by following the respective year’s link to its corresponding
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Additionally, LatCrit(last
has visited
developed
substantial
hl=en&as_sdt=0%2C14
Julya 24,
2014). body of scholarship from
33 See
Coase,
supra note
5, at 2–15
(presenting
the “Parable of
the Rancher
several
other
stand-alone
symposia:
inter
alia the South-North
Exchange,
the
and
theSpace
Farmer”).
See the
also International
F. E. Guerra-Pujol,
Modelling theColloquia.
Coase Theorem,
5
Study
Series,
and Comparative
LatCrit
CTUD
RIT:. 139,
LATC141–42
RIT: LATINA
(2012) &
[hereinafter
LATINO CGuerra-Pujol,
RITICAL LEGAL
Modelling]
THEORY,
EUR. J. LEGAL
Symposia,
LATS
I(combining
NC.,
http://latcrit.org/content/publications/latcrit-symposium/
(last theory);
visited
Coase’s intuitive insights with the formal methods of game
July 5, 2014).
Robert
Ellickson, Of Coase and Cattle: Dispute Resolution Among Neighbors in
6 These
include
Professors
. L. REVMarc-Tizoc
. 623, 624–25
González,
(1986) (reporting
Andrea Freeman,
the resultsand
of
Shasta
County,
38 STAN
César
an attempt
Cuahtémoc
to explore
García
theHernández.
realism ofSee
theAbout
“Parable
LatCrit,
of the
supra
Rancher
note 3and
(listing
the
the
Farmer”).
professors on the LatCrit Board of Directors and their respective law
34 LUCE & RAIFFA, supra note 17; Guerra-Pujol, The Parable of the
schools).
7 Campo
Sano,
ATTucker,
CRIT: LATINA
AND 3.
LATINO CRITICAL LEGAL THEORY,
Prisoners,
supra
noteL6;
supra note
INC,35http://www.latcrit.org/content/campo-sano/
Coase, supra note 5, at 2–15.
(last visited July 5, 2014).
36Id.
8
Tucker, supra note 3.
37Id.
9
Id.; Coase, supra note 5, at 2–15.
130047:4
Vol.
Prisoner’s
47 JO HN
Dilemma
M ARS HALL
andL.
CoRase
EV .Theorem
1300
Vol.1299
1291
47:4
important respect: the ability, or lack thereof, of the parties to
settle their differences through bilateral negotiations or Coasean
bargaining. That is, the most salient distinction between the
hypothetical worlds of the Coase Theorem and the Prisoner’s
Dilemma is the ability to bargain. In the former case, the rancher
and the farmer are fully able to bargain with each other and
3
negotiate a mutually beneficial enforceable agreement. 38 In the
latter story, however, the prisoners have no such option; they are
held in separate cells and unable to talk, much less bargain with
NTRODUCTION
I. Ior
inability, of the parties to deal with
one another. 39 This ability,
each other is of critical importance, at least in the traditional
Building
thethemain
themea Coasean
of this bargain
year’s between
LatCrit
telling
of each upon
tale. In
one case,
Conference,
Building
Crossthe rancher Resistance
and the Rising:
farmer Theorizing
produces anandoptimal
result
or
4 this paper (i.e., our contribution to this larger
Sector
Movements,
Panglossian
outcome
(i.e., an efficient allocation of resources
40 In the
critical conversation)
challenges
oneand
of the
dominant
paradigms
in
other case,
devoted
to the production
of crops
meat).
5 Specifically, we present a
economics
law: the
Coase Theorem.
the
parties’and
inability
to bargain
with each
other inevitably leads to
thought-experiment,
we outcome
shall call(longer
the “pure
Coasean
version”
mutual
betrayal and what
a worse
prison
sentences)
for
of the
famous 41Prisoner’s Dilemma game. 6 In brief, what if the
both
prisoners.
prisoners
allowed the
to
Suffice init tothis
say, game-theory
however, few parable
scholars were
have explored
communicate
and these
bargain
with
each other
insteadOne
of being
held in
relation between
two
important
models.
exception
is
separate
cells, as in
standard
the dilemma?
Wayne Eastman,
a the
professor
at version
Rutgers ofBusiness
School,Would
who
our
prisoners
a mutually-beneficial
collectively-optimal
identified
the strike
conditions
under which and
Coasean
bargaining
7 Or, as
42 Specifically,
Coasean
as Dilemma.
the Coase
Theorem predicts?
he models
Coase’s
constitutesbargain,
a Prisoner’s
predicted
in the
standard
one-shot Dilemma
version ofandthe
Prisoner’s
rancher-farmer
parable
as a Prisoner’s
establishes
a
theyPrisoner’s
still end
Dilemmaidentity
in which
bargaining
is not Theorem
allowed, 8 would
formal
between
the Coase
and the
Dilemma. 43 Our approach in this paper, however, is different than
Eastman’s. Instead of relating the Coase Theorem to the Prisoner’s
3 A.W. Tucker, A Two-Person Dilemma: The Prisoner’s Dilemma (1950), as
Dilemma,
as Eastman does, we do the opposite. 44 We relate the
reprinted in Philip D. Straffin, Jr., The Mathematics of Tucker: A Sampler, 14
Prisoner’s
to J.the
Coase Theorem by constructing a
MATHEMATICS
228 (1983).
TWO-YEAR C. Dilemma
45 Specifically, we pose the
4 Latina
Coasean
version
of
the
dilemma.
& Latino Critical Legal Theory,
Inc., 2013 Biennial LatCrit
Conference questions:
Program Schedule
Related Events),
(2013),
at
following
what if (and
the prisoners
were, in
fact, available
allowed to
http://latcrit.org/media/medialibrary/2013/10/LatCrit2013_Conference_Progra
communicate
and bargain with each other in Coasean fashion?
m_FinalR.pdf.
That
is, what if our hapless prisoners were able to negotiate a
5 The Coase Theorem is named after the late Ronald Coase. Ronald H.
mutually
beneficial
and Cost,
legally
enforceable
Would
1–44 (1960). George
Coase, The Problem
of Social
3 J.L.
& ECON. 1,agreement?
Stigler, however, was the economist who first presented the idea now known
as the Coase Theorem. G EORGE J. STIGLER, THE THEORY OF PRICE 113
38Coase, supra
5, atGeorge
2–15. Stigler stated Coase’s idea as a “theorem”
(MacMillan,
3d ed.note
1966).
LUCE the
& Rterm
AIFFA“Coase
, supraTheorem.”
note 17; Tucker,
supra note 3.
and39coined
Id.
40 Coase,
6
See generally
supra note
WILLIAM
5, at 2–15.
POUNDSTONE , PRISONER’S DILEMMA (Anchor
41 Tucker,
supra note
Books
1993) (providing
an3.overview and history of the origins of the dilemma);
Eastman,
supra note 9. The Parable of the Prisoners, 5–9 (June 21, 2013)
see 42
also
F. E. Guerra-Pujol,
43 Id.
[hereinafter
Guerra-Pujol, The Parable of the Prisoners] (unpublished
44 See id. at 90
deliberately
that his proposition
manuscript)
(onn.7 (noting
file verywith
author),
available “relates
at
the
[Coase] Theorem to the [Prisoner’s] Dilemma, rather than
vice versa” and
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2281593,
(explaining
the
his
reasonsparable).
for electing to do so).
prisoner’s
45Id.
7
See Guerra-Pujol, Modelling, supra note 35 (providing a different game8 See infra
Part I.B.
theoretic
formulation
of the Coase Theorem).
1300
Vol. 47:4
1168
1300
Prisoner’s
47 JO HN
Dilemma
M ARS HALL
andL.
CoRase
EV .Theorem
1168
Vol. 1301
47:4
they stillfrom
different
defect
its or
predecessors,
would theyparticularly
somehow since
decideit to
had
cooperate
the benefit
as
postulated
of
two yearsbyofthe
planning.
Coase Theorem?
Like the shift in conference scheduling, other changes have
taken place
B. within
The Three
the Conditions
LatCrit entity,
of theincluding
Coase Theorem
concerted efforts
to continue a process of institutionalization. In recent years, there
has been
Before
a growing
attempting
focus
to on
answer
how tothe
capitalize
above on
questions,
its critical
we niche,
shall
continue
first identify
cultivating
and review
the nextthegeneration
main conditions
of critical ofscholars,
the Coase
and
ensure
Theorem.
thatProfessor
the baton
Coase
of outsider
introduced
jurisprudence
the counterintuitive
is passed along.
idea
Internally,
now known the
as the
organization
“Coase Theorem”
has shifted,
with aincluding
memorable
a gradual
parable
46 in
Theleadership,
rancher-farmer
parable,ashowever,
changing
about cattle
of trespass.
the guard
so to speak,
well as is
a
really a story
joint interactions
involving
bargaining
downsizing
in about
administration.
For example,
from
2008 to and
the
property the
rights.
is, Coasewas
posed
a well-defined
reciprocal
present,
BoardThat
of Directors
intentionally
downsized,
with
problem
using
the example
cattlebeing
trespass
and then
imagined
a
growing
number
of Boardofseats
occupied
by junior
law
6 happen if the affected parties (i.e., the rancher and the
what would
professors.
Another
development
is LatCrit’s
acquisition
of 47
a
farmer)
could major
solve this
problem through
voluntary
bargaining.
(Ultimately,
thisforisthe
theorganization.
same question
we pose
aboutSano
the
physical
space
Thethat
property,
Campo
prisoners for
in the
Prisoner’s
Dilemma.)
observed
when (i)
(Spanish
“Camp
Healthy,”
or more Coase
literally,
“Campthat
Sanity”),
is
Purchased by
the
costs parcel
of transacting
are zero
(a standard
in
a
ten-acre
of land located
in Central
Florida. 7assumption
LatCrit
in 2011,
the property
space is home
The well-defined,
Living Justice
Center
economics)
and (ii)
rightsto are
“Coasean
8 The physical
serves
and
the LatCrit
bargaining”
(i.e.,Community
voluntaryCampus.
negotiations)
among facility
the affected
48 Although
this
as a means
“to levelan
theefficient
playingeconomic
field andoutcome.
give LatCrit
activists
a
parties
will produce
9 The
space
intended
economic
“theorem”
been
stated
in is
many
different ways over
fighting chance
to be has
heard.”
the years, 49 the necessary elements of the Coase theorem remain
constant:
(i) theasexistence
of aof reciprocal
conflict, (ii)
well-defined
to serve
the hub
their educational,
research,
property
rights,andand
(iii) zero
transactions
costs (i.e.,
advocacy
activism
to remedy
the imbalance
and no
50 Accordingly,
we shallHaving
now show
impediments
to bargaining).
deficiencies
of the current
legal system.
an how
our pure
Coasean physical
version of
the has
dilemma
satisfies
independent
base
become
criticalallasthree
standard
conditionsand
of the
Theorem.
universities
lawCoase
schools
increasingly are even less
1. Reciprocal Nature of the Prisoner’s Dilemma
Naming and Launching a New Discourse of Critical Legal Scholarship, 2
foremost,
HARV .First
LATINOand
L. REV
. 1 (1997). we wish to point out the “reciprocal
51 of LatCrit
the prisoners’
in all versions
LATINA
the Prisoner’s
& LATINO
See also
Biennial plight
Conferences,
LATCRIT: of
nature”
CRITICAL LEGAL
THEORY
, Iaspect
NC., http://latcrit.org/content/conferences/latcritDilemma.
Although
this
of Coase’s work is often overlooked
biennial-conferences/
5, 2013) (providing
the previous
or
neglected in the(last
lawvisited
and July
economics
literature,a list
weofbelieve
it is
conferences, and providing direct links to view symposia articles for some
Coase’s
most
original
and
counterintuitive
insight.
Consider,
for
years (found by following the respective year’s link to its corresponding
webpage).
Additionally, LatCrit has developed a substantial body of scholarship from
46 Coase,
note 5, at
2–15. inter alia the South-North Exchange, the
several
othersupra
stand-alone
symposia:
47 Id.
Study
Space Series, the International and Comparative Colloquia. LatCrit
48 See Coase,
supra
: LAT
note
CRIT
5,: atLATINA
2–15 (noting
& LATINO
whenC“Coasean
RITICAL Lbargaining”
EGAL THEORY
will,
Symposia,
LATCRIT
Iproduce
NC.,
http://latcrit.org/content/publications/latcrit-symposium/
(last
visited
an efficient economic outcome). See also Ronald H. Coase,
The Federal
July
5, 2014).
Communications
Commission, 2 J.L. & ECON. 1, 25–30 (1959) (noting when
6 These
include Professors
Marc-Tizoc
González,
Freeman, and
“Coasean
bargaining”
will produce
an efficient
economicAndrea
outcome).
49 See
STEVEN García
G. MEDEMA
& RICHARD
O. ZERBE
, Thesupra
Coasenote
Theorem,
1
César
Cuahtémoc
Hernández.
See About
LatCrit,
3 (listing
ENCYCLOPEDIA
LAWBoard
AND of EDirectors
CONOMICSand
: Ttheir
HE
H
ISTORY
AND
THE professors
the
on the OF
LatCrit
respective
law
METHODOLOGY OF LAW AND ECONOMICS 837–38 (Boudewijn Bouckaert &
schools).
7 Campo
Sano,
LAT2000)
CRIT: (providing
LATINA AND
ATINO CRITICAL
Gerrit
De Geest
eds.,
anLextensive
listing L
ofEGAL
someTHEORY
of the,
INC, http://www.latcrit.org/content/campo-sano/
(last visited July 5, 2014).
various
statements of the Coase Theorem).
50Id.
8
Coase, supra note 5, at 2–15.
51Id.
9
Id. at 1–2.
130247:4
Vol.
Prisoner’s
47 JO HN
Dilemma
M ARS HALL
andL.
