Social Welfare, Cooperators' Advantage, and the Option of Not Playing the Game
Author(s): John M. Orbell and Robyn M. Dawes
Source: American Sociological Review, Vol. 58, No. 6 (Dec., 1993), pp. 787-800
Published by: American Sociological Association
Stable URL: http://www.jstor.org/stable/2095951
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SOCIAL WELFARE, COOPERATORS'ADVANTAGE,
AND THE OPTION OF NOT PLAYING THIEGAME*
JOHNM. ORBELL
Universityof Oregon
ROBYNM. DAWES
Carnegie-MellonUniversity
We outline a model of how freedom to choose between playing and not playing particular Prisoner's Dilemma games can (1) increase social welfare and (2) provide relative
gains to intending cooperators. When cooperators are relatively more willing to play,
they will interact morefrequently with each other and their payoff per encounter will be
higher-potentially higher than that of intending defectors. Because the cooperate-cooperate outcome produces more wealth than any other, optional entry will increase
social welfare. We report laboratory data showing: (1) Social welfare and the relative
welfare of intending cooperators are higher when subjects are free to choose between
entering and not entering particular Prisoner's Dilemma relationships; and (2) this difference is a consequence of intending cooperators' greater willingness to enter such
relationships, not because of any capacity to recognize and avoid intending defectors.
Wespeculate about the cognitive processes that underlie this result.
focus on the consequences of a neglected aspect of risky cooperative
games-that people do not always have to play
them. Outside of zoos, animals are free to interactor not interactwith others of their kind:
Thereis an escapeclausein theircontract,a getreduces
card,whichprecipitously
out-of-jail-free
the incidenceof mutilationand murder.A few
formalitiesandthey'regone.(SaganandDruyan
1992,p.187)
And outside of prisons and other total institutions (e.g., mental hospitals, prep schools,
ghettos, and the military), humans usually
don't have to interactwith each othereither.In
*
Direct correspondenceto: John Orbell, Political Science Department,University of Oregon, Eugene, OR 97403. This research was supportedby
the National Science Foundation, grant SES9008157; any opinions, conclusions or recommendations are those of the authorsand do not necessarily reflect the views of the National Science
Foundation.Pamela Ferraraassisted in administering all stages of the experiments,and offered valuable insights about subjects' behavior. We were
also helped by Jeffrey Berejikian,Deborah Baumgold, Robert Clemen, Ron Colvin, John Dryzek,
Debbie Frisch, David Goetze, Roberta Herzberg,
George Loewenstein, Michael Macy, Gerry
Mackie, Robert Mauro, Tom Morikawa, Matthew
Mulford, Michael Posner, Carol Rydbom and Peregrine Schwartz-Shea.
fact, humans spend much time, thought, and
energy "tacitlyand explicitly maneuveringout
of bad games with unpromising players and
into good games with promising players"
(Mackie 1992). It would be remarkableif all
that time, thought,and energy were of no consequence for humanwelfare.
Such games traditionallyhave been studied
in terms of the Prisoner'sDilemma. The general form of the game gives two individuals a
binary choice between "cooperate"and "defect" in which (1) defection is dominant-each
individual is privately better off defecting regardless of what the other does, and (2) there
is a deficientequilibriumat mutualdefectionaggregate payoff is lowest, but neither individual has an incentive to cooperate and help
extractthe groupfrom the trap.
The standardmetaphor involves a District
Attorneywho needs one confession from captured (alleged) criminals to get two convictions, and who offers each a schedule of punishments(years in jail). That schedule is
t<c<d<s,
(1)
where t is the temptationfrom unilateralconfession (defection); c is the payoff from mutual denial (cooperation);d is the payoff from
mutualconfession; ands is the payoff to a prisoner who denies any part in the crime when
the otherconfesses (the otherthus "freeriding"
on the denial of the "sucker").
AmericanSociological Review, 1993, Vol. 58 (December:787-800)
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787
AMERICANSOCIOLOGICAL
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788
The power of the metaphorcomes from the
mannerin which it capturesthe everyday understandings(1) that cooperativerelationships
can be productiveto all partiesinvolved-mutual cooperationis more productivein the aggregate than any other outcome; but (2) that
exploiting another'scooperative behavior can
be more rewardingto an individual than mutual cooperation;and (3) cooperativerelationships are risky-there is always the chance of
being "suckered"by a partnerwho "freerides"
on one's own contribution.
Most analyses of the Prisoner's Dilemma
have neglected the fact thatthe two partnersin
the story are prisoners-they have been captured,placed in separatecells, denied communication among themselves, and forced to play
the game inventedby the DistrictAttorney(exceptions are Marwell and Schmitt 1975;
Orbell, Schwartz-Shea and Simmons 1984;
Tullock 1985; Yamagishi 1988; Schuessler
1989; Vanberg and Congleton 1992.) These
prisoners have no option other than choosing
between confessing or denying.
We believe that this neglect occurs because
the "prisoner" metaphor has dominated the
definitionof the problem.We proposean alternative metaphorthatplaces people in afield of
Prisoner's Dilemma games and that leaves
them free to decide which games they will play
and with whom. We are interestedin (1) the
consequences of the freedom to choose between playing and not playing these games for
aggregateor social welfare and (2) the relative
benefit to intendingcooperatorsand intending
defectors. Does the option of not playing the
game influence net wealth in the society? Do
those who intend to cooperate have a relative
advantageor disadvantage?
By definition, in the Prisoner'sDilemma the
orderof outcomes in termsof social welfaregame payoffs aggregatedacrossboth playersiS
cc>dc>dd.
(2)
That is, social welfare increaseswith the number of cooperators involved in consummated
relationships(i.e., with the numberof cooperate-cooperate relationships). If consummated
relationships are random with respect to the
choices of particularpartnersand if players'
freedom to accept or reject play in particular
games results in more cooperatorsthan defec-
tors choosing to play, social welfare will increase. If that freedom results in cooperators
playing togethermore thanwould otherwisebe
the case, their personal welfare will also increase. When cooperatorsplay with defectors,
they incurthe sucker'spayoff, by definitionthe
lowest in the Prisoner's Dilemma; but when
they play together (cooperate-cooperate),the
payoff to each cooperatoris the second highest
payoff in the matrix.
