Coordination and
institutions: A review of
game-theoretic contributions
Stéphane Straub
University of Edinburgh
Introduction



Institutions are key in enhancing the
efficiency of economic interactions.
Huge variation. Both temporal and spatial.
While the role of institutions as protectors of
property rights has been extensively studied,
a more neglected aspect is that of institutions
as coordination devices (Bardhan, 2005).
Institutions and coordination failures

Institutions can help to correct the coordination
failure that plague basic economic interactions.
-
Developing economies:
Witnesses in commercial exchange (Attali, 2003), contract
enforcement (Fafchamps, 2004), dispute prevention
(McMillan & Woodruff, 99, 2000).
-
Economies in transition to industrial/market stage:
Japan after WWII, East Asian countries (Aoki et al., 1997),
transition countries (Johnson et al., 2002).
-
Specific markets:
US Cotton Market (Bernstein, 2001), Diamond (Bernstein,
1992, Richman, 2005).


Institutional coordination needed because when
individuals act opportunistically, pareto inferior
outcomes may arise. Example: prisoner’s dilemna.
(D,D) is the only Nash equilibrium, and it is
dominated by (C,C).
Player j

Assumptions:
g > x > y > -l
(g - l > 2x)
C
D
C
x,x
-l, g
Player i
D
g, -l
y,y
Application 1: Social Capital (Durlauf &
Fafchamps, 2005)
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‘‘You should always go to other people’s funerals;
otherwise, they won’t come to yours.’’ Yogi Bera.
Social Capital (SK) is “something” that generates
positive externalities for members of a group,
through shared norms, trust and values and their
effects on expectations and behavior. These arise
from informal forms of organizations based on
social networks and associations.
So SK looks very much like “informal
institutions”.
Social Capital
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To matter, SK must compensate for some
inefficiency, i.e. we must be in a 2nd best
world, e.g. because of externalities, freeriding, imperfect information and
enforcement, imperfect competition, etc.
Social capital can act by:



Facilitating information sharing;
Modify preferences, alter identification to
groups;
Facilitate coordination, provide leadership;
Example: modified preferences induce
shift from (D,D) to (C,C)
Player j
C
D
C
x,x
-l, g
D
g, -l
0,0
Player i
Example: altruistic preferences (within
group, kinship, etc.)
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
Each player’s payoff is a weighted sum of hers
and her opponent’s payoff:
Ui = (1-α) πi + α πj
Then we get (see next slide) that (C,C) is a Nash
equilibrium whenever:
α > (g - x) / g + l
which can arise for α << ½.

Players’ payoffs with altruistic preferences:
Player j
C
C
Player i
x,x
(1-α)g-αl,
D αg -(1-α)l
D
αg -(1-α)l,
(1-α)g-αl
0,0
Example: social structure that facilitates
cooperation (Routledge & Amsberg, JME 03)

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Community with N
players, randomly
matched to play a
repeated PD.
Games are private (no
info on other players’
trade).
Agents play C if it is an
equilibrium.
Proba of trade between 2
agents depends on N.
Player j
C
D
C
2,2
0,3
Player i
D
3,0
1,1

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
Nmax trades per period.
If Nmax > N-1, at most N-1 trades.
Proba of trade between 2 agents (i and j):
πij = min (1, Nmax /(N-1))
Discount rate β.
A strategy profile sc that supports (C,C) is to
use trigger strategies: play C if history of play
with agent j contains only (C,C), otherwise
play D.
SK exists if all players following sc is an
equilibrium.


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For trade between 2 agents (i and j),
strategies sijc and sjic are a SPE iff :
πij > πc = (1-β)/β
Proof: no deviation if
3 + β [(πij .1)/(1-β)] < 2 + β [(πij .2)/(1-β)]

πij > (1-β)/ β
Intuition: no deviation as long as agents
value future cooperative trade more than
one-time deviation gain + unfriendly trade
forever thereafter.

Nmax = 3, β = 0.55, πc = 0.818

In closed communities, probability of trade
π(3) = 1 > πc . Each agent trades twice, for a
utility of 4: 2 trades times 2, since cooperation
is sustained.