CoRase
EV .Theorem
1302
Vol.1301
1291
47:4
example, Coase’s parable of the rancher and the farmer. 52
According to Coase, it is a fallacy to think that the problem of
cattle trespass is caused solely by the rancher. 53 In reality, cattle
trespass (i.e., the risk of potential harm to the farmer’s crops) is a
joint problem. 54 Just as the rancher can reduce the risk of harm by
reducing the size of his herd or erecting a boundary fence, so too
3
can the farmer, either by planting cattle-resistant crops or by
putting up the fence himself. 55 Likewise, the Prisoner’s Dilemma
also presents a reciprocal problem insofar as the payoffs for both
I. independently
INTRODUCTIONmade choices to defect or
prisoners stem from their
cooperate. 56 Thus, if both prisoners end up defecting in the
Building
uponversion
the main
of game
this year’s
LatCrit
standard
one-shot
of the theme
game (as
theory predicts
Conference,
Rising: Theorizing
and Building
Crossthey will do),Resistance
then the prisoners
have only themselves
to blame
for
4 this
Sector
Movements,
57 paper
(i.e.,the
our prisoners’
contribution
to this
larger
In short,
plight,
like
the
their collective
plight.
critical conversation)
challenges
of theofdominant
paradigmsthe
in
problem
of cattle trespass,
is theone
product
a joint interaction:
Specifically,
weofpresent
a
economicsinand
theisCoase
Theorem. 5 by
outcome
bothlaw:
cases
not determined
the actions
just one
thought-experiment,
what
we shall
call
Coasean
version”
party,
but rather by the
choices
made
bythe
both“pure
of them
jointly.
of the famous Prisoner’s Dilemma game. 6 In brief, what if the
in Property
this game-theory
parable were allowed to
2.prisoners
Well-Defined
Rights
communicate and bargain with each other instead of being held in
separate
as in the
standard
version
the dilemma?
Doescells,
the second
condition
of the
Coase of
Theorem
(i.e., theWould
legal
our
prisoners
a mutually-beneficial
and
assignment
of strike
well-defined
property rights to
onecollectively-optimal
of the conflicting
Or, as
Coasean
bargain,
as Prisoner’s
the CoaseDilemma?
TheoremIf predicts?
parties) apply
to the
so, what7 property
predicted
the traded
standard
one-shot
Prisoner’s
rights are in
being
in the
standardversion
versionofof the
the Prisoner’s
Dilemma in which bargaining is not allowed, 8 would they still end
Dilemma?
Recall that the Prisoner’s Dilemma is a compelling parable
about betrayal and loyalty, a secular morality tale about the
3 A.W. Tucker, A Two-Person Dilemma: The Prisoner’s Dilemma (1950), as
conflict
between individual and collective rationality. Strictly
reprinted in Philip D. Straffin, Jr., The Mathematics of Tucker: A Sampler, 14
speaking,
the
Prisoner’s J.
Dilemma
is not a story about property per
MATHEMATICS
228 (1983).
TWO-YEAR C.
se; 4 however,
property
rights
do
play aInc.,
secondary
role in
the
Latina & Latino Critical Legal Theory,
2013 Biennial
LatCrit
Conference From
Program
(and
Events),
availablethe
at
dilemma.
a Schedule
libertarian
or Related
classical
liberal(2013),
perspective,
http://latcrit.org/media/medialibrary/2013/10/LatCrit2013_Conference_Progra
prisoners
have a vested property right in their personal liberty,
m_FinalR.pdf.
and
although personal liberty is often considered to be an
5 The Coase Theorem is named after the late Ronald Coase. Ronald H.
58
plea(1960).
bargain
but
inalienable
(i.e., non-negotiable)
1, a1–44
George
Coase, The Problem
of Social Cost, right,
3 J.L. & what
ECON. is
Stigler, however, was the economist who first presented the idea now known
as the Coase Theorem. G EORGE J. STIGLER, THE THEORY OF PRICE 113
52 Id. at 2–15.
(MacMillan,
3d ed. 1966). George Stigler stated Coase’s idea as a “theorem”
Id. the term “Coase Theorem.” Id.
and53coined
54 Id.
6
Seeatgenerally
1–2.
WILLIAM POUNDSTONE , PRISONER’S DILEMMA (Anchor
55 See
F. (providing
E. Guerra-Pujol
& Orlando
I. Martinez-Garcia,
Clones
and the
Books
1993)
an overview
and history
of the origins of
the dilemma);
OF L
AW & of
SOCIAL
DEVIANCE
65-73
Coase
2 JOURNAL The
see alsoTheorem,
F. E. Guerra-Pujol,
Parable
the Prisoners,
5–943,
(June
21,(2011)
2013)
(providing an Guerra-Pujol,
extended discussion
of the reciprocal
nature of the
rancher[hereinafter
The Parable
of the Prisoners]
(unpublished
farmer parable). (on
manuscript)
file
with
author),
available
at
56 Tucker, supra note 3.
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2281593,
(explaining the
57 Tucker,
supra note 3.
prisoner’s
parable).
58Id.
7
See, e.g., Margaret Jane Radin, Market Inalienability, 100 HARV . L. REV .
8 See
infra Part
I.B.(discussing the commoditization of negative liberty). Of
1849,
1903–06
(1987)
1302
Vol. 47:4
1168
1302
Prisoner’s
47 JO HN
Dilemma
M ARS HALL
andL.
CoRase
EV .Theorem
1168
Vol. 1303
47:4
a judicially
different
fromsanctioned
its predecessors,
trade of
particularly
one’s personal
since liberty?
it had the
When
benefit
a
of
criminal
two years
suspect
of planning.
is offered a plea bargain, the prosecutor is, in
effect,Like
asking
the the
shiftsuspect
in conference
to relinquish
scheduling,
some of other
his personal
changesliberty
have
taken
(i.e., heplace
agrees
within
to a the
certain
LatCrit
but reduced
entity, including
prison sentence
concerted
– x efforts
years)
to
in continue
exchangea for
process
avoiding
of institutionalization.
the possibility ofIna recent
maximum
years, prison
there
59 to capitalize on its critical niche,
has
sentence
been (e.g.,
a growing
5x or 10x
focus
years).
on how
This cultivating
broad definition
of property
(i.e., of“liberty
property”)and
is
continue
the next
generation
criticalasscholars,
consistent
traditional
conceptions
of property
rights.along.
The
ensure
thatwith
the baton
of outsider
jurisprudence
is passed
legal philosopher
Stephen Munzer
the including
late political
theorist
Internally,
the organization
has and
shifted,
a gradual
C.B. Macpherson,
amonginothers,
have described
in detail
different
changing
of the guard
leadership,
so to speak,
as well
as a
conceptions in
of administration.
property rights; For
in example,
particular,from
property
downsizing
2008 in
to the
classical the
or common
sense was
refers
to everything
(tangible
or
present,
Board of law
Directors
intentionally
downsized,
with
intangible)
which ofa Board
person seats
has abeing
right,occupied
includingbythe
rightlaw
to
a
growing to
number
junior
6
60 In the words of Macpherson, “men were said to
personal liberty.
professors.
have Another
a property
major
not development
only in land isand
LatCrit’s
goods and
acquisition
in claimsof on
a
revenues
physical space
for leases,
for the
mortgages,
organization.
patents,
The
monopolies
property,and
Campo
so on,Sano
but
61 Although
this
also
(Spanish
a property
for “CampinHealthy,”
their lives
or more
and literally,
persons.”“Camp
Sanity”),
is
62
7 Purchased
our larger
point here
by
classical
of property
a
ten-acreconception
parcel of land
located isincircular,
Central Florida.
LatCrit
is that personal
in 2011, liberty
the space
is anisintangible
home to property
The Living
right,
Justice
a right
Center
that
8 The physical
facility
serves
and
can the
be bargained
LatCrit Community
away in certain
Campus.
situations,
as in the
Prisoner’s
as
a means “to level the playing field and give LatCrit activists a
Dilemma.
fighting chance to be heard.” 9 The space is intended
3. Zero Transaction Costs, Strategic Behavior, and Non-Strategic
to serve as the hub of their educational, research,
Bargaining
advocacy and activism to remedy the imbalance and
deficiencies
of the
current
legal insystem.
Havingversion
an of
Stated
in Coasean
terms,
the rules
the standard
independent
physical
has become
critical generate
as
the Prisoner’s
Dilemma
(i.e.,base
no bargaining)
artificially
universities costs.
and law
are even
high transaction
But schools
what if increasingly
we change these
rules less
to allow
bargaining? That is, what if we imagine a Coasean version of the
Prisoner’s Dilemma, one with zero transactions costs?
Some scholars of the Coase Theorem, however, have already
Naming and Launching a New Discourse of Critical Legal Scholarship, 2
noted
that parties,
even parties who find themselves in a low
HARV . LATINO
L. REV . 1 (1997).
See also LatCrit Biennial Conferences, LATCRIT: LATINA & LATINO
CRITICAL LEGAL THEORY, INC., http://latcrit.org/content/conferences/latcritcourse,
the most famous
of this
idea (providing
appears inathe
Declaration
biennial-conferences/
(laststatement
visited July
5, 2013)
listU.S.
of the
previous
of
Independence
July 4, 1776.
conferences,
andofproviding
direct links to view symposia articles for some
59 Note
that
do not mean
to expressyear’s
our normative
of plea
years
(found
by we
following
the respective
link to itsapproval
corresponding
bargains
webpage).in criminal cases. We are simply making a descriptive point here
about
the secondary
role has
of property
rights
in the Prisoner’s
Additionally,
LatCrit
developed
a substantial
body ofDilemma.
scholarship from
60
See
B. Macpherson,
of Property,
PROPERTY
several
otherC.stand-alone
symposia: The
inter Meaning
alia the South-North
Exchange,
the:
M
AINSTREAM
CRITICAL
CONCEPTIONSand
1, 8 Comparative
(C. B. Macpherson,
ed., Univ.
of
Study
Space AND
Series,
the International
Colloquia.
LatCrit
CRIT: (identifying
LATCRIT: Lproperty
ATINA & as
LATINO
CRITICAL
LEGAL uncertain
THEORY,
Toronto
Press
“a right
– a somewhat
Symposia,
LAT1978)
Iright
NC., that
http://latcrit.org/content/publications/latcrit-symposium/
(last
, A THEORY
visited
has constantly to be re-asserted”); STEPHEN R. MUNZER
OF
JulyPROPERTY
5, 2014). 90 (Cambridge Univ. Press 1990) (identifying “liberty” among a
Professors
Marc-Tizoc
González,
Andrea
Freeman,
and
list 6of These
items include
that should
be considered
personal
goods (i.e.
personal
property)
César Cuahtémoc
García
See in
About
LatCrit,orsupra
note 3to(listing
insofar
as “they are
oftenHernández.
valued either
themselves
as means
other
the professors
the or
LatCrit
and theirasrespective
things
that are on
valued
both”);Board
CherylofL.Directors
Harris, Whiteness
Property, law
106
ARV . L.R. 1707, 1724–31 (1993) (providing a general overview of the broad
schools).
H
7 Campo
Sano,
LATCRIT: LATINA AND LATINO CRITICAL LEGAL THEORY,
historical
concept
of property).
INC,61http://www.latcrit.org/content/campo-sano/
C.B. Macpherson, supra note 64, at 7.
(last visited July 5, 2014).
62Id.
8
This conception of property is circular, since all it is saying, in effect, is
Id. has a right to what one has a right to.
that9 one
130447:4
Vol.
Prisoner’s
47 JO HN
Dilemma
M ARS HALL
andL.
CoRase
EV .Theorem
1304
Vol.1303
1291
47:4
transaction cost setting, may act strategically and thus fail to
strike a mutually beneficial Coasean bargain. 63 Here, we shall
contribute to the literature on the Coase Theorem in two ways.
First, building on the work of Wayne Eastman, we shall consider
strategic behavior in the form of promises and threats and explain
why such strategic behavior might prevent the formation of
3
Coasean bargains between the prisoners—even when they are
allowed to communicate with each other. Next, building on the
work of John Nash, we shall consider the possibility of nonINTRODUCTION
strategic bargaining by I.
the prisoners.
Building
upon the
main and
theme
of this
LatCrit
4. Strategic
Bargaining,
Threats
Promises
in theyear’s
Prisoner’s
Conference,
Dilemma Resistance Rising: Theorizing and Building CrossSector Movements, 4 this paper (i.e., our contribution to this larger
critical
challenges
of the
dominant
in
Oneconversation)
of the central
lessons ofone
game
theory
is that paradigms
one can often
weadvantage
present a
economics
and law:asthe
–
but not always,
weCoase
shall Theorem.
soon see –5 Specifically,
gain a tactical
thought-experiment,
what
we shall call
the “pure
Coasean version”
during
negotiations by
committing
oneself
(or pre-committing,
so
In costly
brief, threat
what if
of speak)
the famous
Prisoner’s strategy,
Dilemma such
game.as6 a
to
to a particular
or the
an
prisoners promise.
in this64 This
game-theory
wereto as
allowed
to
insight is parable
often referred
the “firstenforceable
65 and with
communicate
and bargain
each other
insteadone’s
of being
held or
in
the ability
to make
threats
mover
advantage,”
separate
as in isthe
standard aversion
of the
dilemma? 66
Would
The
promises cells,
believable
considered
“credible
commitment.”
our prisoners
strike
a mutually-beneficial
and however,
collectively-optimal
Coasean
version
of the
Prisoner’s Dilemma,
poses an
7 Or, as
Coasean bargain,
as the to
Coase
Theorem
predicts?
especially
difficult challenge
the Coase
Theorem
because
there
predicted
in theadvantage
standardin one-shot
version
of the Prisoner’s
is
no-first mover
the Prisoner’s
Dilemma.
they still
Dilemma
in which bargaining
allowed, 8 would
In summary,
there is is
no not
first-mover
advantage
in end
the
Coasean version of the Prisoner’s Dilemma due to the possibility of
strategic behavior. Assume, for example, that Prisoner 1 decides to
3 A.W. Tucker, A Two-Person Dilemma: The Prisoner’s Dilemma (1950), as
reprinted in Philip D. Straffin, Jr., The Mathematics of Tucker: A Sampler, 14
EAR e.g.,
C. MHerbert
ATHEMATICS
Hovenkamp,
J. 228 (1983).
Marginal Utility and the Coase Theorem,
TWO63-YSee,
4 ORNELL
Latina L.
& RLatino
EV . 783,Critical
787–91 Legal
(1990) Theory,
(arguing Inc.,
that the
2013failure
Biennial
of theLatCrit
Coase
75 C
Conference
theorem to predict
Program
realSchedule
world outcomes”
(and Related
is frequently
Events),
explained
(2013),byavailable
“the failure
at
http://latcrit.org/media/medialibrary/2013/10/LatCrit2013_Conference_Progra
of the relevant actors” as opposed to “high transaction costs” Id. at 788);
m_FinalR.pdf.
ROBERT D. COOTER & THOMAS ULEN, LAW AND ECONOMICS 242–44 (Scott
5 The Coase
is named
late Ronald
Coase.and
Ronald
H.