Why might a disproportionatenumberof cooperators choose to play? One possibility is
translucency (Gauthier 1986), the degree to
which a player's intentionto cooperate or defect is recognizable,to some extent, by potential partners.Translucencymeans that, with a
reasonableprobability,intendingdefectorswill
be avoided and intending cooperatorswill be
recognized and accepted as potentially profitable partners.Of course, intending defectors
will seek out intending cooperators,but their
overtures will be thwarted by an intending
cooperator'sability to recognize them. If defectors play at all, it will be largely, and unprofitably,with fellow defectors.
In these terms, Frank (1988) argued that
emotions have evolved to give cues aboutothers' intentions;emotions provide useful cues
because they are largely beyond our control,
and thus difficult to fake. In the same vein,
Cosmedes (1989) providedextensive data supporting her hypothesis that natural selection
has given humans special-purpose cognitive
mechanismsfor detectingcheating in others.
Alternatively,a high proportionof cooperate-cooperaterelationshipsmight be produced
simply because intendingcooperatorsare more
willing to enter play than intendingdefectors.
Even absenttranslucency,if intendingcooperators are more willing to enter play, they will
consummateplay with each other by chance
more frequently than they will if everybody
plays at equal rates.A differentialwillingness
to play also means that cooperatorsconsummate play with defectorsless often than would
occur if.everybodymust play.
Dawes, McTavish, and Shaklee (1977) explored the standardfinding that subjects who
cooperate expect much higher rates of cooperation from others than do subjects who defect. They provided data suggesting that
peoples' expectations about others may depend on their own choices ratherthan the reverse, as is usually assumed. Introspection-
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COOPERATORS'ADVANTAGEAND NOT PLAYINGTHE GAME
based optimism about others' cooperation
would increase the expected value of playing
for people who intend to cooperate,just as introspection-basedpessimism would decrease
the expected value of playing for people who
intend to defect.
This possibility is consistent with the extensive "false consensus" literature that documents our propensityto expect otherpeople to
be like ourselves. While others have argued
that this propensityis egoistic-and is an irrational bias-Dawes (1989, 1990) demonstrated
thatit can be normative.When base incidences
of a behaviorvary,the behaviorof a single individual, including one's self, is diagnostic of
the true rate; hence, projection is a generally
valid guide if used in a properly regressive
mannerand combined with other available information.
Orbell and Dawes (1991a) showed that intending cooperators'greaterwillingness to enter such games (underappropriateparameters)
gives them a higher expectationper-encounter
than intendingdefectors. This has broadtheoreticalimplications.Trivers(1971) commented
that models showing how altruism evolves
"take the altruismout of altruism"by making
the altruisticact advantageous,in some way, to
the altruist.If the freedomto refuse play works
to the relative benefit of intendingcooperators,
then that freedom also contributesto the evolutionarysuccess of cooperationin competition
with defection.
Similarly,marketsare defended in classical
economics because free exchange (withoutexternalities) generates wealth. If intending cooperatorsare more willing to enter Prisoner's
Dilemma games, we have an additionalreason
why freedom to choose one's partnersis socially desirable: It increases the incidence of
mutually cooperative, socially optimal relationships.
We provide a test of this attractivebut untested possibility. We show that: (1) Social or
aggregate welfare is higher when individuals
are free to choose amongpotentialpartners;(2)
payoffs to intendingcooperatorsare then relatively higherthanotherwise-potentially absolutely higher than payoffs to defectors; (3)
these outcomes are not a result of intending
cooperators' abilities to recognize and avoid
intendingdefectors;and (4) these outcomesare
a result of intendingcooperators'greaterwillingness to enter such games.
789
PRISONER'SDILEMMASWITH NO
OBLIGATIONTO PLAY
Consider the metaphor UNIVERSITY RESEARCH. The university's scholarly mission
depends on the work of bright, creative, and
energeticfaculty.But (1) "two heads are better
than one," meaning that this mission is best
advanced when faculty collaborate; and (2)
successful collaboration brings personal rewards, but also involves the possibility of being exploited (i.e., one partnerinvests time, energy, and thought while the other does not).
How can the university'srules increaseproductive collaborations?And how can those rules
make collaborationmore rewardingfor faculty
memberswho are willing to undertakeit?
At this point, the standardmetaphordevelops ways to rewardcooperatorsmore than defectors. For example, the university might reward those who participatein collaborations.
Orto makeparticipationin a collaborativeventure less risky, the university might determine
who contributedwhat to a collaboration and
allocate meritpay accordingly.
While acceptingsuch implications,the UNIVERSITY RESEARCHmetaphoralso draws
attentionto: (1) The universityas a field of opportunitiesfor collaborativeresearch;(2) and
faculty members' freedom to choose among
potentialcollaborators.How might the patterns
of collaborateversusnot collaboratechoices by
faculty members increase the net productivity
of the facultyas well as benefitthose who work
energetically and cooperatively in their collaborations?
If faculty members' collaborate versus not
collaboratechoices are uncorrelatedwith their
cooperateversus defect choices, then the freedom to accept or reject particularcollaborations will make no difference to behavioral
patterns within consummated relationships.
The probability of cooperators working with
defectors, for example, will be defined by the
relative numberof defectors in the university
as a whole. And the probabilitythat cooperators will find other hard-workingcooperators
will be defined by the relative numberof cooperatorsin the university.
The absenceof such a correlationalso means
that defectors have higher expected returns
thantheirhard-workingcooperatorcolleagues.
There will, no doubt, be fewer consummated
collaborationsthan would occur underobliga-
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790
AMERICANSOCIOLOGICAL
REVIEW
tory play, but defectors will have a higher expected returnfrom any given relationshipbecause, by definitionin the Prisoner'sDilemma,
defection pays more than cooperation.
In real universities,of course,rumor,reputation, and experience influence faculty members' decisions about potential collaborators,
but our interest is in the possibility that the
university's research mission and the welfare
of faculty memberswho collaborateand cooperate will be advancedby cooperators'greater
willingness to entercollaborativerelationships.
This possibility arises because,for a collaboration to be consummated, both parties must
agree.