When communities are linked by the bridge, probability
of trade π(6) = 0.6 < πc . Each agent trades 3 times, for
a utility of 3: 3 trades times 1, since cooperation is
not sustained.
More opportunities for trade but reduction in
welfare because SK destroyed (migration parabola).
Repeated PD and cooperation.
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In 2 agents repeated PD, Folk Theorem known to
hold: cooperative outcome can be sustained as an
equilibrium.
Can Folk Theorem-type results be obtained in social
games with (possibly random) matching?
when players have limited information about others
(past) behavior?
Answer is yes, under certain assumptions.
Informational assumptions appear to be crucial.
Refs: Greif, 93; Milgrom, North and Weingast, 90;
Kandori, 92, Ellison, 94, etc.
Greif (1994) – Informal institution
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11th century Maghribi traders used to employ
overseas agents, despite the obvious commitment
problem.
Complete information about past behavior of agents
in the community.
Cooperative relationships sustained by a
multilateral punishment strategy: a merchant offers
an agent a wage W, rehires the same agent if he has
been honest (unless forced separation has occurred),
fires the agent if he has cheated, never hires an agent
who has ever cheated any merchant, and
(randomly) chooses an agent from among the
unemployed agents who never have cheated if
forced separation has occurred.
Kandori (1992) – Informal institution
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With no information, a “contagious” punishment
strategy may sustain cooperation: when one player
cheats in period t, his opponent cheats from t+1
onwards, infecting other players, etc.
For any N, there are payoffs which allow
cooperation, but as N grows large, extreme values of
the payoff are required (to avoid agents not
punishing to slow down contagion and enjoy high
payoffs in the future, the risk associated (getting -l)
must be high).
Ellison (1994) provides several refinements.
Milgrom, North and Weingast (1990)
Formal institution
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The law merchant enforcement system and
Champagne fairs in the 12th and 13th centuries.
There is a specialized agent (judge) serving both
as repository of information and adjudicator of
disputes (both at a cost to trading agents).
Under certain conditions, cooperation is
sustained at a (transaction) cost for trading
agents.
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Osborne & Rubinstein (1994): “…in our opinion
the main contribution of the theory is the
discovery of interesting stable social norms
(strategies) that support mutually desirable
payoff profiles, and not simply the
demonstration that equilibria exist that generate
such profiles.”
Problem: How do agents come up with these
norms in the first place? In particular, how do
they structure their interaction and allocate roles
when some form of formal enforcement is
required?
Sanchez-Pages & Straub 2007

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We model the process through which institutions
such as these may arise.
We characterize:

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The factors that make possible or hinder the formation of
institutions.
The level of efficiency at which they arise.
Their emergence is the equilibrium of a game that
agents play in the state of nature. It has to be selfenforcing.
Otherwise, the economy remains in the status-quo.
Who induces shift from (D,D) to (C,C)?
Player j
C
D
C
x,x
-l, g
D
g, -l
0,0
Player i
The Model
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
In the state of nature, N+1 agents, endowed
with ω, are randomly matched to play the PD
without interference.
Expected unit payoff is then αx.
The parameter α denotes the status-quo level
of coordination or trust (without institution,
they play (C,C) with proba α).
The institution is able to ensure that the (C,C)
profile is played with proba 1.
But someone has to run it (Pepe…).
The Model
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One of the agents becomes the “centre”.
She must relinquish the ability to trade.
But is compensated in exchange.
Agents must pay a fee a ≤ ω to interact under
the centre’s umbrella (trade certification,
dispute prevention / resolution, reputation
management…).
The procedure of institution
formation
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
Our procedure of institution formation starts with a
lottery over the set of agents who freely participate
in it, to determine who will become the central
agent.
Justification:
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All equally likely to be center.
centre is randomly drawn each period.
the institution must emerge in the most
decentralized way possible. No commitment is
assumed.
The procedure of institution
formation
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First, the fee is freely chosen by the central agent:
The institution is a revenue-maximizer.
Having observed a, agents must decide whether
to become formal or not.
2 problems (IR constraints):


Ex ante, agents may not want to participate.
Ex post center may renege.
Two sources of inefficiency (1)

Efficient institution may not arise

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
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This is more likely for economies of intermediate size
and high levels of trust α.
If N small: WF lower than informality payoff.
If N large: incentive to become the central agent
increases (more revenue).
High trust undermines the position of the institution
(reminiscent of identification problem in social capital
literature. See Durlauf and Fafchamps, 2005).
Two sources of inefficiency (2)

Institution may be sub-efficient (too extractive).