Foresman
& Co.,Theorem
2d ed. 1982);
and after
Robertthe
Ellickson,
“Of Coase
Cattle:
CON. 1, 38
1–44
(1960).
. L. REV
George
. 623,
Coase, The
ProblemAmong
of Social
Cost, 3inJ.L.
& ECounty,
Dispute
Resolution
Neighbors
Shasta
STAN
Stigler,
625 n.4 however,
(1986) (proposing
was the economist
that “negotiations
who firstinpresented
bilateral the
monopoly
idea now
situations
known
STIGLER
, THE THEORY OF PRICE 113
as
can the
be costly
Coasebecause
Theorem.
the parties
G EORGE
mayJ.act
strategically”).
VINASH
K. DStigler
IXIT &stated
BARRY
J. Nidea
ALEBUFF
THINKING
(MacMillan,
ed. A
1966).
George
Coase’s
as a, “theorem”
64 See, 3de.g.,
STRATEGICALLY
124–26
Norton,
and
coined the term
“Coase(W.W.
Theorem.”
Id. reprt. ed. 1993) (asserting that
6 Seemoves
generally
WILLIAM POUNDSTONE
, PRISONER
ILEMMA
strategic
are two-pronged:
(i) the planned
course’SofDaction
and(Anchor
(ii) the
AIRD
, ET AL.,
Books 1993) (providing
anthis
overview
historysee
of also
the origins
of B
the
dilemma);
commitment
that makes
course and
credible);
DOUGLAS
G AME
THEORY
AND THE LAW 43-44
(1994).of the Prisoners, 5–9 (June 21, 2013)
see
also
F. E. Guerra-Pujol,
The Parable
65 Roger A.Guerra-Pujol,
Kerin, P. Rajan
Varadarajan
A. Peterson,(unpublished
First-Mover
[hereinafter
The
Parable &
ofRobert
the Prisoners]
Advantage: A Synthesis,
Conceptual
Framework,
and Research
Propositions,
manuscript)
(on
file
with
author),
available
at
56 J. MARKETING , Oct., 1992, at 33, 33.
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2281593,
(explaining the
66 See, parable).
e.g., Douglass C. North, Institutions and Credible Commitment, 149
prisoner’s
Id. ’L THEORETICAL ECON 11-12 (Mar. 1993) (identifying that the
J. 7INST
8 See infra
I.B. to credible commitment”).
enforcement
isPart
“central
1304
Vol. 47:4
1168
1304
Prisoner’s
47 JO HN
Dilemma
M ARS HALL
andL.
CoRase
EV .Theorem
1168
Vol. 1305
47:4
pre-commit
different
fromtoitscooperation
predecessors,and
particularly
is able since
to communicate
it had the benefit
his
of
cooperative
two yearscommitment
of planning. to Prisoner 2, say by taking a sincere and
solemn
Like
oath
theinshift
Prisoner
in conference
2’s presence
scheduling,
to remain
other
silent
changes
“no matter
have
Also,
assume
that Prisoner
2 truly concerted
believes in
the
taken
what.” 67
place
within
the LatCrit
entity, including
efforts
sincerity
anda seriousness
of the other prisoner’s
solemnyears,
oath. there
That
to
continue
process of institutionalization.
In recent
is, he
knows
that Prisoner
is a to
man
of his word.
the
has
been
a growing
focus on1 how
capitalize
on itsPerversely,
critical niche,
logic of defection
continues
to prevail,
for defection
confessingand
is
continue
cultivating
the next
generation
of criticalor scholars,
still Prisoner
2’s baton
dominant
strategy.
In fact, Prisoner
2 has
an
ensure
that the
of outsider
jurisprudence
is passed
along.
even stronger
to defect
this situation
because
he is
Internally,
theincentive
organization
has inshifted,
including
a gradual
now certain
to obtain
theleadership,
temptationso payoff,
given
the other
changing
of the
guard in
to speak,
as well
as a
prisoner’s binding
promise not to For
defect.
downsizing
in administration.
example, from 2008 to the
Knowing
this, of
what
if Prisoner
1 took a different
approach
present,
the Board
Directors
was intentionally
downsized,
with
andgrowing
made anumber
credibleofthreat
of a mere
promise?
Thatlaw
is,
a
Board instead
seats being
occupied
by junior
6
assume now
that Prisoner 1 is able to make and communicate a
professors.
Another
development
LatCrit’s
acquisition
a
credible
threatmajor
to punish
the other isprisoner
in the
event thatofthe
physical
space tofordefect.
the organization.
Thetactical
property,
Sano
latter decides
Introducing the
use Campo
of a credible
(Spanish
for “Camp
Healthy,” or
more literally,
“Camp
Sanity”),
is
threat, however,
dramatically
changes
the payoffs
of the
game. 68
7
by
Inten-acre
other words,
up Purchased
by a credible
a
parcel an
of enforceable
land locatedagreement
in Centralbacked
Florida.
69
LatCrit
in 2011, the space
home
The Living
Justice
Center
threat changes
valuesis of
the topayoffs
of the
prisoners.
8
Thefacts,
physical
serves
Therefore,
strictly
speaking, Campus.
under these
the facility
prisoners
are
and
the LatCrit
Community
as longer
a means
“to level
the playing
field and give LatCrit activists a
no
playing
a Prisoner’s
Dilemma.
9 The space
is intended
fighting
chance
to be heard.”
Stated
formally,
a credible
threat
changes Prisoner 2’s
temptation payoff, T; specifically, the value of T decreases as the
But,educational,
let us put research,
this technical
to of
serve
as the increases.
hub of 70
their
severity
the threat
objection
to oneand
side activism
and consider
the possibility
of non-strategic
advocacy
to remedy
the imbalance
and
bargaining
by the
in legal
the Coasean
version an
of the
deficiencies
of prisoners
the current
system. Having
dilemma.
independent physical base has become critical as
universities and law schools increasingly are even less
5. Non-Strategic Coasean Bargaining
Assume that the prisoners can bargain with each other and
Naming and Launching a New Discourse of Critical Legal Scholarship, 2
can
threats and binding promises. 71 Without a
H
ARV .make
LATINO credible
L. REV . 1 (1997).
See also LatCrit Biennial Conferences, LATCRIT: LATINA & LATINO
CRITICAL LEGAL THEORY, INC., http://latcrit.org/content/conferences/latcrit67 For clarity, we (last
shall visited
follow July
Luce5,&2013)
Raiffa’s
interpretation
theprevious
parable
biennial-conferences/
(providing
a list ofofthe
and continue and
to refer
to Player
A aslinks
“Prisoner
1” and
Player articles
B as “Prisoner
2”
conferences,
providing
direct
to view
symposia
for some
in the remainder
this paper.
years
(found by offollowing
the respective year’s link to its corresponding
68 Cf. Wayne Eastman, Everything is up for Grabs: The Coasean Story in
webpage).
EW ENG. L.
REV . 1, 1–37
(1996)
(discussingfrom
the
Game-Theoretic
Terms, 31
Additionally, LatCrit
hasNdeveloped
a substantial
body
of scholarship
idea of “payoff
mutability”) symposia: inter alia the South-North Exchange, the
several
other stand-alone
69 See,
e.g.,Series,
Elinor the
Ostram,
et al., Covenants
with and Colloquia.
without a LatCrit
Sword:
Study
Space
International
and Comparative
LATCRIT:86LATINA
& LP
ATINO
OLITICAL
CRITICAL
SCIENCE
LEGAL
REVIEW
THEORY
404,,
Self-Governance
Is : Possible,
AMERICAN
Symposia, LATCRIT
INC.,
http://latcrit.org/content/publications/latcrit-symposium/
(last or
visited
413–414
(1992) (reviewing the “payoff consequences” of selecting
not
July 5, 2014).
selection
a sanctioning mechanism in a common-pool resource game).
70 These
6
Recall include
that a Prisoner’s
ProfessorsDilemma
Marc-Tizoc
occurs
González,
when the
Andrea
values Freeman,
of the payoffs
and
César
are T >
Cuahtémoc
R > P > S.García
(See supra
Hernández.
part I.B..)
SeeThe
About
employment
LatCrit, supra
of a credible
note 3 threat,
(listing
the
however,
professors
changes
on this
the payoff
LatCrit
structure
Board to
of RDirectors
> P > S >and
T, or
their
to R respective
> P > T > S,law
or
schools).
perhaps to R > T > P > S, depending on the severity of the threat and the
7 Campo
LAT
resulting
new Sano,
value of
T.CRIT: LATINA AND LATINO CRITICAL LEGAL THEORY,
INC,71http://www.latcrit.org/content/campo-sano/
Recall that the payoffs in the dilemma (last
can visited
be stated
Julynumerically
5, 2014). or
8 Id.
algebraically
by the variables T, R, P, and S. We will follow this convention in
Id.
the 9remainder
of this paper.
130647:4
Vol.
Prisoner’s
47 JO HN
Dilemma
M ARS HALL
andL.
CoRase
EV .Theorem
1306
Vol.1305
1291
47:4
Coasean bargain, both prisoners will most likely end up confessing
– or “defecting” in the parlance of game theory – because defection
is the only Nash equilibrium in the standard one-shot version of
the Prisoner’s Dilemma. Since the defection payoff is equal to P
(i.e., the “punishment” payoff for mutual defection), Prisoner 1’s
payoff is equal to P1, while Prisoner 2’s payoff is P2. In the
3
standard version of the Prisoner’s Dilemma, however, P1 is equal
to P2, since the payoffs are symmetrical. Following convention, and
because these are the payoffs the prisoners will most likely receive
I. INTRODUCTION
if they are unable to bargain
with each other, we shall refer to
these defection payoffs as the “outside options” or “disagreement
Building
upon the
72 main theme of this year’s LatCrit
values”
of the prisoners.
Conference,
Resistance
Rising: Theorizing
and Building
If, however,
the prisoners
agree to cooperate
– a Crosslikely
4 this paper (i.e., our contribution to this larger
Sector
outcomeMovements,
if bargaining
is allowed – the prisoners will receive R, the
critical conversation)
challenges
one of the
dominantboth
paradigms
in
“reward”
payoff for mutual
cooperation.
Therefore,
prisoners
5 Specifically, we present a
economics
law: the Coase
Theorem.
are
better and
off cooperating
because
cooperation
produces a collective
thought-experiment,
what
weRshall
the another
“pure Coasean
version”
gain
for both prisoners
(i.e.,
> P).call
Or put
way, the
gains
In brief, what
if the
of thea famous
Dilemma
game. 6 Dilemma
from
CoaseanPrisoner’s
bargain in
the Prisoner’s
are positive
prisoners
game-theory
were
allowed
to
(i.e., R – P in
> 0).this
(This all
assumes, of parable
course, that
neither
prisoner
communicate
and bargain
each other
of beinglater.)
held in
breaches the agreement
– awith
possibility
that instead
we will explore
separate
as in
standard
version
of the dilemma?
But cells,
how will
thethe
prisoners
split
the collective
gains fromWould
their
our
prisoners
strike
a mutually-beneficial
Coasean
bargain?
Stated
formally, Prisoner and
1 willcollectively-optimal
receive (R + P1 –
7 Or, as
Coasean
thereceive
Coase(R Theorem
predicts?
Prisoner as
2 will
+ P2 – P1)/2.
Therefore,
each
P2)/2, andbargain,
predicted
in theof the
standard
version
of the
the value
Prisoner’s
prisoner’s share
payoffs one-shot
depends, not
only on
of his
8 would they still end
Dilemma
whichorbargaining
is not
allowed,
gains
fromin trade
the Coasean
bargain
(i.e.,
the reward payoff,
R), but also on the prisoners’ outside options or disagreement
values (i.e., P1 and P2). 73 Nevertheless, in the standard version of
3
Tucker, A Two-Person Dilemma: The Prisoner’s Dilemma (1950), as
the A.W.
dilemma,
since the prisoners’ outside options are the same
reprinted in Philip D. Straffin, Jr., The Mathematics of Tucker: A Sampler, 14
1
=
P
2
)
neither
prisoner
in the Coasean version of the game
(i.e.,
P
J. 228 (1983).
TWO-YEAR C. MATHEMATICS
can4 improve
his
bargaining
position
improving
his outside
Latina & Latino Critical Legal Theory,byInc.,
2013 Biennial
LatCrit
Conference
Program Schedule
Related
Events),(i.e.,
(2013),
at
option
or decreasing
that of (and
the other
prisoner
eachavailable
prisoner’s
http://latcrit.org/media/medialibrary/2013/10/LatCrit2013_Conference_Progra
payoff for mutual cooperation is equal to R/2). Accordingly, since
m_FinalR.pdf.
the5 payoffs in the standard version of the Prisoner’s Dilemma are
The Coase Theorem is named after the late Ronald Coase. Ronald H.
symmetrical,
they of
will
splitCost,
their3 gains
Coase,
The Problem
Social
J.L. &evenly.
ECON. 1, 1–44 (1960). George
Thus
far,
this
analysis
suggests
that
the prisoners
every
Stigler, however, was the economist who first
presented
the idea have
now known
STIGLERand
, THEcooperate,
THEORY OFsoPRICE
as
the Coase
Theorem.
G EORGE J.bargain
incentive
to strike
a Coasean
long 113
as
(MacMillan,
3d ed.
1966).what
George
stated
Coase’s
ideaus.
as aIt“theorem”
R/2 > P. But,
notice
thisStigler
analysis
does
not tell
does not
and coined the term “Coase Theorem.” Id.
tell6 us whether the prisoners will, in fact, keep their mutual
See generally WILLIAM POUNDSTONE , PRISONER’S DILEMMA (Anchor
Books 1993) (providing an overview and history of the origins of the dilemma);
see also F. E. Guerra-Pujol, The Parable of the Prisoners, 5–9 (June 21, 2013)
72 Cf. LUKE
M. FROEB, BThe
RIAN T.
MCCANN
IKHAEL
SHOR &(unpublished
MICHAEL R.
[hereinafter
Guerra-Pujol,
Parable
of, M
the
Prisoners]
WARD, MANAGERIAL
ROBLEM Sauthor),
OLVING APPROACH
190 (3d ed.,
manuscript)
(onECONOMICS
file : A Pwith
available
at
2014).)
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2281593,
(explaining the
73 See John
F. Nash, The Bargaining Problem, 18 ECONOMETRICA 155, 157prisoner’s
parable).
Id.
158 7(1951).
Note that Nash uses the term “anticipations” to refer to the outside
8 Seeor
infra
Part I.B. values of the players.
options
disagreement
1306
Vol. 47:4
1168
1306
Prisoner’s
47 JO HN
Dilemma
M ARS HALL
andL.