Suppose, for example, thatfaculty intending
to cooperatechoose to collaboratewith a probability of .75 when an opportunityarises,while
faculty intending to defect collaboratewith a
probabilityof .25.1Also supposethatthe population is evenly divided between intendingcooperators and intending defectors. Then the
probabilityof an intendingcooperatorconsummating a relationship with another intending
cooperatoron any given opportunityfor collaborationis
nity is lower underthese circumstancesthan it
would have been with perfectknowledge about
others' intentions (.28 comparedto .5), his or
her probabilityof collaboratingwith an intending defector who would exploit the work is
lower still (.09 compared to .5). Clearly this
differenceprovidesa relative gain to intending
cooperators, and under some circumstances,
they might do betterthan intendingdefectors.
Also, intendingcooperatorsdo muchbetterunder these circumstancesthanthey would if everyone played with the same probability.2
Although UNIVERSITY RESEARCH,like
all metaphors,simplifiesthe complexityof real
situations,it shows the importanceof structural
and institutionalfactorsin defining the population in which an individual'sencountersoccur.
Because the frequencyof cooperate-cooperate
collaborationsis a functionof the relativenumber of cooperatorsin the population,universities will do better if the structureof colleges,
departments,and institutes provides cooperatively-mindedfacultyeasy access to each other,
or when the university'spolicies facilitatetheir
finding each other across institutionalboundaries.This predictionis independentof the productivityof faculty membersworking singly.
(3)
(.75) (.75) (.5) = .28,
The critical empirical issues, then, are: (1)
and the probabilityof two intendingdefectors does the optionof refusingto participatein particularPrisoner'sDilemmagames contributeto
consummatinga collaborationis
social welfare and to individual cooperators'
(4)
(.25) (.25) (.5) = .03.
relative advantage? And (2) if so, is this a
The probabilityof an intendingcooperatorand consequence of differentialplay rates (as we
an intendingdefectorconsummatinga collabo- propose)or is it a consequenceof translucency
and the consequentavoidanceof intendingderationis:
fectors?
(5)
(.75) (.25) (.5) = .09.
While an intendingcooperator'sprobability
of collaboratingwith anotherhard-workingco- LABORATORYTEST
operator on any given collaborative opportu- ExperimentalDesign
1 Our model does not require that intending cooperators always play or that intending defectors
never play-only that all individuals have some
probability,however biased, of cooperatingor defecting. The model does require negative payoffs
for playing with a defector-time and energy
wasted by the cooperatingfaculty member,and less
time and energy wasted by the defecting faculty
member. The model also requirespositive payoffs
for playing with a cooperator-a modestly productive relationship for a cooperator and a more rewarding free ride for a defector. Thus the general
form of the payoff matriximplied here is:
t > c > 0 > d > s.
We provided each of six strangers3 seated
around a large room in full view of each
2If intendingcooperatorsand intendingdefectors
played with a probabilityof .75, for example, cooperatorswould still consummateplay with other cooperatorswith a probability.28, but they would also
consummateplay with defectors with a probability
.28. Defectors, of course, would more often play
with a cooperator than if there were differential
probabilitiesof playing.
I Subjects were recruited through an advertisement in a studentnewspaperand a local daily newspaper. The advertisementoffered between $5 and
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COOPERATORS'ADVANTAGEAND NOT PLAYINGTHE GAME
791
Table 1. Matrices of Dollar Payoffs Used in the Experiment
Table 2. Sequence of Games by Subject (A Through F)
and Payoff Matrix (a Throughe)
Payoff
Matrix
Subject
Cooperate- Cooperate- Defect- DefectCooperate Defect Cooperate Defect
Play 1
Play 2
Play 3
Play 4
Play 5
B(a)
A
F(e)
E(d)
D(c)
C(b)
a
2,2
-7,5
5,-7
-5,-5
B
A(a)
F(b)
E(e)
D(d)
C(c)
b
2,2
-7,5
5,-7
-2,-2
C
B(c)
A(b)
F(d)
E(a)
D(e)
c
2,2
-2,3
3,-2
-1,-i
D
C(e)
B(d)
A(c)
F(a)
E(b)
d
2,2
-2,4
4,-2
-1,-1
E
D(b)
C(a)
B(e)
A(d)
F(c)
e
2,2
-2,3
3,-2
-1,-1
F
E(c)
D(a)
C(d)
B(b)
A(e)
other4 with a field of two-person Prisoner's
Dilemma games-one game with each of the
five others present. We varied the decision
rule under which they operated.Under a "binary choice" rule, subjects played a single
Prisoner's Dilemma game with each of the
other five individuals.In each game, subjects
were obliged to play the game and choose to
cooperate or defect (the "X" and "Y"choices,
respectively).
choice" rule, subjects were
Under a '"trinary
given the option of playing in each of the five
cases. Thus, subjectschose to cooperateor defect only if they choose to play. With the exception of this rule, which requireda few differences in wording, all else was constantbetween the two conditions.
Payoffs were in substantialdollaramountssubstantialenough, we believe, to make sub-
jects take their decisions very seriously.Aside
from the $5 promisedto subjectsfor their participation,payoffs from these five games were
the sole reward.(In fact, no subjectwent home
with less than $8.)
Because of the possibility that subjects
would responddifferentlyto differentincentive
structures(in their play versus not play decisions as well as in their cooperate versus defect ones), we varied the payoff matrices
among the five decisions. The payoff matrices
are shown in Table 1. Matrices a and b provided a substantialincentive to defect-thus,
we expected a substantialfear of others' defection and a consequentreason for refusing to
play. In the other three matrices the incentive
to defect was lower.
The sequence of plays and the payoff matrices subjectsencounteredon each play are listed
in Table 2.5 The sequence meant that partners
were randomly assigned to matrices within
in
study,
$40 for participating a decision-making
each
replication,thus permittingbetween-mathe exact sum dependingon "yourdecisions and the
simultaneousdecisions of others in the study."Ini- trix analysis.All matriceshave the structure:
tial contact was made by phone, at which time subt>c>O>d>s.
(6)
were assigned to time slots to suit their conve-
jects
nience (efforts were made to schedule people who
knew each otherat differenttimes). Time slots were
then randomlyassigned to experimentalconditions
and replications. The only exclusions were by age
(no one under age 18 was accepted) and by previous participationin the experiment. About 86 percent of the subjects were students, the rest were
townspeople, often unemployed; 57 percent were
females.