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When status-quo trust is high, revenue and welfare
maximisation are aligned.
Otherwise, with low status-quo trust, the institution
arises at a sub-optimal level of efficiency (that is when
it is most needed).
The rent associated with being the centre are the key
motivation for agents to participate. With a high
extractive fee, all other agents are just indifferent.
Appendix: The formal model




One of the agents becomes the “centre”.
She must relinquish the ability to trade.
But is compensated in exchange.
Agents must pay a fee a ≤ ω to interact under
the centre’s umbrella (trade certification,
dispute prevention / resolution, reputation
management…).
Participation decisions


Having observed a, agents must decide whether to
become formal or not.
If they become formal, interacting with another
formal agents yields per unit return
v  x(a)
F

where xa> 0, xaa< 0 and x(0) > 1/α.
The efficiency of interactions depends on the fee
paid to the institution.
Participation decisions

Interacting with an informal agent yields
v  x(a)
I

regardless of your status.
Expected payoffs when K formal agents:
K 1
N K
V (K ) 
(  a) x(a) 
(  a)x(a)
N 1
N 1
F
V I ( K )  x(a)
Participation decisions

Define

K formal agents can be supported in equilibrium if
and only if
( N  1)
a( K )   (1 
)
K  1  ( N  K )
a( K  1)  a  a( K )

But a (K) is increasing in K, so only corner solutions
prevail (full formality or full informality)
Participation decisions
Proposition 1: For a given level of the fee a
(i) Informality can be supported in equilibrium only if
a(1)=0
(ii) Full formality can be supported in equilibrium only if
a(N)
Multiple equilibria: full
formality or informality
0
Formality sustainable
Informality sustainable
Only informality
a(N)
a≥
a≤
First-best level of the fee a
Planner objective function:
max WF = N[(ω-a)x(a)+(a-c)]+ ω
s.t. a < a(N)
This defines a*. The first best fee is then:
aF = min{a*,a(N)}
and there is a threshold α* s.t a*>a(N) if α > α*, so in this case
the revenue maximizing fee coincides with the first best level.
Finally, informality may dominate for N and ω small and α high.
The procedure of institution
formation




Our procedure of institution formation starts with a
lottery over the set of agents who freely participate
in it, to determine who will become the central agent.
One justification: All equally likely to be center.
game repeated infinitely and centre is randomly
drawn each period.
See Morgan (2000) for an application of lotteries to
reduce free-riding on public goods financing.
Timing
time
t=1
t=2
t=3
t=4
Agents decide whether to
participate or not in a
lottery that will determine
who will run the
institution.
If the institution has emerged,
the fee a to be paid by formal
agents is set. If not, the
status-quo remains (informal
exchanges).
Agents decide whether
to become formal or not.
Agents are randomly
matched and play G.
Payoffs are realized.
The fully decentralized procedure
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In this procedure, the institution must emerge
in the most decentralized way possible. No
commitment is assumed.
First, the fee is freely chosen by the central
agent: The institution is a revenue-maximizer.
So it will set the maximum fee compatible
with formality, a(N).
The fully decentralized procedure


Second, the agent that runs the institution can
renege ex-post.
For the institution to arise, an ex-post participation
constraint must be satisfied:
N (a  c)    x(0)

That’s for the centre. It is trivially satisfied for other
agents.
The fully decentralized procedure

Ex-ante participation constraint given the fee a
1
N
( N (a  c)   ) 
(  a) x(a)  x(a)
N 1
N 1

because either all agents or none participate in the
lottery.
With a(N), the institution arises iff the (stronger) exante constraint is met. It rewrites:
N (a( N )  c)    x(a( N ))
The fully decentralized procedure
Proposition 2: If the ex-ante constraint holds, there exists a SPE of
the fully decentralized procedure that implements formality under
a(N).
Two sources of inefficiency
Corollary 1: There exists a range of parameters for which a
potentially welfare enhancing institution does not arise.
This is the case when parameters are such that the level of
individual welfare obtained under formality dominates the
level of welfare under full informality but is not high enough to
induce ex ante participation in the lottery:
x(0)  WaF( N )  x(a( N ))
where WaF( N ) 
1
N
( N (a  c)   ) 
(  a) x(a)
N 1
N 1
Two sources of inefficiency