CoRase
EV .Theorem
1168
Vol. 1307
47:4
promises from
different
or whether
its predecessors,
they willparticularly
breach them.
since
In itfact,
had a
theCoasean
benefit
bargain
of
two years
mayof planning.
not solve the Coasean version of the Prisoner’s
Dilemma
Like the
because
shift T,
in the
conference
temptation
scheduling,
payoff, other
still changes
lurks in have
the
taken
background.
place So
within
long the
as TLatCrit
remainsentity,
largerincluding
than R, each
concerted
prisoner
efforts
has
to
a countervailing
continue a process
incentive
of institutionalization.
to breach his promise
In recent
of cooperation:
years, there
the
has
larger
been
T is,
a growing
relative focus
to R, on
thehow
more
to likely
capitalize
it is on
that
its one
critical
or both
niche,
of
continue
the prisoners
cultivating
will defect.
the next generation of critical scholars, and
ensure that the baton of outsider jurisprudence is passed along.
U NCERTAINTYhas
, EXPONENTIAL
DISCOUNTING
, AND
IV.
Internally,
THE ROLE
theOF organization
shifted, including
a gradual
ELASTICITY
IN THE in
COASEAN
VERSION
THE PRISONER
changing
of the guard
leadership,
so toOFspeak,
as well ’Sas a
downsizing in administration.DILEMMA
For example, from 2008 to the
present, the Board of Directors was intentionally downsized, with
Even when
the ofprisoners
are allowed
to bargain
with each
a growing
number
Board seats
being occupied
by junior
law
6
other – either
strategically or non-strategically, as in our Coasean
professors.
Another major above
development
is when
LatCrit’s
acquisition
of a
thought-experiment
– and even
they are
able to make
physical
space for
organization.
Campo
credible threats,
thethe
prisoners
may stillThe
endproperty,
up defecting.
It is Sano
true
(Spanish
Healthy,”
or more
literally,
“Camp
is
that the for
use“Camp
of credible
threats
might
change
the Sanity”),
temptation
Purchased
by
a
ten-acre
parcel
located
in Central
Florida.
payoff
relative
to of
theland
other
payoffs;
however,
there 7are
three nonLatCrit
in 2011,
theit space
home
to The
Living Justice
trivial reasons
why
mightisnot.
First,
uncertainty
poses a Center
major
8 The
physical
serves
and
the LatCrit
Community
problem
with threats,
since Campus.
there will
always
exist facility
some level
of
as a means as
“to to
level
the playing
field will
and in
givefact
LatCrit
activists
a
uncertainty
whether
a threat
be carried
out.
space
is intended discounting or
fighting chance
be heard.”
Another
salient to
problem
with9 The
threats
is exponential
the time dimension of a given threat; this is particularly relevant
serve
as the
hub credible,
of their will
educational,
research,
since to
most
threats,
however
not be carried
out until
advocacy
andfuture.
activism
to remedy
imbalance
and with
sometime
in the
Lastly,
another the
potential
problem
deficiencies
of the
legal system.
Havingsince
an the
threats
is the issue
of current
price elasticity
of demand,
independent
physical
hasmay
become
prisoners’
responsiveness
to abase
threat
vary critical
dependingason a
universities
number
of factors. and law schools increasingly are even less
A. Uncertainty
“Uncertainty” refers to the positive probability that any
Naming and Launching a New Discourse of Critical Legal Scholarship, 2
Coasean
bargain
between the prisoners will not be enforced
HARV . LATINO
L. REVmade
. 1 (1997).
LATINAEssentially,
& LATINO
also LatCrit
LATCRIT:factor.
dueSee
to judicial
error Biennial
or some Conferences,
other extrajudicial
CRITICAL
LEGALto Tdefect
HEORY, inINC
., Coasean
http://latcrit.org/content/conferences/latcritone’s
decision
the
version of the dilemma will
biennial-conferences/
(last visited
5, 2013)
(providing
a list
the previous
not
only be a function
of the July
severity
of the
penalty
forofbreach
(i.e.,
conferences, and providing direct links to view symposia articles for some
any
threats
or
promises
made
during
the
course
of
the
prisoners’
years (found by following the respective year’s link to its corresponding
negotiations),
but it will also be a function of the probability of
webpage).
Additionally, Both
LatCritofhasthese
developed
a substantial
body ofofscholarship
enforcement.
functions
– severity
penalty from
and
several otherofstand-alone
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alia the ex
South-North
the
probability
enforcement
– areinter
uncertain
ante (i.e.,Exchange,
at the time
Studymust
Spacedecide
Series,
the International
andnot).
Comparative
Colloquia.
LatCrit
one
whether
to defect or
Generally
speaking,
the
Symposia, LATCRIT: LATCRIT: LATINA & LATINO CRITICAL LEGAL THEORY,
less likely
enforcement is, or the less severe the penalty(last
for breach
INC.,
http://latcrit.org/content/publications/latcrit-symposium/
visited
is,
the
more
likely
the
prisoners
will
defect.
July 5, 2014).
6 One
These possible
include Professors
González,ofAndrea
Freeman,is and
response Marc-Tizoc
to the problem
uncertainty
to
César
Hernández.
See Aboutcosts
LatCrit,
note 3 (listing
extendCuahtémoc
the logicGarcía
of zero
transactions
to supra
the enforcement
the
professors
on the
LatCrit
Board assumes
of Directors
and their
respectivewhy
law
stage.
Since the
Coase
Theorem
costless
bargaining,
schools).
not7 further
assume costless enforcement? Could we not assume
Campo Sano, LATCRIT: LATINA AND LATINO CRITICAL LEGAL THEORY,
that
the
prisoners
are not only allowed
bargain
make
INC, http://www.latcrit.org/content/campo-sano/
(last to
visited
July 5,and
2014).
8 Id.
credible
threats and promises, but also that any resulting
9
Id.
130847:4
Vol.
Prisoner’s
47 JO HN
Dilemma
M ARS HALL
andL.
CoRase
EV .Theorem
1308
Vol.1307
1291
47:4
agreement to cooperate will be enforced perfectly and costlessly?
This, in turn, raises a new question: does Coasean bargaining
solve the Prisoner’s Dilemma even when enforcement is costless
and perfect? Not necessarily, for the answer to our question now
depends on how far in the future such enforcement will occur.
B.
3
Exponential Discounting
The next question we shall consider is what role does time
I. INTRODUCTION
play in the Coasean version
of the Prisoner’s Dilemma? In general,
notice that the Prisoner’s Dilemma presents an intertemporal
Building
upon the
this
year’s that
LatCrit
choice.
Each prisoner
mustmain
weigh theme
not onlyofthe
probability
the
Conference,
Resistance
Theorizing
and Building
Crossother
will defect
in theRising:
absence
of a Coasean
bargain (or
the
4 this paper (i.e., our contribution to this larger
Sector Movements,
probability
of breach
even with a Coasean bargain), but each
critical conversation)
challenges
one ofvalue
the dominant
paradigms
in
prisoner
must also weigh
the present
of his own
defection or
5 Specifically, we present a
economics
and the
law:future
the Coase
breach
versus
value Theorem.
of cooperation.
thought-experiment,
what
we shall
the “pure
Coasean
version”
Assume that the
prisoners
arecall
allowed
to bargain
with
each
In order
brief, towhat
if the
of theand
famous
Dilemma
game. 6 in
other
have Prisoner’s
each promised
to cooperate
obtain
the
prisoners
in this
parable
allowedEven
to
higher
collective
payoffsgame-theory
generated from
mutualwere
cooperation.
communicate
andbargain
bargain in
with
eacheach
otherprisoner
instead must
of being
heldthe
in
with
a Coasean
place,
weigh
separate value
cells, ofasbreaching
in the standard
version
of defecting)
the dilemma?
Would
present
his promise
(i.e.,
versus
the
our prisoners
strike a mutually-beneficial
and (i.e.,
collectively-optimal
future
or discounted
value of cooperating
keeping his
7 Or, as
Coasean bargain,
Coase must
Theorem
predicts?
promise).
That is, as
eachtheprisoner
still decide
whether
he
predicted
in the sentence
standardin one-shot
version
Prisoner’s
prefers
a reduced
the present,
whichofis athe
higher
payoff
8 would they still end
Dilemmatoinhis
which
is notthe
allowed,
relative
otherbargaining
choices, versus
possibility
of a penalty for
breach in the future.
According to the standard economic model of behavior,
3 A.W. Tucker, A Two-Person Dilemma: The Prisoner’s Dilemma (1950), as
intertemporal
choices are no different from other choices, except
reprinted in Philip D. Straffin, Jr., The Mathematics of Tucker: A Sampler, 14
that
some
consequences
delayed and hence must be
(1983).
TWO-YEAR C. MATHEMATICS J. 228are
4 Latina and
anticipated
“discounted”
(i.e.,
recalibrated
take
into account
& Latino Critical Legal Theory, Inc., to
2013
Biennial
LatCrit
74
Conference
Program
(and Related
Events),the
(2013),
available at
ButSchedule
discounting
generates
possibility
of
the
delay).
http://latcrit.org/media/medialibrary/2013/10/LatCrit2013_Conference_Progra
“exponential discounting.” That is, given two similar rewards,
m_FinalR.pdf.
people
generally prefer the one that arrives sooner rather than the
5 The Coase Theorem is named after the late Ronald Coase. Ronald H.
equivalent
one later.
Stated
formally,
or
1–44 “discount”
(1960). George
Coase, The Problem
of Social
Cost,
3 J.L. & people
ECON. 1,often
reduce
the
value
of
the
later
reward
by
a
factor
that
increases
with
Stigler, however, was the economist who first presented the idea now known
STIGLER, THE
THEORY
PRICE 113
as the
CoaseofTheorem.
G EORGE
the
length
the delay.
This J.discounting
process
is OF
traditionally
(MacMillan,
ed. 1966). as
George
Stigler
stated Coase’s
idea as a “theorem”
modeled in3deconomics
a form
of exponential
discounting,
a timeand coined the term “Coase Theorem.”75Id.
consistent
model
of
discounting.
6
See generally WILLIAM POUNDSTONE , PRISONER’S DILEMMA (Anchor
Books 1993) (providing an overview and history of the origins of the dilemma);
see also F. E. Guerra-Pujol, The Parable of the Prisoners, 5–9 (June 21, 2013)
74 See, e.g.,
A DICTIONARY
ECONOMICS
108–09
(John Black,
Nigar
[hereinafter
Guerra-Pujol,
TheOFParable
of the
Prisoners]
(unpublished
Hashimzade & Gareth
Myles
4th ed. author),
2012) (providing
a standard
manuscript)
(on
file eds.,with
available
at
definition of “discount” and “discounting the future” in economics).
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2281593,
(explaining the
75 Some
experimental research has shown that the constant discount rate
prisoner’s
parable).
7 Id.
assumed
in exponential discounting is systematically being violated. Shane
8 See infra
Part I.B.
Frederick,
George
Loewenstein & Ted O’Donoghue, Time Discounting and
1308
Vol. 47:4
1168
1308
Prisoner’s
47 JO HN
Dilemma
M ARS HALL
andL.
CoRase
EV .Theorem
1168
Vol. 1309
47:4
different
In the
from
case
itsofpredecessors,
the Prisoner’s
particularly
Dilemma, since
our prisoners
it had the
arebenefit
more
likely
of two to
years
engage
of planning.
in exponential discounting when calculating the
present
Likevalue
the of
shift
a reduced
in conference
prison scheduling,
sentence (i.e.,
other
the changes
greater their
have
taken
discount
place
ratewithin
is, the the
more
LatCrit
they value
entity,present
including
personal
concerted
libertyefforts
over
to
future
continue
liberty,
a process
and thus
of institutionalization.
the more they value
In present
recent years,
libertythere
over
has
future
been
liberty,
a growing
the more
focuslikely
on how
they
to are
capitalize
to defect).
on its
Does
critical
a Coasean
niche,
continue
bargain between
cultivating
the the
prisoners
next generation
change thisof outcome?
critical scholars,
Not at all
and
–
ensure
the outcome
that the
will baton
not change
of outsider
if thejurisprudence
present valueis or
passed
utilityalong.
of a
Internally,
reduced sentence
the organization
today is greater
has than
shifted,
the expected
includingor adiscounted
gradual
changing
disutility of
of athe
penalty
guard for
in breach
leadership,
in the
so distant
to speak,
future.
as well
In other
as a
downsizing
words, it is in
possible
administration.
that the temptation
For example,
payoff,
from
which
2008
is certain
to the
present,
and will the
occur
Board
at of
time
Directors
T1, might
was outweigh
intentionally
the downsized,
possibility with
of a
a
breach
growing
penalty,
number
which
of is
Board
uncertain
seats and
beingwill
occupied
not occur
by junior
until time
law
6
professors.
T2.
Another
majorany
development
is LatCrit’s
acquisition
of a
Thus,
because
penalty for breach
will occur
in the future,
physical
space
for from
the organization.
The property,
Camponow
Sano
the present
utility
a (certain) reduced
prison sentence
is
(Spanish
for “Campthe
Healthy,”
or more of
literally,
“Camp Sanity”),
is
likely to outweigh
future disutility
an (uncertain)
penalty for
7 Purchased
by
a
ten-acre
parcel
of land
Centralthe
Florida.
breach
in the
future!
Of located
course, inwhether
discounted
disutility
LatCrit
in 2011,
the for
space
is home
to Thethe
Living
Justice
Center
of
a future
penalty
breach
outweighs
present
value
of a
The physical
facility
serves
and the LatCrit
reduced
sentenceCommunity
depends onCampus.
several 8 critical
variables,
including
as the
a means
“tothe
level
the playing
field and
give LatCrit
activists a
(i)
size of
future
or expected
penalty,
(ii) the probability
The(iii)
space
is intended
fighting
heard.” 9and
that
the chance
breach to
is be
enforced,
each
prisoner’s discount rate.
More to the point, however, we have identified the conditions
serve
the hub
theirto educational,
research,
under to
which
ourasprisoners
areoflikely
defect even with
a Coasean
advocacy
andAnd,
activism
to remedy
the imbalance
and in
bargain
in place.
even under
the standard
assumptions
deficiencies
the current
legal system.
an or
modern
economic of
theory,
these conditions
are notHaving
implausible
independent physical base has become critical as
far-fetched.
universities
law schools
increasingly
are even(i.e.,
less time
Compare,
for and
example,
the related
idea of interest
value of money), a foundational concept in finance theory. 76 A
certain amount of money today has a different buying power
(value)
than the same amount of money in the future because the
Naming and Launching a New Discourse of Critical Legal Scholarship, 2
value
of
money
a future point of time includes the interest
HARV . LATINO
L. REVat
. 1 (1997).
