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Editor's Note


Volume 1, Issue 1, September 26, 1995

Manuscript submitted September 5, 1995
Resubmitted September 19, 1995
Accepted September 20, 1995

"Four Kinds of Social Dilemmas within Exchange Networks"

Phillip Bonacich 

University of California, Los Angeles


    Exchange networks implicitly contain four types of social 
dilemmas: prisoner's dilemmas, assurance games, chicken games, and 
coordination games. People in powerless positions can potentially 
agree on a common strategy with respect to their exploiters, 
generating a prisoner's dilemma. In unstable exchange networks, 
people may agree to form a stably exchanging pair, providing 
assurances for themselves. People in relatively equal positions 
can bargain cooperatively or aggressively, engaging in a chicken 
game. Or people may choose their partners in an uncoordinated 
manner, causing suboptimal patterns to arise. Yet, by not 
including any type of communication other than the presentation 
and acceptance of offers, experimental research on exchange 
networks has been particularly inauthentic. The study of power 
within exchange networks can, therefore, be enriched by 
recognizing this deficiency and by compensating for it through the 
incorporation of concepts like trust, which have in the past 
proven useful in the study of social dilemmas. 

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   Communication plays an especially important role in the 
resolution of social dilemmas (Dawes et al, 1977).  It is a 
limitation of existing experimental work on power within social 
exchange networks that the only communication permitted is that 
between positions involving exchange offers and acceptances. For 
in fact there are many types of networks that connect positions 
apart from such exchanges, networks that may overlap and influence 
the interaction. 

   Experiments on power within exchange networks allow for the 
creation of binding agreements between players. Thus, when two 
players accept a division of points, the division that they accept 
is accomplished. Hence, the complete transparency of agreements 
guaranteed by the experimenter makes trust between the positions 
unnecessary.  It has been discovered, however, that allowing for 
nonbinding agreements would create the conditions necessary for 
the development of trust (Kollock 1993). 

   The study of social dilemmas was initially the almost exclusive 
domain of economists (Olson, 1965).  Their conclusion was that 
cooperation was impossible, or that it could occur only in the 
presence of "selective incentives" for cooperation.  More 
recently, social processes that facilitate cooperation have become 
more prominent, especially processes like trust (Marwell and 
Oliver, 1988; Kollock, 1994).  Yet, most of the existing theories 
of power in exchange networks are either based on rational choice 
or have a strong rational choice inclination.  Thus, it seems only 
proper to begin to "open up" exchange networks to other phenomena. 

   Four kinds of two-person social dilemmas have already been 
examined (the N-person versions are similar):                              

I   The Prisoner's Dilemma (PD)

   In the PD game, each player has a cooperative and uncooperative 
choice. In the symmetric case, the rewards can be represented by 
the following diagram. 

                                       Player B
                              Cooperation     Non-cooperation
               Cooperation       b,b       |       d,a
Player A                     --------------|-------------------
           Non-cooperation       a,d       |       c,c

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The values are ordered such that a > b > c > d and (a + d) < 2b.  
Because of this ordering, non-cooperation uniformly "dominates" 
cooperation; each player is better off off choosing not to 
cooperate no matter what the other player has chosen. 

II  The Assurance Game

   In an assurance game, each player wants to cooperate if his/her 
partner cooperates, but will balk if s/he thinks his/her partner 
is defecting.  In such a scenario, the values are ordered such 
that b > c > d, but b > a. 

III   The Chicken Game

   The game of chicken, like the PD, offers each player a 
cooperative and non-cooperative choice. The difference, however, 
is that non-cooperation does not dominate cooperation. That is, if 
one's partner cooperates, one is better off not cooperating. 
Likewise, if one's partner does not cooperate, one is better off 
cooperating.  The values in such a game, then, are ordered such 
that a > b > c, but d > c. 