4 Although having subjectsinteractvia computer
terminalsis a useful techniquefor addressingmany
theoretical issues, the use of terminalswould have
subvertedthe theoretical-requirementthat subjects
make discriminations about other individuals qua
individuals. Randomassignmentof subjectsto replications and conditions ensured that individual
characteristicswere not correlatedwith experimental variables.
Thus, anticipatedpayoffs to individual cooperatorsand defectors from playing with a cooperatorarepositive, while anticipatedpayoffs
from playing with a defectorare negative.This
structure is an important constraint on our
model-it provides an unambiguousbasis for
5 Although pairs of subjects could not "encounter"each other at the same time (as Table 2 shows)
by the end of the sequence each individual had
played with (or had the option of playing with) each
of the other five, and pairs of subjects played with
each other on the same matrices. This sequencing
was made explicit in the instructionsread to subjects. Notice that matricesc and e are the same; because our analysis was play-by-play, we analyzed
subjects' responses to these separately.
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REVIEW
AMERICANSOCIOLOGICAL
792
predictingthatsubjectswill not play if they expect a potentialpartnerto defect, and thatthey
will play if they expect a partnerto cooperate.6
The possibility of loss from playing with a
defector raised the awkwardproblem that we
could not take money out of our subjects'
pockets. Our solution was to involve subjects
in two separate studies: a prior study lasting
about40 minutesandinvolving paper-and-pencil responses7 for which they were paid $20,
and the subsequent "decision making" study.
Subjects were told at the outset that the $20
earned in the first study would be their "starting money" for the subsequentdecision-making study. In our instructions,we emphasized
that they could lose the $20 or double it from
their participationin the second study.8
6 An early study of exit behavior in an n-person
dilemma offered positive exit payoffs whose attractiveness dependedon the numberof individualsexpected to cooperate (Orbell et al. 1984). In the
world outside the laboratory,an individual rejecting one relationship can make more than 0 (e.g.,
from another relationship),but 0 has an important
meaning in particularinteractions:A payoff above
0 provides a reason for playing, whereas a payoff
below 0 provides no such incentive. This is not to
assert that subjects would be immune to relative
payoffs in their decisions to play versus not play,
but we did not explore thatpossibility in the present
study. The zero point, as demonstratedby prospect
theory, serves as a status quo from which people
evaluate gains and losses, as opposed to evaluating
their final wealth.
7 Subjects read a series of politicians' statements
from Oregon Voters' pamphlets and completed
questionnaires about their responses to the candidates.
8 Subjects would lose all their startingmoney if
they were "suckered"all five times, i.e., if they cooperated with five different defectors. They would
double their starting money if they "free rode" all
five times, i.e., defected with five different cooperators.Of course, subjects could also take home a
variety of amounts between $0 and $40. In the
trinary-choicecases, subjects could keep their $20
starting money simply by opting out of all five
games. Thus:
Always suckered: $20 - $20 = $0
Always mutual defect: $20 - $10 = $10
No play: $20 - $0 = $20
Always mutualcooperation:$20 + $10 = $30
Always free ride: $20 + $20 = $40
Subjects were informed of their right to leave at
any time, but none left before the end of the second
study. Our advertisementpromisedbetween $5 and
$40 "for participatingin two studies that will last
The possibility that any familiarity among
subjects would influence their willingness to
play led us to cross both conditions with "irrelevant discussion." In half of the replications, subjects had 10 minutes for (taped) discussion of a Schelling coordinationproblem.9
As it turned out, this variable had no impact
on subjects' decisions, and we have combined
across "discussion"and "no discussion"replications in reporting our findings. Subjects
were encouraged to ask questions of the experimenter,but there was no opportunityfor
them to discuss their actual decisions among
themselves.
Because of our interest in the effects of
choice structure,we eliminated from our design any factors that might promote cooperation: (1) To eliminatethe effect of interpersonal
coercion, at the outset of the experimentand at
several points thereafter,subjects were promised complete privacy in their decision-making. (2) To eliminate any impact of standing
personal relationships,subjects were assigned
to experiments,conditions, and replicationsas
randomly as possible, and every effort was
made to keep friendsor relatives from signing
up for the same session. (3) Because subjects
interactedwith each otheronly once, strategies
based on experience with prior plays like titfor-tat (Axelrod 1984) or reciprocity (Trivers
1971) were not possible.
Logistics
After the initial study was completed, each
subject was handed $20 "payment for this
work" that they took to the large experiment
room a few doors away. On arrival,they put
about an hour and twenty minutes-with the exact
amountdepending on decisions you make and the
simultaneous decisions of others in the experiment."
9 Subjects were asked to specify a time and a
place within the city boundaries at which they
would meet an anonymousbenefactor.The full text
is available from the senior authoron request. This
discussion was held before the decision-making
problem was explained. A pretest confirmed the
finding of earlier research (Orbell, van de Kragt,
and Dawes 1988; Caporael,Dawes, Orbell, and van
de Kragt 1989; Orbell, Dawes, van de Kragt 1990)
that a period of discussion after the decision problem was known would lead to widespreadpromising and consequentnearly universal cooperation.
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COOPERATORS'ADVANTAGEAND NOT PLAYINGTHE GAME
793
Table 3. Average Payoff by Type of Group
Number
of Groups
Average
Payoff
Estimated
Standard
Deviation
Binary choice
18
$19.34
Trinarychoice
18
$21.59
Type of Group
Number of Groups With:
Average
Gain
Average
Loss
$3.30
7
11
$1.54
16
2
Note: Differences between groups are significant. For the difference in average payoff, t = 2.62, p < .02; for the
difference in standarddeviation, F = 4.56, p < .01; for the numberof groups with gains or losses, chi square= 9.75 (z
= 3.13), 0 = .52, p < .01.
the money in a plastic bag with an identification letter on it, and placed the bag on a table
in the center of the room. Six chairs plainly
markedwith the six identificationletters were
located aroundthe peripheryof the room. The
experimentertook a furtherseat, and aftersubjects settled down, readthe instructions.
After initial instructions emphasizing privacy were read, subjects were led through a
simple Prisoner'sDilemma matrix,afterwhich
they completed a four-questionquiz about the
basic structure.Answers were checked andfurther explanationsgiven as needed. Only when
the experimenterwas satisfied that everyone
understoodtheirchoices and the consequences
thatcould follow from those choices did actual
decision-makingproceed.