CRIT: of
LATINA
& In
LATINO
the
See also
LatCrit Biennial
Conferences,
earned
or inflation
accrued over
a givenLAT
period
time. 77
CRITICAL LEGAL
HEORY
, INC.,of http://latcrit.org/content/conferences/latcritalternative,
the Ttime
value
money can also be stated formally:
biennial-conferences/
visited
July 5,to
2013)
list of
the year
previous
the
sum of FV (last
(future
value)
be (providing
receiveda in
one
is
conferences, and providing direct links to view symposia articles for some
discounted
at
the
rate
of
interest
r
to
give
a
sum
of
PV
(present
years (found by following the respective year’s link to its corresponding
value)
webpage).at present (i.e., PV = FV – r*PV = FV/(1+r)). This
Additionally,
LatCrit has
a substantial
body ofsum,
scholarship
from
expression
measures
the developed
present value
of a future
discounted
several
stand-alone
symposia:equal
inter to
aliathe
the time
South-North
Exchange,
to
the other
present
by an amount
value of
money. the
In
Study words,
Space Series,
the International
Comparative
Colloquia.
LatCrit
other
this concept
allows theand
valuation
of a future
stream
of
Symposia, LATCRIT: LATCRIT: LATINA & LATINO CRITICAL LEGAL THEORY,
INC.,
http://latcrit.org/content/publications/latcrit-symposium/
(last
visited
July 5, 2014).
6 These
Time
Preference:
include
A Critical
Professors
Review,
Marc-Tizoc
40 J. ECON
González,
. LITERATURE
Andrea351
Freeman,
(2002). This
and
César
paper, Cuahtémoc
however, will
García
follow
Hernández.
the standard
See About
economic
LatCrit,
approach
supraand
noteassume
3 (listing
a
the
constant
professors
discount
onrate.
the LatCrit Board of Directors and their respective law
76 DAVID G. LUENBERGER, INVESTMENT SCIENCE ch. 2 (Oxford Univ. Press
schools).
7 Campo Sano, LATCRIT: LATINA AND LATINO CRITICAL LEGAL THEORY,
1998).
INC,77http://www.latcrit.org/content/campo-sano/
That is, the value of money changes over
(last time
visited
because
July 5, there
2014).is an
8 Id.
opportunity
to earn interest on the money and because inflation will tend to
9 Id.
drive
prices up, thus reducing the “value” of the money in the future. Id. at 12.
131047:4
Vol.
Prisoner’s
47 JO HN
Dilemma
M ARS HALL
andL.
CoRase
EV .Theorem
1310
Vol.1309
1291
47:4
income, such that the future steam is “discounted” and then added
together, thus providing a lump-sum “present value” today of the
entire income stream.
Like the time value of money, there is also a time value of
time, so to speak. One way of measuring the magnitude of each
prisoner’s incentive to breach (i.e., the probability that either
3
prisoner will breach or defect), even with a Coasean bargain in
place, is by analyzing the role that time plays in his or her
decision-making. The prisoners not only prefer personal liberty to
I. inINTRODUCTION
the absence thereof (time
prison), but we would also expect the
value or utility of liberty in the present to be worth more to each
Building
upon in
thethemain
of words,
this year’s
LatCrit
prisoner
than liberty
future.theme
In other
the “time
value
Conference,
Resistance
Rising:
Theorizing
and Building
of time” means
that personal
liberty
in the present
is worthCrossmore
Sector
(i.e.,time
our contribution
thispresent
larger
than inMovements,
the future,4 this
and paper
likewise,
in prison intothe
critical conversation)
challenges
of in
theprison
dominant
paradigms
in
imposes
a greater disutility
thanone
time
in the
future. In
Specifically,
a
economicsindependent
and law: theofCoase
Theorem.
addition,
the effect
that 5time
has on we
the present
decisionthought-experiment,
what we
we must
shall call
the consider
“pure Coasean
version”
making
of the prisoners,
further
the prisoners’
6 In brief, what if the
of the famous to
Prisoner’s
Dilemma
responsiveness
the payoffs
in the game.
Prisoner’s
Dilemma. That is,
prisoners
this the
game-theory
parable
allowed
to
in predictingin whether
prisoners will
defect were
or cooperate
in the
communicate
andofbargain
with each
of being
held in
Coasean version
the dilemma,
the other
price instead
elasticity
of demand
of
separate
cells, must
as inalso
thebestandard
version of the dilemma? Would
each prisoner
considered.
our prisoners strike a mutually-beneficial and collectively-optimal
Coasean bargain, C. asPrice
the Elasticity
Coase Theorem
of Demandpredicts? 7 Or, as
predicted in the standard one-shot version of the Prisoner’s
8 would they still end
Dilemma
which
not allowed,
Here,inwe
posebargaining
one last is
important
question
regarding our
Coasean version of the Prisoner’s Dilemma. If a prison sentence
operates like a price, 78 then what happens when the price
3 A.W. Tucker, A Two-Person Dilemma: The Prisoner’s Dilemma (1950), as
elasticity
of demand of each prisoner is different? In economics,
reprinted in Philip D. Straffin, Jr., The Mathematics of Tucker: A Sampler, 14
the
term
“elasticity”
generally
refers to the percentage change in
MATHEMATICS
J. 228 (1983).
TWO-YEAR C.
one4 variable
with
respect
to
percentage
change
in another
Latina & Latino Critical Legala Theory,
Inc., 2013
Biennial
LatCrit
Conference or
Program
Schedule
(andlogarithmic
Related Events),
(2013), of
available
at
variable,
the ratio
of the
derivatives
the two
http://latcrit.org/media/medialibrary/2013/10/LatCrit2013_Conference_Progra
79 Specifically, the “price elasticity of demand” is a
variables.
m_FinalR.pdf.
numerical
or quantitative measure of how responsive the demand
5 The Coase Theorem is named after the late Ronald Coase. Ronald H.
of
a
given
good
or of
service
to a 3change
the
price
that good
or
. 1,
1–44of(1960).
George
Coase, The Problem
SocialisCost,
J.L. & in
ECON
service.
In
the
case
of
the
Prisoner’s
Dilemma,
for
example,
the
Stigler, however, was the economist who first presented the idea now known
EORGE
STIGLER, isTHE
THEORYliberty
OF PRICE
as the being
Coase demanded
Theorem. Gby
“good”
the J.prisoners
personal
(i.e.,113
a
(MacMillan,
3d ed. 1966).
GeorgeElasticity
Stigler stated
idea aswould
a “theorem”
reduced prison
sentence).
in Coase’s
this case
thus
and coined the term “Coase Theorem.” Id.
measure
the prisoners’ responsiveness to changes in the prison
6 See generally W ILLIAM POUNDSTONE , PRISONER’S DILEMMA (Anchor
sentence.
Books 1993) (providing an overview and history of the origins of the dilemma);
see also F. E. Guerra-Pujol, The Parable of the Prisoners, 5–9 (June 21, 2013)
[hereinafter Guerra-Pujol, The Parable of the Prisoners] (unpublished
78 See generally
S. Becker,
Crime and
Punishment:
An Economic
manuscript)
(on Gary file
with
author),
available
at
Approach,
76 JOURNAL OF POLITICAL ECONOMY 169, 179-180 (1968).
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2281593,
(explaining the
79 HARRY
H. PANJER, FINANCIAL ECONOMICS WITH APPLICATIONS 101
prisoner’s
parable).
7 Id.
(Actuarial
Found. 1998). See also CAMPBELL MCCONNELL, STANLEY BRUE ,
See
EANinfra
FLYNN
Part
, EI.B.
CONOMICS 114-116 (18th ed. 2009).
AND8 S
1310
Vol. 47:4
1168
1310
Prisoner’s
47 JO HN
Dilemma
M ARS HALL
andL.
CoRase
EV .Theorem
1168
Vol. 1311
47:4
different
Thusfrom
far,itshowever,
predecessors,
we have
particularly
assumed
since
that
it had
the the
prisoners’
benefit
elasticities
of two yearsare
of planning.
the same, a standard but unstated assumption in
most,Like
if not
theall,shift
treatments
in conference
of the Prisoner’s
scheduling,Dilemma.
other changes
Specifically,
have
taken
we have
place
assumed
withinthat
theboth
LatCrit
prisoners
entity,
share
including
a “unitary
concerted
elastic”efforts
(i.e.,
to
e =continue
1) demand
a process
schedule.
of institutionalization.
In other words, we have
In recent
assumed
years,
that
there
the
has
prisoners
been ashare
growing
the focus
sameonset
how
of totime
capitalize
preferences
on its regarding
critical niche,
the
continue
payoffs incultivating
the Prisoner’s
the next
Dilemma:
generation
theyof both
critical
uniformly
scholars,prefer
and
ensure
shorter that
prisonthe
sentences
baton oftooutsider
longer ones.
jurisprudence
Stated formally,
is passed
wealong.
have
Internally,
not only assumed
the organization
that the prisoners
has shifted,
derive including
a greater aamount
gradual
of
changing
utility (or ofa the
lower
guard
levelin ofleadership,
disutility)sothe
to speak,
shorter as
their
wellprison
as a
downsizing
sentences are,
in but
administration.
we have also For
assumed
example,
that the
from
prisoners
2008 to
obtain
the
present,
the samethe
levels
Board
of “utility”
of Directors
or “disutility,”
was intentionally
as the case
downsized,
may be, from
with
a
thegrowing
payoffs number
(prison sentences)
of Board seats
in the
being
Prisoner’s
occupiedDilemma.
by junior(Note
law
6
professors.
that in economics,
“utility” is an abstract or mathematical
Another major
developmentover
is LatCrit’s
a
representation
of preferences
some set acquisition
of goods ofand
) In the
of the Prisoner’s
additional
physical
for case
the organization.
The Dilemma,
property, an
Campo
Sano
services. 80space
unit of time
in prison
generates
additional,
perhaps
(Spanish
for “Camp
Healthy,”
or moreanliterally,
“Campand
Sanity”),
is
diminishing,
levelofof land
disutility
on in
theCentral
prisoners.
a
ten-acre parcel
located
Florida. 7 Purchased by
LatCrit
in 2011,
the space
is home
to The
Livingif Justice
Center
Thus,
the question
above
(i.e., what
happens
the prisoners’
8 The physical
facility serves
and
the LatCrit
Community
Campus.becomes:
elasticities
of demand
are different?)
what happens
when
as
a means
“to level for
thepersonal
playing liberty
field and
LatCritsentence)
activists is
a
Prisoner
1’s demand
(i.e.give
a reduced
9 The
1 <
while
Prisoner
space is
2’sintended
demand for liberty is
fighting
be 1),
heard.”
inelastic chance
(i.e., eto
elastic (i.e., e2 > 1)?
Before
we as
proceed
to answer
thiseducational,
question, let
us explain
to serve
the hub
of their
research,
“inelastic”
and “elastic”
demand
illustrate
these concepts
advocacy
and activism
to and
remedy
the imbalance
and with
a simple
numerical
The legal
demand
of a good
is “elastic”
deficiencies
of example.
the current
system.
Having
an
(i.e., independent
more responsive
to price
when critical
the percentage
physical
base changes)
has become
as
change
in the price
of that
is less
than the are
percentage
change
universities
and
law good
schools
increasingly
even less
in quantity demanded. 81 For example, when e = 1.5, this means
that a 50% decline in price will cause a 75% increase in the
quantity
demanded. 82 In contrast, demand is “inelastic,” or less
Naming and Launching a New Discourse of Critical Legal Scholarship, 2
responsive
in price, when the percentage change in the
HARV . LATINOtoL.changes
REV . 1 (1997).
: LATINA
LATINO
See of
alsoa LatCrit
Biennial the
Conferences,
LATCRIT
price
good exceeds
percentage
change
in &quantity
83 ForTHEORY
CRITICAL LEGAL
, INCwhen
., http://latcrit.org/content/conferences/latcritexample,
e = 0.5, this means that a 50%
demanded.
biennial-conferences/
(lastonly
visitedcause
July 5,a2013)
thequantity
previous
decline
in price will
25%(providing
increasea list
in of
the
conferences,84and providing direct links to view symposia articles for some
Thus, in the case of the Prisoner’s Dilemma, the
demanded.
years (found by following the respective year’s link to its corresponding
concept
of
elasticity
refers to the prisoners’ responsiveness to
webpage).
changes
in theLatCrit
payoffs
the game.
For example,
1 might
Additionally,
hasofdeveloped
a substantial
body Prisoner
of scholarship
from
several
otherresponsive
stand-alone to
symposia:
inter alia the
South-North
Exchange, the
be
highly
small changes
in the
prison sentence;
as
Study Space
Series, the
and Comparative
LatCrit
such,
his demand
for International
personal liberty
would be Colloquia.
elastic. On
the
Symposia, LATCRIT: LATCRIT: LATINA & LATINO CRITICAL LEGAL THEORY,
INC.,
http://latcrit.org/content/publications/latcrit-symposium/
(last
visited
July 5, 2014).
80 These
6
For aninclude
influential
Professors
treatment
Marc-Tizoc
of utilitiesGonzález,
in economics,
Andrea
see VON
Freeman,
NEUMANN
and
& MORGENSTERN
supra note
21, at ch.
17–31
(providing
mathematical
César
Cuahtémoc, García
Hernández.
See 3,
About
LatCrit,
supraa note
3 (listing
treatment
of utilities
assigning
to probability
of
the professors
on the and
LatCrit
Board utilities
of Directors
and their distributions
respective law
alternatives).
schools).
81 C
7
Campo
OOTER Sano,
& ULEN
L,AT
supra
CRIT:note
LATINA
67, atAND
29. LATINO CRITICAL LEGAL THEORY,
INC,82http://www.latcrit.org/content/campo-sano/
Id.
(last visited July 5, 2014).
83Id.
8
Id.
84Id.
9
Id.
131247:4
Vol.
Prisoner’s
47 JO HN
Dilemma
M ARS HALL
andL.
CoRase
EV .Theorem
1312
Vol.1311
1291
47:4
other hand, Prisoner 2 might be far less responsive even to large
changes in the payoffs, and therefore, his demand for liberty would
be inelastic.