IV   The Coordination Game

   In a pure coordination game, each player is motivated to match 
the other's behavior.  Thus, there is no distinctive "cooperative" 
or "non-cooperative" choice.  Rather, all choices are equally 
valuable if both actors behave in an identical fashion. In the 
absence of communication between the players, however, this 
coordination can be difficult to achieve.  Hence, in this game, 
the values are ordered such that b > a, c > d, and b = c. 


   In social exchange network experiments, subjects negotiate with 
each other on the division of a certain number of points, usually 
twenty-four.  Pairs of subjects who can agree with each other 
divide the points, the points being convertible into money at the 
end of the experiment. Subjects who do not exchange receive 
nothing. Further, not all pairs of subjects can negotiate with one 
another. But the pairs that are able to negotiate form a network, 
within which each position is allowed to conclude an agreement 
with at most one other position per game. 

   It is my claim that, in such exchange networks, four kinds of 
social dilemmas become implicit. To facilitate understanding, I 
will illustrate each of these dilemmas via a simple network. 
However, my use of such an illustration should in no way suggest 
that these dilemmas cannot occur in a wide variety of exchange 

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I Solidarity of the weak against the strong - a prisoner's dilemma

     A   C
      \ /

In such a network, A and C are likely to bargain against one 
other, giving B an opportunity to wield a great deal of power in 
negotiations. However, should A and C come to an agreement 
concerning the offers they give and accept from B, then, as a 
pair, they will exert power equal to B. Nevertheless, B can 
attempt to vitiate this agreement by making high offers to A or to 
C and then by playing them off against each other. Yet, in such a 
scenario, A and C are better off resisting these offers, which 
prove detrimental in the long run, despite their immediate appeal. 

   The following table is meant to illustrate this situation. The 
entries refer to the probabilities of being included in an 
exchange multiplied by the expected proportion of the returns from 
that exchange.  So, for example, if players A and C agree to 
accept not less than 50% from B, each might expect to be included 
in half the exchanges, averaging .50 x .50, or .25 in reward.  If 
C accepts no offer less than .50, but A accepts lower offers, A 
will be included in all the exchanges, even if A does not earn as 
much as B (e.g., .40). But, should both A and C compete against 
one another, they would each earn almost nothing (.10). 

Player C
                              Cooperation     Non-cooperation
               Cooperation       .25,.25   |       0,.40
Player A                     --------------|-------------------
           Non-cooperation        .4,0     |       .1,.1

   If free communication were permitted between the positions so 
that agreements on common strategies with respect to other 
positions were allowed, we might expect power differences within 
exchange networks to be reduced.  Moreover, if agreements between 
weak players vis-a-vis strong players were unenforceable, then we 
might expect affective and trusting relations to develop between 
successful coalition partners. 

II   Solidarity of exchange partners - an assurance game

     A - B
      \ /   
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   Supposing that A and B have come to a tentative agreement to 
exchange and that C is faced with the possibility of having no 
partner, no matter what the terms of the agreement are between A 
and B, C can always make an offer to A or to B or to both that 
results in his inclusion.  For example, if A and B have agreed to 
a 12-12 split, C can offer 14 to either A or B, resulting in 10 
for C. 

   The following table is meant to illustrate the hypothetical, 
yet plausible, long-term probabilities of being included in an 
agreement when two players maintain their agreement to exchange 
and when one accepts the higher offer from an excluded other. In 
the latter instance, each participant may calculate that s/he has 
an equal chance (2/3) of being included in an agreement. Moreover, 
if in such a scenario one player maintains a preference for 
his/her partner while the others bargain freely, the loyal partner 
will be excluded from agreements with C while the disloyal partner 
will continue to be included in all exchanges. S/he may not lose 
by not cooperating, but neither will s/he gain. 

                                      Player B
                              Cooperation     Non-cooperation
               Cooperation         1,1      |       1/2,1
Player A                     ---------------|-----------------
           Non-cooperation         1,1/2    |       2/3,2/3

   This type of social dilemma is particularly likely to arise 
when exchange patterns are unstable, when sheer self-interest does 
not drive positions into stably exchanging pairs. Using 
simulations and experiments, Bonacich and Bienenstock (1995a) have 
demonstrated that networks without game-theoretic "cores" are 
inherently unstable in their exchange patterns. Yet, these are the 
very networks that would be affected greatly if free communication 
between positions were permitted since pairs of positions could 
develop affective bonds, cementing their stable trading relations. 
Instability in trading patterns would therefore be reduced. 