Each subjectwas given five decision sheets,
each with an identificationletterfor one of the
other five subjects, one of the five Prisoner's
Dilemma payoff matrices, a place for recording a choice between "X" (cooperate)and "Y"
(defect), and a place for recordingtheir expectations about what the other person would do.
These sheets were turnedover one by one in
the series of five plays; all subjectscompleted
the first sheet before the second sheet was
turnedover.
Once completed, these decision sheets were
collected and takento an adjoining"payroom"
where each subject'spayoff, aggregatedacross
all five interactions,was computed.Duringthis
time, subjectscompleted a final questionnaire.
They were then taken individually to the
payroom,told theirown payout (althoughthey
were not told aboutthe decisions by othersthat
had contributedto it) and were dismissed.
We ran 18 replicationsin the binary-choice
formatand 18 in the trinary-choiceformat.
FINDINGS
Social Welfareand Choice Structure
Table 3 reportsthe aggregatepayoff or social
welfare from decision-making under the binary- and trinary-choicerules. Subjects in the
18 binary-choicegroupsended the five-choice
Prisoner'sDilemma sequence poorer,on average, than they startedit ($19.34), while those
in the 18 trinary-choicegroupsended richeron
average ($21.59). Mean take-homepay in the
trinary-choice groups was $2.25 more than
mean take-home pay in the binary-choice
groups.Both differencesare significant.
Further, there was a significantly greater
standarddeviationin averagepayoff for the binary-choice groups, an unanticipatedfinding;
some did modestly well while others did very
badly. Thus, freedom to choose between playing and not playing in our laboratory"society"
was not only socially productive;it was also
reliablyso.
An average gain of $1.59 from five (possible) Prisoner'sDilemma games in the trinarychoice groups may seem trivial, particularly
when the potentialgain if everyone had played
and cooperated was $10. No doubt sustained
interaction with attendant reputation effects
and other factors discussed in the literature
would have increased gains still more. Our
data,.however,show that without such factors,
a play versusno play option improvesthings.10
10 The average individual payoff in the binarychoice groups beyond the $20 stake was negative.
Consequently, we were concerned that the advantage for the trinarychoice groups resulted from inclusion in the trinary-choicegroup average of the
zero payoffs resultingfrom opting out. To calculate
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794
Table 4.
AMERICANSOCIOLOGICAL
REVIEW
Number of Subjects by Type of ConsummatedRelationship,Payoff Matrix, and Type of Group
Percent in
CooperateCooperate
Type of ConsummatedRelationship
Payoff Matrix and
Type ofGroup
CooperateCooperate
CooperateDefect
DefectDefect
Total
Subjects
Relationships
Percent
Cooperators
Matrix a
Binary choice
Trinarychoice
30
16
50
4
28
2
108
22
28
73
51
82
Matrix b
Binary choice
Trinarychoice
8
6
60
18
40
10
108
34
7
18
35
44
Matrix c
Binary choice
Trinarychoice
32
26
50
32
26
12
108
70
30
37
53
60
Matrix d
Binary choice
Trinarychoice
18
20
52
32
38
10
108
62
17
32
41
58
Matrix e
Binary choice
Trinarychoice
32
26
52
32
24
10
108
64
30
41
54
66
Mutual Cooperationin Trinary-Choice
Games
the five payoff matricesfor subjects in the binary-choicecondition, and equivalentdata for
consummated pairings in the trinary-choice
Are these differences attributable to the pres- condition.Thereare, of course, fewer consumence of more wealth-producing cooperators in matedrelationshipsin the trinarycondition beconsummated trinary-choice relationships, in cause of the option not to play.11In each maparticular, more cooperate-cooperate relation- trix, the percentage of subjects who were inships? Table 4 reports the pairings for each of volved in consummatedrelationshipsand who
cooperatedis higherfor the trinary-choiceconthe expected individual net payoffs in the trinary- dition; and the percentageof subjects in conchoice groups if opting out were unrelatedto coop- summatedrelationshipsinvolving socially operationor defection, we first multipliedthe average timal mutualcooperationis also higher for the
individualgain or loss in each matrixfor the binary- trinary-choicecondition.
choice groups by the relative frequencyof consummated plays in the trinary-choicegroups. We then
summed this figure across matrices.We concluded
that if opting out had been independentof cooperation versus defection, the averagegain in individual
payoff (beyond the $20) in the trinary-choice
groupswould have been +$.41. We then treatedthis
average expected gain in the trinary-choicegroups
as a point null hypothesis, using groups as our unit
of analysis. Our resulting t-value was 3.25 (d.f. =
17, p < .01). This test provides strongersupportfor
our hypothesis than does a direct comparisonof binary-choice versus trinary-choice groups, despite
the negative average individual net gain in the binary-choice groups, because the between-group
variance in net payoffs was much smaller in the
trinary-choice groups than in the binary-choice
groups.
Recognitionof Defectors?
Can subjects' abilities to recognize and refuse
play with intending defectors (cf. Gauthier
1986; Frank1988; Cosmides 1990) explain the
preponderanceof cooperate-cooperategames
in the trinarychoice groups?We test this posversionof matrixa,
l Thus,in thetrinary-choice
for example,22 subjectsof the 108 totalwereinvolvedin consummated
relationships;
cooperators
or defectorswho chose to play with an individual
who optedout areexcludedfromthe table.In this
eitheroptedoutorofferedplay
case,86 individuals
withan individualwhooptedout.
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COOPERATORS'ADVANTAGEAND NOT PLAYINGTHEGAME
795
Binary-ChoiceGroups
cooperating)
(Proportion
(Proportion
defecting)
Trinary-ChoiceGroups
p-q
q
cooperatiing)
(Proportion
(Intending
cooperators)
r
(1-p)-r
defectors)
(Intending
(Proportion
defecting)
Figure 1. Estimation of IntendingCooperatorsand IntendingDefectors in Trinary-ChoiceGroups
sibility by comparing the actual number of
mutually cooperativerelationshipsagainst the
number expected under random pairing for
each of the five matricesin the two conditions.
Because ourdesign has each playermakinga
choice in each of the 5 matrices,choices arenot
independent. However, our model does not
posit a general disposition to cooperateor defect independentof the payoffs in the matrices;
instead,the model hypothesizesthat,faced with
the payoff structureof each matrix,subjectswill
play or not play dependingon theirdisposition
to cooperateor defect in thatparticularmatrix.