The most important determinant of the price elasticity of
demand is the availability of substitutes for the good in question. 85
Generally speaking, the elasticity of demand will be greater where
3
there are more substitutes for a particular good, and, likewise, the
elasticity will be lower where there are fewer substitutes. 86 In the
case of the Prisoner’s Dilemma, however, the responsiveness of the
INTRODUCTION
prisoners to the payoffsI.may
vary depending on certain individual
factors unique to each prisoner. Although there are few, if any,
Buildingfor upon
the liberty
main theme
of are
thiseither
year’sfreeLatCrit
substitutes
personal
(i.e., you
or in
Conference,
Rising: Theorizing
andprison
Building
prison), the Resistance
level of disutility
of being in
mayCrossvary
4 this paper (i.e., our contribution to this larger
Sector
Movements,
depending
on a wide
variety of individual factors, such as, inter
criticalone’s
conversation)
challenges
one of
the dominant
paradigms
in
alia,
age, income,
marital
status,
or history
of prior
5 Specifically, we present a
economics and
theexpect
Coase aTheorem.
convictions.
Welaw:
would
young prisoner,
a wealthy prisoner,
thought-experiment,
shall
call the for
“pure
Coasean
or
a prisoner with what
a wifeweand
children,
example,
to version”
behave
In one
brief,
what
if the
of the famous
Dilemma
game.
differently
than Prisoner’s
an old prisoner,
a poor
one,6 or
with
no family
prisoners
in a
thisprisoner
game-theory
were
allowed
to
ties. Likewise,
who is aparable
first-time
offender,
might
communicate
and bargain
with each other
insteadwhereas
of beingaheld
in
qualify for probation
or a rehabilitation
program,
repeat
separate
in the
version of the prison
dilemma?
Would
offender cells,
mightas face
a standard
mandatory-minimum
term.
In
our
prisoners
strike expect
a mutually-beneficial
and prison
collectively-optimal
addition,
we would
the quality of the
sentence or
Or, as
Coasean
bargain,
the security
Coase prison
Theorem
type
of prison
(i.e., as
a high
withpredicts?
limited7 visitation
predicted
in the
standard
version type
of the
Prisoner’s
rights
versus
a low
security,one-shot
college-campus
prison
with a
8 would they still end
Dilemma
in which
bargaining
is notliberal
allowed,
good
library,
internet
access, and
visitation
rights) – and
not just the quantity of time in prison – to influence the behavior
of the prisoners in the Prisoner’s Dilemma.
3 A.W. Tucker, A Two-Person Dilemma: The Prisoner’s Dilemma (1950), as
In other words, the use of general labels, such as “Prisoner 1”
reprinted in Philip D. Straffin, Jr., The Mathematics of Tucker: A Sampler, 14
and
2” (or “A”J. and
“B”), to describe the players in the
EAR C. MATHEMATICS
228 (1983).
TWO-Y“Prisoner
4 Latina &
Prisoner’s
Dilemma
is
too
possibly LatCrit
even
Latino Critical Legalreductionist
Theory, Inc., and
2013 Biennial
Conference Program
(and Related
Events),
available of
at
misleading
becauseSchedule
such labels
abstract
away(2013),
the problem
http://latcrit.org/media/medialibrary/2013/10/LatCrit2013_Conference_Progra
elasticity.
Accordingly, we need more – not less – information
m_FinalR.pdf.
about
the prisoners’ individual circumstances and specific
5 The Coase Theorem is named after the late Ronald Coase. Ronald H.
characteristics
in order
to measure
their
CON. 1, 1–44responsiveness
(1960). George
Coase, The Problem
of Social
Cost, 3 J.L.
& Erespective
to
the
payoffs
in
the
Prisoner’s
Dilemma
game.
Stigler, however, was the economist who first presented the idea now known
STIGLER,information,
THE THEORY let
OF Pus
RICE now
113
as the
Coase Theorem.
G EORGE
Instead
of ignoring
this J.critical
(MacMillan,
3d ed.a1966).
Georgeset
Stigler
stated Coase’s idea
as a following
“theorem”
proceed
under
different
of assumptions.
In the
and coined the term “Coase Theorem.” Id.
three
examples, assume that we have sufficient information about
6 See generally W ILLIAM POUNDSTONE , PRISONER’S DILEMMA (Anchor
the
individual
prisoners
in and
order
measure
least
Books 1993) (providing
an overview
historytoof the
origins oforthe at
dilemma);
approximate
their
actual
elasticities.
Example
#1
assumes
that
see also F. E. Guerra-Pujol, The Parable of the Prisoners, 5–9 (June 21, 2013)
[hereinafter
Guerra-Pujol,
The Parable
of the
Prisoners]
(unpublished
the
price elasticity
of demand
for personal
liberty
of both
prisoners
manuscript)
(on
file
with
author),
available
at
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2281593, (explaining the
85 Id. at
29.
prisoner’s
parable).
86Id.
7
“The more substitutes for a good, the greater the elasticity of demand;
See infra
Part I.B. the lower the elasticity.” Id. at 29–30.
the 8fewer
the substitutes,
1312
Vol. 47:4
1168
1312
Prisoner’s
47 JO HN
Dilemma
M ARS HALL
andL.
CoRase
EV .Theorem
1168
Vol. 1313
47:4
is elastic from
different
(i.e., its
e >predecessors,
1). Exampleparticularly
#2 considers
since
the itmore
had interesting
the benefit
case
of
twoofyears
a highly
of planning.
inelastic prisoner playing against a highly elastic
one. Like
And, the
Example
shift in
#3 conference
considers prisoners
scheduling,
with
other
inelastic
changes
demand
have
taken
curves place
(i.e., ewithin
< 1). the LatCrit entity, including concerted efforts
to continue a process of institutionalization. In recent years, there
has been a Example
growing focus
#1: eon
> 1how to capitalize on its critical niche,
continue cultivating the next generation of critical scholars, and
ensure
To that
begin,theassume
baton that
of outsider
both prisoners
jurisprudence
are highly
is passed
elasticalong.
(i.e.,
Internally,
responsive) to
thechanges
organization
in the payoffs
has shifted,
in the standard
including
version
a gradual
of the
changing
Prisoner’s ofDilemma.
the guard
In in
thisleadership,
case, we would
so to speak,
expect no
as change
well as in
a
downsizing
the prisoners’
in responses
administration.
to the payoffs
For example,
in the game
from because
2008 totheir
the
present,
levels of the
utility
Board
or of
disutility
Directors
from
wasthe
intentionally
payoffs remain
downsized,
unchanged
with
a
relative
growing
to number
each other.
of Board
So long
seats as
being
the occupied
responsiveness
by junior
of law
the
6 changes in the payoffs run in the same direction (i.e.,
professors.
prisoners to
Another
major
development
LatCrit’s
acquisition
a
so long
as both
prisoners
are price iselastic
or price
inelastic), of
both
physical
for the
organization.
property,
Campo
prisoners space
still prefer
to spend
less timeThe
in prison
to more
time.Sano
(Spanish for “Camp Healthy,” or more literally, “Camp Sanity”), is
a ten-acre parcel
of land
Florida. 7 Purchased by
Example
#2: located
e > 1, ein< Central
1
LatCrit in 2011, the space is home to The Living Justice Center
8 The
physical
facility
serves
and the
LatCrit
Community
Next,
consider
the moreCampus.
interesting
case
of a highly
inelastic
as
a means
“to level
the aplaying
and
give
LatCrit to
activists
a
prisoner
playing
against
highly field
elastic
one.
Contrary
the first
9 The
space is intended
fighting
to bethat
heard.”
example,chance
assume
the
corresponding
elasticities of the
prisoners in the standard one-shot version of the Prisoner’s
to serve
as opposite
the hub directions:
of their educational,
Dilemma
run in
Prisoner 1’sresearch,
demand for
10),imbalance
while Prisoner
advocacy
activism
to (i.e.,
remedy
and 2’s
personal
liberty and
is highly
elastic
e1 >the
2 < 0.1).an
Under
desire deficiencies
to stay out of prison
is highlylegal
inelastic
(i.e., eHaving
the current
system.
these independent
conditions, both
prisoners
stillhas
prefer
short prison
physical
base
become
criticalsentences
as
to long
ones, butand
Prisoner
1 is much
more responsive
to any
universities
law schools
increasingly
are even less
changes in the payoffs of the Prisoner’s Dilemma than Prisoner 2
is. Does this scenario alter the likely outcome or equilibrium of the
dilemma?
Naming and Launching a New Discourse of Critical Legal Scholarship, 2
believe
it . does.
Under this scenario, Prisoner 1 is much
HARV .We
LATINO
L. REV
1 (1997).
CRIT: LATINA
& L1,
ATINO
See likely
also LatCrit
Biennial
more
to defect
than Conferences,
Prisoner 2 LAT
because
Prisoner
as
CRITICAL Lby
EGAL
HEORY, INC
., http://latcrit.org/content/conferences/latcrit“defined”
his Telasticity
curve,
is more responsive to the payoffs
biennial-conferences/
(last visitedPrisoner
July 5, 2013)
a list of
previous
of
the game. In particular,
1 – (providing
like Prisoner
2 the
– wants
(i)
conferences, and providing direct links to view symposia articles for some
the
lowest
possible
sentence
(i.e.,
T,
the
Temptation
Payoff)
and
years (found by following the respective year’s link to its corresponding
(ii) to avoid the worst possible payoff (i.e., S, the dreaded Sucker’s
webpage).
Additionally,
LatCritPrisoner
has developed
body of scholarship
from
Payoff).
However,
1 –a substantial
unlike Prisoner
2 – is more
several othertostand-alone
symposia:
inter
alia the South-North
Exchange,
the
responsive
the possibility
of (i)
obtaining
the Temptation
Payoff,
Study
the the
International
and Sucker’s
Comparative
Colloquia. LatCrit
as
wellSpace
as (ii)Series,
avoiding
humiliating
Payoff.
Symposia, LATCRIT: LATCRIT: LATINA & LATINO CRITICAL LEGAL THEORY,
What
about Prisoner 1’s inelastic cohort, Prisoner
2?
By
INC.,
http://latcrit.org/content/publications/latcrit-symposium/
(last
visited
definition,
Prisoner
2
is
less
responsive
to
changes
in
the
payoffs
July 5, 2014).
6 These
include
Professors
Marc-Tizoc
Andrea
Freeman,
and
than
Prisoner
1 because
Prisoner
2’s González,
demand for
liberty
is highly
César Cuahtémoc
Hernández.
See2’s
About
LatCrit, therefore,
supra note 3will
(listing
< 0.1).
Prisoner
behavior,
be
inelastic
(i.e., e2García
the
professors
LatCrit
of Directors
andOn
their
respective
law
much
harder onto the
predict
forBoard
multiple
reasons.
the
one hand,
schools).
Prisoner
2 –Sano,
like Lall
prisoners, presumably – prefers a short prison
7 Campo
ATCRIT: LATINA AND LATINO CRITICAL LEGAL THEORY,
sentence
to
a
long
one.
On the other hand,
Prisoner
2 (i.e.,
e2 < 0.1)
INC, http://www.latcrit.org/content/campo-sano/
(last
visited July
5, 2014).
Id. responsive to changes in the payoffs than the average
is 8less
9
Id.
131447:4
Vol.
Prisoner’s
47 JO HN
Dilemma
M ARS HALL
andL.
CoRase
EV .Theorem
1314
Vol.1313
1291
47:4
prisoner (i.e., e = 1), and is far less responsive to such changes
than Prisoner 1 (i.e., e1 > 10). We would thus expect Prisoner 2 to
be highly unresponsive to the prosecutor’s strategic offer of
leniency in exchange for his confession.
Therefore, whether Prisoner 2 decides to defect or to
cooperate will, most likely, depend on his personal value system
3
and other relevant or applicable extra-strategic factors (e.g. age,
income, marital status, etc.). And yet, it is these factors that are
completely ignored or abstracted away in game theory. Put
I. 2INTRODUCTION
another way, if Prisoner
is already predisposed to reject any
potential plea bargain or offer of leniency from the prosecutor (e.g.
Building
upon the
main system),
theme ofthen
thishe year’s
LatCrit
because
of Prisoner
2’s value
is unlikely
to
Conference,
Resistance
Rising: ex
Theorizing
Crossconfess or accept
a plea bargain
post (i.e., and
after Building
the prosecutor’s
4 this paper (i.e., our contribution
Sector
to this larger
offer of Movements,
a reduced sentence
is on the table). 87
critical conversation) challenges one of the dominant paradigms in
economics and
law: the
Example
#3:Coase
e < 1 Theorem. 5 Specifically, we present a
thought-experiment, what we shall call the “pure Coasean version”
6 In brief, what if the
of the
famous
Prisoner’s
game.
Lastly,
what
happensDilemma
when both
prisoners’
demand curves
prisoners
this Or,
game-theory
parable
to
are
highly in
inelastic?
what is the
most were
likely allowed
outcome or
communicate of
andthe
bargain
withwhen
each other
of being
in
equilibrium
game
both instead
prisoners
are held
highly
separate cells,toaschanges
in the standard
version
of the of
dilemma?
Would
unresponsive
in the payoff
structure
the Prisoner’s
our prisoners
strike
a all
mutually-beneficial
andscenario.
collectively-optimal
Dilemma?
Simply
put,
bets are off in this
Similar to
7 Or, as
Coasean
bargain,
as thePrisoner
Coase 2Theorem
predicts?
the
discussion
concerning
in example
#2 above,
factors
predicted toin the
the Prisoner’s
standard Dilemma
one-shot version
of the
Prisoner’s
external
model will
influence
the
8 would they still end
Dilemma of
in the
which
bargaining
is not
allowed,more
behavior
prisoners
in this
example
than the actual
payoffs.
D. Lessons and Discussion
3 A.W. Tucker, A Two-Person Dilemma: The Prisoner’s Dilemma (1950), as
reprinted in Philip D. Straffin, Jr., The Mathematics of Tucker: A Sampler, 14
These
examples
of the
role of elasticity in the Prisoner’s
EAR C.three
MATHEMATICS
J. 228
(1983).
TWO-Y
4 Latinateach
Dilemma
us
an
important
non-trivial
about
the
& Latino Critical Legal and
Theory,
Inc., 2013lesson
Biennial
LatCrit
Conference
Events),theory
(2013), in
available
at
Prisoner’s Program
DilemmaSchedule
model (and
and Related
about game
general.
http://latcrit.org/media/medialibrary/2013/10/LatCrit2013_Conference_Progra
Game theory is best able to predict the behavior of players in the
m_FinalR.pdf.