This is more likely for economies of intermediate size
and high levels of trust α.
If N small: WF lower than informality payoff.
If N large: incentive to become the central agent
increases (more revenue).
High trust undermines the position of the institution
(reminiscent of identification problem in social capital
literature. See Durlauf and Fafchamps, 2005).
Two sources of inefficiency
Corollary 2: The utilitarian first best fee can be implemented in a
SPE of the fully decentralized procedure only for high enough of
status-quo trust α.


When status-quo trust is high, revenue and welfare maximisation
are aligned (see first best fee a*).
Otherwise, the institution arises at a sub-optimal level of efficiency.
The rent associated with being the centre are the key motivation
for agents to participate. With a = a(N), all other agents are just
indifferent.
Two types of commitment

1.
2.

Now imagine that commitment can be
imposed along two lines:
Individual: Agents cannot renege ex-post
whatever their role.
Collective: The fee is chosen collectively
before the lottery takes place.
Different procedures arise from different
combinations of assumptions.
Limited commitment
(ex post participation
constraint)
Strong commitment
(ex ante participation
constraint)
Center maximizes
revenue (sets a) ex
post
1. Agents’ only commitment is
to participate in the lottery ex
ante. The center may refuse to
cooperate ex post and is free to
set a.
2. Agents commit ex ante to
participate in the lottery and not
to renege ex post if chosen as the
center.
Fee a set ex ante
3. Agents commit ex ante to
participate in the lottery. If
chosen as the center, they may
renege, but have no freedom to
set a if they accept to fulfill
their role.
4. Agents commit ex ante to
participate in the lottery and not
to renege ex post if chosen as the
center. Furthermore, the center
has no freedom to set a ex post.
Other procedures

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
One can consider alternative procedures by
combining these 2 types of commitment.
Imposing individual commitment alone has no effect.
Collective commitment alleviates the second type of
inefficiency.
Only when commitment is imposed in both
dimensions, does the institution arise whenever it is
welfare enhancing.
Endogenous commitment


1.
2.
These two types of commitment rely on
some exogenous enforcement mechanism.
We consider two ways to endogenize
commitment:
Trigger-like strategies.
Threat of secession.
Secession



When there is no commitment, secession is
an issue.
No group in society should be able to
improve its situation by withdrawing and
forming its own mini-society.
We study when the institution will be
secession-proof and the impact of this threat
on welfare.
Secession
Definition: Denote by aN the fee set by the institution. A coalition of S
interacting agents is said to be blocking if and only if
1
S 1
(  a N ) x(a N )  ( S (a( N )  c)   ) 
(  a( N )) x(a( N ))
S
S


Note that when a group secedes, it sets a
self-enforcing fee.
A fee is secession-proof (it is in the core of
the procedure of institution formation) if it
does not spawn any blocking coalition.
Secession
Proposition 4 : The set of secession-proof fees is non-empty if and
only if N is low enough.


The reason for blocking is the prospect of
becoming the central agent in the new mini
society.
When the level of status-quo trust is low
enough, the threat of secession can tame the
central agent.
Secession
N
Secession and efficiency



A natural question is whether secession is
bad or good for efficiency.
Let us look at the eventual outcome of the
secession process.
We say that a coalition structure is
secession-proof if all coalitions in it can set
a (possibly different) fee that does not spawn
any blocking coalition.
Secession and efficiency
Proposition 5 : For high enough levels of status-quo trust, the total
sum of payoffs under a secession-proof structure is never greater
than under a single institution.

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In our model, only the center gets positive rents.
This creates strong incentives for secession.
Proliferation of institutions is however socially
inefficient because of duplication of costs.
A trade-off may arise if transaction costs of
institution are lower in small groups.
Conclusions



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We have presented a model where an institution
emerges as the equilibrium of a game played in the
state of nature.
The institution may not emerge despite being
welfare enhancing
This happens for intermediate population sizes and
high levels of status quo coordination.
But even if it emerges it can do it at a suboptimal
level. This is because the rent associated with being
the centre are the key motivation for agents to
participate.