In the following analyses, therefore, we are
obliged to analyzematricesone-by-one.To address the experiment-widepossibilityof Type 1
error that results from this, we required that
each matrixyield a result significantat the .01
level, thereby assuring by the Bonferroni inequality that the result across all five matrices
will have a maximumerrorrate of .05.
In the binary-choicegroups, the chi-squares
evaluating the actual numberof mutually cooperativechoices againstthe numberexpected
underrandompairingfor matricesa throughe
are, respectively, .19, 2.45, .17, .00, and .03.
Even considered singly, none of these contingencies would be significant at the .05 level,
and the one that comes closest is in the direction opposite that predicted by translucency
(fewer mutuallycooperativechoices than predicted by chance).
In the trinary-choicegroups,the chi-squares
evaluating the actual numberof mutually cooperativechoices againstthe numberexpected
underrandompairingfor matricesa throughe
are, respectively, 6.17, .44, .81, .29, and .20.
Our Bonferroniproceduredoes not permit us
to conclude thatthereis some nonrandompairing in matrix a, but the contingency (which is
in the directionpredictedby a capacity to recognize defectors) would be significant if considered singly. Thus, if subsequenttests of our
model were positive only for matrix a, we
should be dubious of its support.As we will
see, however, they are not.
Given the overall lack of contingency between choices, we know thatfor any given consummatedplay (in binary-choiceand trinarychoice groups), cooperatorswill do less well
than defectors. Are our social outcomes explained by intendingcooperators'greaterwillingness to enterPrisoner'sDilemma games?
Different Play Rates?
A test of the hypothesis that the observed differences are a result of cooperators' greater
willingnessto enterPrisoner'sDilemma games
requiresinferences about the cooperate versus
defect choices of those who chose not to play,
had they chosen to play. Simply asking subjects for theirintentions,of course, would have
been unreliable,and various within-subjectalternativesall involved difficulties.12
12 In a pretest, we tried having subjects make
separateplay versus not play and cooperate versus
defect choices, but if subjects decided to not play,
we encouraged them to take the cooperate versus
defect choice seriouslyby telling them that"we will
take one of your play versus not play choices randomly and reverse it for purposes of figuring your
final payout." Because subjects knew that one of
their play versus not play choices would be reversed, this tactic provided a reason for subjects to
take the play versus not play option less seriously
than they would otherwise have done. We attributed the very low incidence of not play choices in
this pretest,in part,to the ambiguitiesthis tactic introduced. Alternatively, subjects could have made
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796
AMERICANSOCIOLOGICAL
REVIEW
Table 5. Observed Cooperators and Defectors Who
Played and Estimated Cooperatorsand Defectors Who Opted Out
44
proportiondefecting,thus 1 - (q + r) is the proportionnot playing. Extrapolatingfrom the binary-choice situation,p - q is our estimate of
the proportion intending to cooperate in the
trinary-choicesituation,and (1 - p) - r is our
estimateof the proportionintendingto defect.
To test the hypothesis that intending cooperatorsplay morefrequentlythanintendingdefectors, we comparep - q as a proportionof p
with (1 - p) - r as a proportion of 1 - p. Further,we can assess the financial consequences
of the not play alternativefor intendingcooperatorsby comparingthe mean observed payoff for the p cooperatorsin the binary-choice
groups with the mean observed payoff for the
q cooperatorsin the trinary-choicegroups divided by p.13 The financial consequences for
intendingdefectorscan be assessed by comparing the mean observed payoff for the 1 - p defectors in the binary-choicesituation with the
mean observedpayoff for the (1 - p) - r defectors in the trinary-choicesituationdivided by 1
Defectors
36
28
64
-p.
Total
80
28
108
Payoff
Matrix
and Choice
Trinary-Choice
Groups
Played
Opted Out
Matrix a (%2 = 5.46; 4 = .22; p < .025)
31
Cooperators
24
BinaryChoice
Groups
55
Defectors
18
35
53
Total
49
59
108
Matrix b (X2 = 7.80; 4 = .27; p < .005)
9
Cooperators
29
38
Defectors
34
36
70
Total
63
45
108
Matrix c (X2= 4.68; 4 = .21; p <.05)
8
Cooperators
49
57
Defectors
35
16
51
Total
84
24
108
Matrix d (X2= 25.99; 4 = .49; p < .000)
44
0
Cooperators
Matrix e (%2 = 7.47; 4 = .26; p < .005)
51
7
Cooperators
58
Defectors
33
17
50
Total
84
24
108
We can, however, make reasonable inferences aboutnumbersof cooperatorsand defectors opting out by extrapolatingfrom the observed numbersin the binary-choicegroups to
estimated numbersof "intendingcooperators"
and "intendingdefectors"in the trinary-choice
groups. We recognize, of course, that the
games are different. By "intending cooperators" and "intendingdefectors"we mean simply the numbers of subjects who could have
been expected to cooperate or defect if refusing play was not possible.
The structureof inference we propose is set
out in Figure 1 wherep is the proportioncooperating in the binary-choicegroups and 1 - p
the numberdefecting; q is proportioncooperating in the trinary-choicesituationand r is the
a prior cooperate versus defect choice in a game
unrelated to a subsequent trinary-choice situation,
but this design would have entailed a considerable
cost in time and money, as well as posing major
logistical complexities in the laboratory.
We are estimating proportions, and cannot
say anything about how actual individuals
would have chosen. Our estimates may not be
exactly correct,but any errorswill not be systematicallybiased for or againstthe hypothesis
that intendingdefectors refuse play more frequentlythando intendingcooperators.14
- q intendingcooperatorsare
assumednot to have played and hence to have zero
payoff.
14 Subjects who defect in the binarychoice situation may cooperate in the trinary-choice situation
because they feel optimistic about the cooperative
intentions of those who voluntarilyplay the game.
If so, our inferringfrom the proportionscooperating and defecting in the binary-choice situation to
proportions who would have cooperated and defected in the trinary-choice situation is flawed.
However, this argument (1) grants what we are
seeking to demonstratethat people who choose to
play are more likely to cooperate than are people
who choose not to play, or at least that people believe that to be true; and (2) provides no basis for
predictingthat intending cooperatorswill respond
to such a belief with more frequent"play"choices
than do intendingdefectors. While intendingcooperatorscould respondby playing in the expectation
of meeting anothercooperator,intending defectors
could respond by playing in the expectation of
meeting a cooperator too, and enjoying an
exploiter's payoff.