Prisoner’s
Dilemma (and other games) when their demand curves
5 The Coase Theorem is named after the late Ronald Coase. Ronald H.
are
inelastic
(i.e., of
e <
1) but
when
the
are
CONdemand
. 1, 1–44 schedules
(1960). George
Coase, The Problem
Social
Cost,not
3 J.L.
& E
elastic
(i.e.,
e
>
1)
or
when
their
elasticities
are
unitary
(i.e.,
e
=
1).
Stigler, however, was the economist who first presented the idea now known
J. STIGLER
, THE
PRICE
113
as
the the
Coase
Theorem.
G EORGE
Since
behavior
of such
inelastic
players
willTHEORY
dependOFless
on the
(MacMillan,
ed. 1966).
George
stated
Coase’s idea
as aoutside
“theorem”
payoffs of a3d given
model
and Stigler
more on
real-world
factors
of
and coined the term “Coase Theorem.” Id.
the6 formal model, the predictive power of game theory will
See generally WILLIAM POUNDSTONE , PRISONER’S DILEMMA (Anchor
decrease
the prisoners’
preferences
become
more
responsive
Books
1993)as
(providing
an overview
and history of
the origins
of the
dilemma);
(i.e.,
their
demand
curves
become
more
elastic).
Indeed,
this
see also F. E. Guerra-Pujol, The Parable of the Prisoners, 5–9 (June 21,lesson
2013)
[hereinafter Guerra-Pujol, The Parable of the Prisoners] (unpublished
manuscript)
(on
file
with
author),
available
at
87 But it is worth noting that if Prisoner 2 is already predisposed
ex antethe
to
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2281593,
(explaining
confess orparable).
strike a deal with the prosecutor (for reasons not captured in the
prisoner’s
7 Id. Prisoner’s Dilemma model), then he will probably still confess ex post,
abstract
8 Seehis
infra
Partinelastic
I.B.
despite
highly
demand curve.
1314
Vol. 47:4
1168
1314
Prisoner’s
47 JO HN
Dilemma
M ARS HALL
andL.
CoRase
EV .Theorem
1168
Vol. 1315
47:4
is not only
different
fromconsistent
its predecessors,
with one
particularly
of the key
since
insights
it had of
theThomas
benefit
Schelling’s
of
two yearsclassic
of planning.
study “The Strategy of Conflict.” 88 It also builds
uponLike
Schelling’s
seminal
work byscheduling,
specifying other
the limits
of game
the shift
in conference
changes
have
theory.place
By studying
the LatCrit
theoretical
relation
between
the behavior
taken
within the
entity,
including
concerted
efforts
andcontinue
choices a of
the players
and their respective
of
to
process
of institutionalization.
In recentelasticities
years, there
demand,
our
work focus
has identified
in critical
which niche,
game
has
been a
growing
on how tocircumstances
capitalize on its
theory models
are likely
be generation
helpful and ofwhen
theyscholars,
are likelyand
to
continue
cultivating
the to
next
critical
prove incomplete,
misleading,
or wrong.
ensure
that the baton
of outsider
jurisprudence is passed along.
Internally, the organization has shifted, including a gradual
EGARDING
THEso
ROLE
OF THIRD
ARTIES
V.changing
A BRIEFofDIGRESSION
the guard Rin
leadership,
to speak,
as Pwell
as IN
a
DILEMMA from 2008 to the
THE PRISONER
downsizing in administration.
For ’Sexample,
present, the Board of Directors was intentionally downsized, with
Before number
proceeding
further,
shall
return by
onejunior
last time
a growing
of any
Board
seats we
being
occupied
law
6
to
the standard,
or non-Coasean version, of the Prisoner’s
professors.
Another
major the
development
is LatCrit’s
acquisition
a
Dilemma
to explore
relation between
the prisoners
andofthe
physical space
for the
organization.
property,
Campo
Sano
prosecutor
in the
standard
version The
of this
parable.
Stated
in
(Spanishterms,
for “Camp
Healthy,”
or more
“Camp
Sanity”), is
general
we shall
consider
the literally,
relation of
the “third-party
7 Purchased
by
a ten-acre
parcel of land
located in
Central
payoff
administrator”
to Players
1 and
2 inFlorida.
the general
or logical
LatCrit
in 2011,
form
of the
game. the space is home to The Living Justice Center
8 The thought-experiment
physical facility serves
and the
LatCritone
Community
Whatever
thinks ofCampus.
our Coasean
or
as a means
“to level
playing field
and give
activists
a
Coasean
version
of thethe
Prisoner’s
Dilemma,
it isLatCrit
worth noting
that
9 The
spaceplace,
is intended
fighting chance
to be isheard.”
Coasean
bargaining
already
taking
even in the standard
versions of the parable presented above. But instead of direct
to serve
as the
hub of their
educational,
bargaining
between
the prisoners
themselves
(which research,
as we saw is
advocacy
activism version
to remedy
thePrisoner’s
imbalanceDilemma),
and
not allowed
in and
the standard
of the
deficienciesthat
of isthe
current
system.
an each
the bargaining
taking
placelegal
in this
game Having
is between
independent
physical separately.
base has become critical as
prisoner
and the prosecutor
universities
law schools increasingly
are even Dilemma
less
The
standardandformulations
of the Prisoner’s
presuppose not just two prisoners or players but also a “thirdparty payoff administrator” (such as the prosecutor in the original
formulation
of the parable). That is, in addition to the players or
Naming and Launching a New Discourse of Critical Legal Scholarship, 2
prisoners,
the
HARV . LATINO L. RPrisoner’s
EV . 1 (1997).Dilemma also requires a third-party to
CRIT: depending
LATINA & on
LATINO
See also the
LatCrit
Biennial
administer
payoffs
of thisConferences,
game, withLAT
payoffs
the
CRITICAL made
LEGAL byTHEORY
, INC., 89
http://latcrit.org/content/conferences/latcritThis third party is not really a
choices
the players.
biennial-conferences/
visited“payoff
July 5, 2013)
(providing a list
of the previous
neutral
arbiter or(last
mere
administrator.”
Instead,
he is
conferences, and providing direct links to view symposia articles for some
trying
to
manipulate
the
choices
of
the
players
by
getting
them
to
years (found by following the respective year’s link to its corresponding
confess
or
“snitch”
in
the
classic
version
of
the
parable,
and,
webpage).
Additionally,
has is
developed
body of scholarship
moreover,
his LatCrit
conduct
anothera substantial
form of “bargaining”
with from
the
several other stand-alone symposia: inter alia the South-North Exchange, the
players.
StudyThe
Spacepresence
Series, theofInternational
and Comparative
Colloquia. LatCrit
the prosecutor
or “third-party
payoff
Symposia, LATCRIT: LATCRIT: LATINA & LATINO CRITICAL LEGAL THEORY,
administrator”
in
the
standard
versions
of
the
parable
thus
poses
INC.,
http://latcrit.org/content/publications/latcrit-symposium/
(last
visited
90 Doesn’t the
an
important
but
neglected
subsidiary
question.
July 5, 2014).
These include Professors Marc-Tizoc González, Andrea Freeman, and
César Cuahtémoc García Hernández. See About LatCrit, supra note 3 (listing
See generally
THOMAS
C. Board
SCHELLING
, THE STRATEGY
OFrespective
CONFLICT law
(2d
the 88professors
on the
LatCrit
of Directors
and their
ed. 1980).
schools).
89 Campo
7
For example,
Sano, Richard
LATCRITDawkins
: LATINA refers
AND Lto
ATINO
the role
CRITICAL
of theL“banker”
EGAL THEORY
in his,
Ipresentation
NC, http://www.latcrit.org/content/campo-sano/
THE visited
SELFISH
July
G AME
5, 2014).
203, 206–
of the parable. RICHARD DAWKINS,(last
8 Id.
07, 217–18,
225–26 (2d ed. 1989).
90Id.
9
See, e.g., F. E. Guerra-Pujol, The Poker-Litigation Game 3, n.5 (Dec. 26,
6
131647:4
Vol.
Prisoner’s
47 JO HN
Dilemma
M ARS HALL
andL.
CoRase
EV .Theorem
1316
Vol.1315
1291
47:4
presence of this third party (i.e., his ability to offer lighter
sentences or more favorable payoffs to the prisoners) affect the
outcome of the game? Would the prisoners still defect in the oneshot version of the parable if the role of the prosecutor or other
third party were removed from the game?
Recall that the standard or “canonical” version of the
3
Prisoner’s Dilemma is classified as a “non-cooperative game”
because the prisoners in the dilemma are not allowed to
communicate or negotiate with each other. 91 Nevertheless,
INTRODUCTION
although the prisonersI. are
not allowed to bargain with one
another, it is critical to note that the prosecutor is, in fact, allowed
Building upon
the main
of thisThe
year’s
LatCrit
to communicate
and bargain
with theme
the prisoners.
prosecutor
in
Conference,
Theorizing
Building
Crossthe standardResistance
versions ofRising:
the dilemma
is, inand
essence,
bargaining
4 this paper (i.e., our contribution to this larger
Sector
Movements,
with each
prisoner
separately and sequentially, making a
critical conversation)
challenges
one to
of each
the dominant
paradigms
in
tempting
“take it or leave
it” offer
one. Although
neither
5 Specifically, we present a
economicsisand
law: to
themake
Coasea Theorem.
prisoner
allowed
counteroffer
to the prosecutor, each
thought-experiment,
what whether
we shall to
call
the “pure
Coasean version”
prisoner
must still decide
accept
the prosecutor’s
initial
brief,
what if both
the
of the In
famous
Prisoner’sone-shot
Dilemmaversion
game. 6ofInthe
offer.
the standard
dilemma,
prisoners
in most
this likely
game-theory
were
to
prisoners will
accept the parable
prosecutor’s
offerallowed
(i.e., agree
communicate
and bargain
with each
insteadstrategy
of beingorheld
in
to confess), because
confession
is theother
dominant
Nash
separate
cells,
as in
the standard version of the dilemma? Would
equilibrium
of this
game.
our prisoners
strike
a mutually-beneficial
and collectively-optimal
In short, the
prisoners
are, in fact, already
engaged in a form
7 Or, as
Coasean
as the
Coase in
Theorem
predicts?
of Coaseanbargain,
or voluntary
bargaining
the standard
version
of the
predicted
the standard
one-shot
version
of the toPrisoner’s
Prisoner’s in
Dilemma.
Although
they are
not allowed
bargain
they with
still end
Dilemma
which
bargaining
is not
allowed, 8sowould
with each in
other,
they
are allowed
to bargain,
to speak,
the
prosecutor. But, the collective outcome of these separate Coasean
bargains with the prosecutor leaves both prisoners much worse off
3
Tucker, A Two-Person Dilemma: The Prisoner’s Dilemma (1950), as
thanA.W.
if they
had decided to reject the prosecutor’s offer and remain
reprinted in Philip D. Straffin, Jr., The Mathematics of Tucker: A Sampler, 14
silent.
TWO-YEAR C. MATHEMATICS J. 228 (1983).
4 This
the dilemma
thus refutes
the Coase
Theorem;
Latinaanalysis
& Latinoof Critical
Legal Theory,
Inc., 2013
Biennial
LatCrit
Conference
Schedule (and
Related bargaining
Events), (2013),
at
it shows Program
how self-seeking
Coasean
(i.e.,available
Coasean
http://latcrit.org/media/medialibrary/2013/10/LatCrit2013_Conference_Progra
bargaining between each prisoner and the prosecutor) generates a
m_FinalR.pdf.
worse
collective outcome for the prisoners. One could argue that
5 The Coase Theorem is named after the late Ronald Coase. Ronald H.
this
conclusion
is ofpremature
structure
of the
1, 1–44
(1960). George
Coase, The Problem
Social Cost,because,
3 J.L. & given
ECON. the
payoffs
in
the
standard
version
of
the
Prisoner’s
Dilemma,
it is
Stigler, however, was the economist who first presented the idea now known
STIGLER
, THE
THEORYanyways.
OF PRICE But
113
as
thelikely
Coase that
Theorem.
G EORGE J.would
very
the prisoners
have
defected
(MacMillan,
3d ed.is1966).
George Stigler
stated
ideawith
as arespect
“theorem”
this conclusion
not premature
at all,
at Coase’s
least not
to
and coined the term “Coase Theorem.” Id.
the6 Prisoner’s Dilemma. For the prisoners to defect, they must be
See generally WILLIAM POUNDSTONE , PRISONER’S DILEMMA (Anchor
able to1993)
strike
a bargain
with the
prosecutor.
That
is, there
must be
Books
(providing
an overview
and
history of the
origins
of the dilemma);
see also F. E. Guerra-Pujol, The Parable of the Prisoners, 5–9 (June 21, 2013)
[hereinafter Guerra-Pujol, The Parable of the Prisoners] (unpublished
2012) (unpublished
(on file author),
with author),
available at
manuscript)
(on manuscript)
file
with
available
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2193993
(providing thea
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2281593,
(explaining
simple model
in which the role of the banker is made explicit).
prisoner’s
parable).
91Id.
7
See Tucker, supra note 3 and accompanying text; LUCE & RAIFFA, supra
See at
infra
Partand
I.B.accompanying text.
note8 17,
94–95
1316
Vol. 47:4
1168
1316
Prisoner’s
47 JO HN
Dilemma
M ARS HALL
andL.
CoRase
EV .Theorem
1168
Vol. 1317
47:4
someone from
different
(i.e., its
thepredecessors,
prosecutor) particularly
with the ability
since to
it had
offerthe
a benefit
lighter
prison
of
two years
sentence
of planning.
in exchange for the prisoners’ confessions. By
contrast,
Like if
thethe
shift
District
in conference
Attorneyscheduling,
is prevented
other
from
changes
bargaining
have
taken
with the
placeprisoners,
within theorLatCrit
if theentity,
prisoners
including
are concerted
prevented efforts
from
to
bargaining
continue with
a process
the D.A.,
of institutionalization.
then it is less likely
In recent
that the
years,
prisoners
there
has
will been
end aup
growing
defecting.
focus In
on how
short,to in
capitalize
a world
on its
in critical
which niche,
“plea
continue
bargaining”
cultivating
is prohibited,
the next
thegeneration
prisoners of
arecritical
probably
scholars,
better and
off
ensure
going tothat
trial the
and baton
takingoftheir
outsider
chances.
jurisprudence is passed along.