13 Rememberthatp
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COOPERATORS'ADVANTAGEAND NOT PLAYINGTHE GAME
797
Table 6. Mean Dollar Payoff to Cooperatorsand Defectors in Binary-Choice Groups Comparedto Estimated Mean
Dollar Payoff to IntendingCooperatorsand Defectors in Trinary-ChoiceGroups
Trinary-ChoiceGroups
Binary-Choice Groups
Payoff Matrix
Cooperators
Defectors
Difference
Itdi
Cooperators
Intending
Defectors
Cooperators
Defectors
.00
2.42
.28
a
-2.09
-.28
.33
b
-5.10
.43
-1.16
.36
3.89
-.07
c
.25
.96
.35
.69
.10
-.27
d
-.36
1.03
.18
.84
.54
-.19
e
.21
1.08
.43
.60
.22
-.48
would createa huge differencein the variances
within cells. Also arguingagainst using actual
payoffs as our dependent variable is the fact
that possible payoffs differ for the two experimentalconditions.
Therefore, we used a nonparametricanalysis. Withineach type of choice group,we computed the Spearmanrank ordercorrelation(p)
between cooperateversus defect (with cooperate rankedhigher)andlevel of payoff. Because
a Spearmanp is equivalentto a Pearsoncorrelation between ranks, we then converted to
Fisher z-scores and tested for significant difIntendingCooperators'Relative Fitness
ferences between these scores in the binaryWe adaptedthe extrapolationmethod to esti- choice groupsversusthe trinary-choicegroups.
mate mean payoffs to intending cooperators Results are presentedin Table 7.
and intending defectors by dividing summed
payoffs for cooperators (defectors) who did DISCUSSIONAND CONCLUSIONS
play in the trinary situation by the observed
numberof cooperators(defectors)in the binary Our data supportthree main conclusions: (1)
situation.Table 6 reportsobservedpayoffs for When individuals are free to accept or reject
cooperatorsand defectors in the binary situa- play in Prisoner's Dilemma games, social or
tion, the estimatedpayoffs for intendingcoop- aggregatewelfare increases. (2) This increase
eratorsand intending defectors in the trinarychoice situation,andthe differencebetweenthe
two. Undertrinaryrules, intendingcooperators Table 7. Rank Correlation Between Cooperate versus
Defect and Payoff by Matrix and Type of
gain in every payoff matrix,particularlyin maGroup
trices a and b where opting out was more frequent, whereas intendingdefectors lose in evSpearmanRank Correlation(p)
ery matrix but a. Intending cooperators'gain Payoff
Binary-Choice Trinary-Choice
producesan absolute advantageonly in matrix Matrix
z
Groups
Groups
a, but the benefit from trinaryrules is substan-.16
5.64*
a
+.55
tial in every case.
+.24
b
-.31
4.10*
For statisticalpurposes, we have a simple 2
by 2 design involving cooperatorsversus de1.60
c
-.16
+.06
fectors as one factorandthe binary-choicesitu-.20
1.98**
d
+.07
ation versus trinary-choice situation as the
-.19
2.27**
e
+.12
other. If we were to use actual payoffs as the
* Significant under the Bonferroni procedure.
dependentvariable,however,the large number
Significant if considered alone.
of $0 payoffs in the trinary-choice groups
Table 5 presents the estimated numbers of
intending cooperatorsand intendingdefectors
for subjectswho opted out in the trinary-choice
situation.In all cases, the resultsare in the predicted direction, with phi values rangingfrom
.21 to .49. The chi-square values for payoff
matrices a throughe, except that for matrixc,
are significant at the .01 confidence level considered singly, and can thereforebe considered
significant at the .05 level by our Bonferroni
inequalityanalysis.
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AMERICANSOCIOLOGICALREVIEW
798
in welfare occurs because intending cooperators are more willing to enter such games than
are intending defectors, which increases the
probability of socially productive cooperatecooperate relationships.15(3) When individuals are free to acceptor rejectplay in Prisoner's
Dilemma games, the welfare of intending cooperatorsrelative to thatof intendingdefectors
also increases,providingintendingcooperators
with a potentialabsoluteadvantage.This increment occurs because the cooperate-cooperate
payoff is also the best outcome for those who
intend cooperation.
There are two reservations,however. First,
our findings only applyto Prisoner'sDilemmas
with the payoff structure
t > c > 0 > d > s,
not necessarily to otherpossible structures.We
have theorized on the basis of this particular
structurebecause it provides a clear prediction
that anyone expecting a partnerto cooperate
will play, whereas anyone expecting a partner
to defect will not play. The structures
0> t>c>d>s
and
t> c > d > s >0
produce, respectively, the less interestingpredictions that everyone will refuse play and that
everyone will accept play, but a range of other
more interesting possibilities remains to be
studied.
Second, cooperators'relative willingness to
enter Prisoner'sDilemma games will have the
effects we describe only in social contexts in
which cooperators are relatively frequent. In
contexts in which cooperatorsarerelativelyinfrequent, cooperators' relative willingness to
enter the game will underminetheir personal
15 A reviewer of an earlier draft has suggested
that subjectsconcernedaboutothers' payoffs could,
in effect, convert the Prisoner's Dilemma into an
assurancegame (in which c > t > d > s). Such subjects would cooperateif they expected others to cooperateand defect if they expected othersto defect.
And, given the opportunity,they would exit rather
than damage other people. However, we define a
dilemma in terms of actual payoffs. To say that a
subject cares about the other individual's payoff is
indistinguishable from saying that a subject has a
cooperative disposition in that case, for whatever
reason.
wealth by ensuringa large numberof sucker's
payoffs (the worst in the payoff matrix) and,
by the same token, will contributeto the evolutionarydemise of cooperation.Clearly,then,
we must look for interactions between coop-
erators' relative willingness to play and other
mechanismsthatsupportcooperativebehavior.
Thus, our failure to demonstratean absolute
cooperators' advantage under trinary-choice
rules in four of the five payoff matrices is not
particularlytelling. Ourpoint is to demonstrate
that relative gain accrues to intending coopera-
tors because of the option. The possibility of
their capturingan absolute advantagethen depends on game parameters.For example, more
demandingnormativeconstraintsor an experimental design that allows subjects to discuss
their choices could increase the base of cooperation sufficiently to transform the relative
advantageaccruing to cooperatorsfrom their
greaterwillingness to play into an absoluteadvantage.