Internally,
Despite the
this organization
analysis, most
has game
shifted,
theorists
including
woulda probably
gradual
changing
agree that,of due
the to
guard
the in
structure
leadership,
of the
so payoffs
to speak,
in as
the well
standard
as a
downsizing
“one-shot” version
in administration.
of the Prisoner’s
For Dilemma,
example, defection
from 2008
is still
to the
present,
most likely
the Board
outcome
of Directors
in one-shot
was dilemmas
intentionally
– downsized,
even whenwith
all
bargaining
a
growing number
is prohibited.
of Board
Once
seatswebeing
allow
occupied
Coasean
by bargaining
junior law
6 prisoners, however, we see that there are three sets of
between the
professors.
Another
major
development
LatCrit’s
acquisition
of is
a
potential
bargains
in the
Prisoner’s is
Dilemma.
Specifically,
there
physical
space for
organization.
The between
property, the
Campo
Sano
the
possibility
of the
a Coasean
bargain
prisoners
(Spanish for especially
“Camp Healthy,”
or more version
literally,of“Camp
Sanity”),but
is
themselves,
in the Coasean
the dilemma,
7 Purchased
by
a ten-acre
parcel
of land located
in Central
Florida.
there
is also
the possibility
of a separate
bargain
between
Prisoner
LatCrit
in 2011,
the space
is home
The Livingof Justice
Center
1
and the
prosecutor
as well
as theto possibility
an additional
8 The physical
serves
and the between
LatCrit Community
Campus.
bargain
Prisoner 2 and
the prosecutor.
Thefacility
possibility
of
as a means
“tosets
level
playing
and give LatCrit
activists
a
three
separate
of the
bargains
in field
the Prisoner’s
Dilemma
suggests
The space is intended
fighting
to be
that
thechance
outcome
of heard.”
such a9 three-person
interaction might be a
complex one and possibly unpredictable. We thus conclude this
as the a hub
of their exploration
educational,of research,
paper tobyserve
conducting
preliminary
the relation
advocacy
and activism
to remedy
the imbalance
between
complexity
theory and
the Coasean
version and
of the
deficiencies
of the current legal system. Having an
Prisoner’s
Dilemma.
independent physical base has become critical as
HOUGHTS
THE COMPLEXITY
OF THE
and T
law
schoolsON
increasingly
are even
less
VI.universities
SOME CLOSING
PRISONER’S DILEMMA
The classic or standard version of the Prisoner’s Dilemma
Naming and Launching a New Discourse of Critical Legal Scholarship, 2
paints
a misleading
picture of the game being played and the
HARV . LATINO
L. REV . 1 (1997).
ATINA &
LATINO
See also
LatCrit It
Biennial
Conferences,
LATCRIT: Lmodel
number
of players.
purports
to be a two-player
when,
in
CRITICAL there
LEGAL
, Ithree
NC., http://latcrit.org/content/conferences/latcritreality,
areTHEORY
at least
different persons playing this game:
biennial-conferences/
2013)
(providing a(and
list ofthe
the previous
the
two prisoners(last
as visited
well July
as 5,
the
prosecutor
police).
conferences, and providing direct links to view symposia articles for some
Therefore,
instead
of
a
dyad
or
two-party
interaction,
we
have
a
years (found by following the respective year’s link to its corresponding
triad
or
three-party
interaction,
one
that
is
more
complex
and
with
webpage).
Additionally,
LatCrit hasvariables.
developed aSuch
substantial
bodyasof the
scholarship
from
many
more relevant
stories
Prisoner’s
several
otherand
stand-alone
symposia: inter alia
the South-North
Exchange,
the
Dilemma
the Rancher-Farmer
Parable,
however,
purposely
Study Space
the International
and Comparative
ignore
such Series,
endogenous
and exogenous
variables –Colloquia.
variablesLatCrit
that
Symposia, LATCRIT: LATCRIT: LATINA & LATINO CRITICAL LEGAL THEORY,
could
very
well influence the outcome of these interactions.
In a
INC.,
http://latcrit.org/content/publications/latcrit-symposium/
(last
visited
real-life
Prisoner’s
Dilemma,
for
example,
the
prisoners
are
likely
July 5, 2014).
6 These
include Professors
González,
Andrea
Freeman,
to find
themselves
embeddedMarc-Tizoc
in a larger
network
of players,
alland
of
César Cuahtémoc
García
Hernández.
About
supraliterature
note 3 (listing
whom
are ignored
in the
existingSee
legal
andLatCrit,
economics
on
the Coase
professors
on the and
LatCrit
of Directors
and their respective law
the
Theorem
the Board
Prisoner’s
Dilemma.
schools).
it to say, the different variables that shape the
7 Suffice
Campo Sano, LATCRIT: LATINA AND LATINO CRITICAL LEGAL THEORY,
preferences
of the prisoners and the
INC, http://www.latcrit.org/content/campo-sano/
(lastprosecutor
visited July 5,make
2014). the
8 Id.
Prisoner’s
Dilemma a potentially very complex game. Moreover, as
9
Id.
131847:4
Vol.
Prisoner’s
47 JO HN
Dilemma
M ARS HALL
andL.
CoRase
EV .Theorem
1318
Vol.1317
1291
47:4
more variables and degrees of elasticities influence the triadic
relation among the prisoners and prosecutor, the more complex
their interaction becomes. Such a triadic and multivariable
interaction thus invites the use of a different approach, such as
complexity theory. 92 This, however, will be the subject of a future
paper.
3
VII. CONCLUSION
Before concluding, I.we INTRODUCTION
wish to say a few words about our
general approach to the question posed in the title of our paper as
upon theon main
theme
this to
year’s
LatCrit
well Building
as our emphasis
questions
(as ofopposed
answers)
or
Conference,
Resistance
Rising: Theorizing
andparaphrase
Building Stuart
Cross93 throughout
this paper. To
“known
unknowns”
4 this paper (i.e., our contribution to this larger
Sector
Movements,
Firestein,
a neurobiologist
at Columbia University, our implicit
critical conversation)
challenges
one of theignorance
dominant(that
paradigms
in
premise
in these pages
is that communal
which we
5 Specifically, we present a
economics
and know)
law: the
Theorem.
do
not yet
is Coase
the main
fountain
of knowledge and
94 According
thought-experiment,
what
we shall call
the “pure
Coaseandiscovery
version”
to Firestein,
ignorance
promotes
discovery.
In brief,towhat
if the
of the famous
Prisoner’s
Dilemma
game.
because
it motivates
persons
engaged
in6 science
search
for
prisoners and
in this
this pursuit,
game-theory
parable
were
to
answers,
in turn,
leads to
newallowed
questions:
communicate is
andnot
bargain
with each other
of being held
“[ignorance]
an individual
lack instead
of information
but in
a
separate cells,
the standard
version
of the dilemma?
Would
communal
gap as
in in
knowledge
. . . This
is knowledgeable
ignorance,
our
prisoners
strike ainsightful
mutually-beneficial
collectively-optimal
perceptive
ignorance,
ignorance. and
It leads
us to frame
7 Or,
95 We
as
Coasean
bargain, the
as first
the step
Coase
Theorem
predicts?
better questions,
to getting
better
answers.”
predictedthis
in counterintuitive
the standard one-shot
version
the applies
Prisoner’s
believe
and critical
logicof also
to
8 would they still end
Dilemma inand
which
is social
not allowed,
economics
law,bargaining
and to the
sciences
generally. Rather
than restating what we already know (or think we know), as many
conventional legal scholars and economists tend to do, we make
3 A.W. Tucker, A Two-Person Dilemma: The Prisoner’s Dilemma (1950), as
greater
progress when we pose new and non-trivial questions (i.e.,
reprinted in Philip D. Straffin, Jr., The Mathematics of Tucker: A Sampler, 14
questions
toMwhich
we doJ.not
know the answers).
ATHEMATICS
228yet
(1983).
TWO-YEAR C.
4 In
this
paper,
then,
we
identified
the Inc.,
essential
of the
Latina & Latino Critical Legal Theory,
2013 elements
Biennial LatCrit
Conference two-player
Program Schedule
(and Dilemma,
Related Events),
(2013), available
at
one-shot,
Prisoner’s
the simplest
and most
http://latcrit.org/media/medialibrary/2013/10/LatCrit2013_Conference_Progra
famous
of all models in game theory, and then presented a pure
m_FinalR.pdf.
Coasean
version of the dilemma, one in which the prisoners are
5 The Coase Theorem is named after the late Ronald Coase. Ronald H.
allowed
to
communicate
and
bargain
each
and not
just
. 1,other,
1–44 (1960).
George
Coase, The Problem
of Social
Cost,
3 J.L. with
& ECON
with
the
prosecutor.
We
found
that
even
when
the
prisoners
are
Stigler, however, was the economist who first presented the idea now known
STIGLERwith
, THE each
THEORY
OF Pthere
RICE 113
as the Coase
Theorem. G EORGE
allowed
to communicate
and J.
bargain
other,
is
(MacMillan, 3d ed. 1966). George Stigler stated Coase’s idea as a “theorem”
and coined the term “Coase Theorem.” Id.
692 See generally
, COMPLEXITY
: A ’G
TOUR (Anchor
(2009).
generallyMELANIE
WILLIAMMITCHELL
POUNDSTONE
, PRISONER
S UIDED
DILEMMA
For applications
to law, an
seeoverview
Orlando I.
Martínez-García,
The Person
Law,
Books
1993) (providing
and
history of the origins
of theindilemma);
the Number
in Guerra-Pujol,
Math, 18 AM. The
U. J.Parable
OF GENDER
SOC. POL’Y
L. 50321,
(2010).
see
also F. E.
of the Prisoners,
5–9&(June
2013)
93 Moran Cerf,
Known Unknowns,
336 SCI
(reviewing
STUART
[hereinafter
Guerra-Pujol,
The Parable
of. 1382
the (2012)
Prisoners]
(unpublished
FIRESTEIN, IGNORANCE
SCIENCEauthor),
(2012)).
manuscript)
(on : HOW
fileIT DRIVES
with
available
at
94 By “ignorance,” we follow Firestein in meaning “the (explaining
absence of fact,
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2281593,
the
understanding,
insight, or clarity about something.” STUART FIRESTEIN,
prisoner’s parable).
7 Id.
: HOW IT DRIVES SCIENCE 6 (2012).
IGNORANCE
95See
8
Id. infra
at 7. Part I.B.
1318
Vol. 47:4
1168
1318
Prisoner’s
47 JO HN
Dilemma
M ARS HALL
andL.
CoRase
EV .Theorem
1168
Vol. 1319
47:4
some positive
different
from its
probability
predecessors,
that particularly
they might since
not strike
it had the
a Coasean
benefit
bargain.
of
two years
Furthermore,
of planning. we found that even if they are able to
negotiate
Like the
a mutually
shift in conference
beneficial scheduling,
agreement other
(e.g. through
changes have
nontaken
strategic
place
bargaining),
within thethere
LatCrit
is also
entity,
some
including
positive concerted
probabilityefforts
that
to
they
continue
could still
a process
breachof such
institutionalization.
an agreement and
In recent
end up
years,
defecting,
there
has
contrary
been to
a growing
what thefocus
Coase
on Theorem
how to capitalize
predicts.on
Inits
either
critical
case,
niche,
the
continue
probabilitycultivating
of defection
theisnext
a function
generation
of various
of critical
factors,
scholars,
including
and
ensure
such things
that theasbaton
uncertainty,
of outsider exponential
jurisprudencediscounting,
is passed along.
and
Internally,
elasticity. the organization has shifted, including a gradual
changing
This of
conclusion
the guard
– the
in leadership,
possibility ofso defection
to speak,in as
thewell
Coasean
as a
version of dilemma
downsizing
in administration.
– is theoretically
For example,
significantfrom
because
2008it all
to but
the
refutes
present,orthe
falsifies
Boardthe
of Directors
Coase Theorem.
was intentionally
It is also worth
downsized,
noting with
that
our
a growing
conclusion
number
is notofbased
Boardonseats
ad hoc
being
behavioral
occupiedorbypsychological
junior law
quirks of 6human behavior. Uncertainty, exponential discounting,
professors.
is LatCrit’s
acquisition
a
and Another
elasticity major
are all development
part of the standard
economics
toolkit ofand
physical
for standard
the organization.
The
property, of
Campo
Sano
are
basedspace
on the
rationality
assumption
economics.
(Spanish
“Camp Healthy,”
or more literally, “Camp
Sanity”),
is
The
mainfor
contribution
of the thought-experiment
presented
in this
7 Purchased
a ten-acre
of land
located
in Prisoner’s
Central Florida.
paper
– ourparcel
Coasean
version
of the
Dilemma
– is thatby
it
LatCrit
in 2011,
the space
is questions,
home to The
Justice
Center
poses many
deep and
difficult
and Living
this paper
is our
first
8 The
physical facility serves
and
the in
LatCrit
attempt
searchCommunity
of answers Campus.
… and new
questions.
as a means “to level the playing field and give LatCrit activists a
fighting chance to be heard.” 9 The space is intended
to serve as the hub of their educational, research,
advocacy and activism to remedy the imbalance and
deficiencies of the current legal system. Having an
independent physical base has become critical as
universities and law schools increasingly are even less
Naming and Launching a New Discourse of Critical Legal Scholarship, 2
HARV . LATINO L. REV . 1 (1997).
See also LatCrit Biennial Conferences, LATCRIT: LATINA & LATINO
CRITICAL LEGAL THEORY, INC., http://latcrit.org/content/conferences/latcritbiennial-conferences/ (last visited July 5, 2013) (providing a list of the previous
conferences, and providing direct links to view symposia articles for some
years (found by following the respective year’s link to its corresponding
webpage).
Additionally, LatCrit has developed a substantial body of scholarship from
several other stand-alone symposia: inter alia the South-North Exchange, the
Study Space Series, the International and Comparative Colloquia. LatCrit
Symposia, LATCRIT: LATCRIT: LATINA & LATINO CRITICAL LEGAL THEORY,
INC.,
http://latcrit.org/content/publications/latcrit-symposium/
(last
visited
July 5, 2014).
6 These include Professors Marc-Tizoc González, Andrea Freeman, and
César Cuahtémoc García Hernández. See About LatCrit, supra note 3 (listing
the professors on the LatCrit Board of Directors and their respective law
schools).
7 Campo Sano, LATCRIT: LATINA AND LATINO CRITICAL LEGAL THEORY,
INC, http://www.latcrit.org/content/campo-sano/ (last visited July 5, 2014).
8 Id.
9 Id.