The lack of evidence for a capacityto recognize others' intentionsdoes not mean thatindividuals do not make accurate judgments in
naturalsituations.We restrictedour subjectsto
a single play with each other individual in order to isolate the effects of the decision-making structure,but an iterated-playdesign with
feedback could greatly improve subjects' "hit
rate." People do learn from experience with
others' behavior.
The benefit to intending cooperators from
theirgreaterwillingness to play when given the
option to play or not play suggests that genes
supportingthe joint attributesof cooperating
and expecting others to cooperate have a fitness advantage over genes supporting other
combinations. Thus our findings provide an
additional way by which cooperation may
evolve beyond those, like tit-for-tat,reputation
and reciprocity,which depend on iteration of
the game and the implied stabilityof social relations.
Consistent with Cosmedes and Tooby
(1987), however, it is useful to speculateabout
the psychology that links such an evolutionary
outcomeandthe behaviorobservedin the laboratory. Willingness to enter Prisoner's Dilemma games implies trust in potential partners' cooperativeintentions,and evidence suggests that the willingness to trustothers is correlatedwith one's own trustworthiness.(Rotter
1971, 1980). Perhapsthese attributeshave been
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COOPERATORS'ADVANTAGEAND NOT PLAYINGTHE GAME
jointly selected as the emotional motivators
supporting cooperators' willingness to enter
Prisoner'sDilemma relationships.(For related
ideas, see Trivers 1971, p. 48.)
An alternative hypothesis that emphasizes
cognitive processes rather than personality
variables is the "projection"hypothesis. This
hypothesis argues that a person's expectations
about others are a function of his or her own
behavioralintentions.Thus, a personintending
cooperation in a particularcase "samples" a
potentialpartner'sintentionsfrom a subjective
distributionof others' intentions (viz a model
of the relevantpopulation)thatis tilted toward
cooperation, while a person intending defection "samples" intentions from a distribution
tilted toward defection. This hypothesis proposes, in effect, that people are guided by.the
rule: "Expect others to do what you intend to
do yourself."
Such a "golden rule of expectations"does
not mean thatpeople intendingcooperationare
always optimistic about other individuals' intentions, or thatpeople intendingdefection are
always pessimistic about them. The rule requiresonly thatintendingcooperatorsare optimistic (and thus choose to play) more frequently than intendingdefectors.16 The plausibility of this rule is increasedby the fact thatit
is compatiblewith the extensive "falseconsensus" literature.
Further,the cognitive simplicity of the rule
means that it has an evolutionaryadvantagein
comparisonwith moredemandingalternatives.
Of course, a simple rule that producesconsistent (and costly) errorswill not be favored by
evolution,but this simple rule will producecorrect estimatesfor most people most of the time.
If, for example, 70 percent of the population
intends cooperation,then projectingfrom their
own intentions will produce accuratepredictions for that70 percent.Conversely,if 70 percent intenddefection, the rule will still provide
16 In fact, the model implies that most people are
capable of both cooperationand defection and that,
confrontedwith a particularsituationand particular
potential partner,they "sample"theirown behavior
from a probabilitydistributiontilted one way or the
other. More important,the model requiresonly that
individuals projectfrom their own intentionsin the
particularcase-therefore their expectations may
be quite different in different cases (see the exchange between McLean 1991 and Orbell and
Dawes 1991b.)
799
correctpredictionsfor 70 percentof the population.
Trivers (1971) has suggested that humans'
largebrainsmight resultfrom an armsrace between our capacity to see through others' intentions and our capacity to hide our own intentions (for related ideas, see Dawkins 1976;
Goffman 1959, 1969; Wilson 1975), both of
which give an evolutionaryadvantageto their
possessor.Arms races are expensive, however,
and in the context of this race, a rule that requires no elaborate cognitive investment and
that worksis likely to be favoredby evolution.
By this hypothesis, therefore,the "golden rule
of expectations"evolves because of its cognitive advantages,and independentof any consequences it might have for cooperators'personal advantageor for aggregatewelfare.
Countervailingevolutionarypressures may,
of course, exist. As Michael Macy has pointed
out to us, growthin the proportionof cooperators could reduce selection pressurefor pessimism among defectors, eventually bringing
cooperators' and defectors' expectations into
line with each other and eliminating any advantageto cooperatorsresultingfrom differing
"play"propensities.
Similarly,repeatedplays with particularindividuals or repeatedencountersfrom a given
population could provide sufficient information to override any "golden rule of expectations" with the same eventual effect. Contrary
arguments can also be made, however. The
benefitsfrom the proposedrule's simplicity,for
example, could outweigh the costs from whatever occasional errorsit produces-in particular when the rule will usuallyproduceaccurate
estimates.
We areparticularlyinterestedin the possibility thatthe heuristicwill be sustainedby biased
feedback: Cooperators' frequent interactions
with othercooperatorswill reinforcetheiroptimism (even if thatoptimismdoes not matchthe
objective "facts"of the situation), and defectors,encounteringmanycooperatorswhen they
do play, will be reinforcedfor their capacity to
"spot suckers"-the capacity that provides the
only justificationfor theirplaying.
Professor of Political Science and
member of the Instituteof Cognitive and Decision
Sciences at the Universityof Oregon. His major interests lie at the intersection of rational choice
theory,evolutionarytheory,and ethics. As a hobby,
he studies the application of decision theory to
JOHN ORBELL is
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800
AMERICANSOCIOLOGICAL
REVIEW
Shakespeare-his paper, "Hamletand the Psychology of Rational Choice Under Uncertainty," appeared recently in Rationalityand Society.
ROBYNDAWES
is
UniversityProfessor in the Department of Social and Decision Sciences at Carnegie
Mellon University. He is interested in individual
and social decision-making and in judgement. He
recently completed a book titled House of Cards:
Psychology and Psychotherapy Built on a Myth
(Free Press, forthcoming). His previous book, Rational Choice in an Uncertain World (Harcourt,
Brace, and Jovanovich, 1988) received the 1990
WilliamJames BookAwardfromtheAmericanPsychological Association.
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