III    Bargaining failures - a chicken game

     A - B    

   If either A or B employs a tough bargaining strategy, 
buffaloing the other with high demands, the result may be 
advantageous for the tough bargainer.  However, if both attempt to 
use this strategy, there may be no agreement at all. This problem 
is particularly likely to occur when there is a time limit placed 
on negotiations.  Players may attempt to bluff others by making 
high demands until just before the time runs out, but time may run 
out before an agreement is reached. 

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   The following table represents hypothetically this situation. 
If both players are willing to compromise, they agree on an equal 
split (.5). If one player employs a tough bargaining strategy and 
the other is willing to compromise, the tough bargainer earns more 
(.9). However, if both participants employ uncompromising 
strategies, they will fail to conclude an agreement and earn 

                                      Player B
                              Cooperation     Non-cooperation
               Cooperation         .5, .5    |      .1, .9
Player A                     ----------------|-----------------
           Non-cooperation         .9, .1    |       0, 0

IV   Irrational Patterns - a coordination game

                 /   \
                B     F
                |     |
                C     E
                 \   /

   In this scenario, five different patterns can result in 
completed exchanges, wherein no further exchanges can occur 
because there are no connected players who are not already 
involved in an exchange. The five patterns are AB/CD/EF, BC/DE/FA, 
AB/DE, BC/EF, and CD/AF.  The latter three patterns, involving 
only two trades, are suboptimal from every position's point of 
view; for no matter what the terms of trade between the two pairs 
might be, there is always a trade involving three pairs in which 
some players will be better off, but none will be worse. For 
example, suppose the pairs AB and DE both divide the profits from 
their exchange evenly.  Alternatively, suppose that B and C trade 
(B earning 60% of the profits), A and F trade (A earning 60% of 
the profits), and D and E trade evenly.  Four of the players are 
strictly better off, but the other two are not in a worse 

   This type of suboptimality is different from the others in that 
it does not so clearly result from short-term self-interest.  The 
important group problem is to coordinate so that one of the two 
optimal patterns occurs. In that respect, this exchange is much 
like a coordination game. The suboptimal patterns may occur if 
subjects concerned about the possibility of exclusion are too 
eager to accept suboptimal agreements. As such, open and 
unrestricted communication between positions might reduce the 
frequency of suboptimal exchange patterns. 

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   What is the advantage of conceiving exchange networks as rife 
with potential social dilemmas?  One implication is that social 
exchange networks might be richer and more interesting if we 
allowed more open communication between subjects and if we allowed 
for nonbinding agreements between positions.  Under such 
conditions, some of the phenomena that have interested 
psychologists recently could be studied within exchange networks.  
In addition, allowing more open communication between positions 
would positively affect distributions of power, exchanges, and the 
stability of exchange patterns. 


Bonacich, Phillip and Elisa J. Bienenstock. 1995a. "When 
Rationality Fails: Unstable Exchange Networks with Empty Cores." 
Rationality and Society 7:293-320. 

Bonacich, Phillip and Elisa J. Bienenstock. 1995b. "Latent Classes 
in Exchange Networks: Sets of Positions with Common Interests." 
Unpublished paper, University of California, Los Angeles. 

Dawes, Robyn M. 1977. "Behavior, Communication, and Assumptions 
about Other People's Behavior in a Common Dilemma Situation." 
Journal of Personality and Social Psychology 35:1-11. 

Kollock, Peter. 1993. "'An Eye for an Eye Leaves Everyone Blind'; 
Cooperation and Accounting Systems." American Sociological Review 

Marwell, Gerald, Pamela E. Oliver, and Ralph Prahl. 1988. "Social 
Networks and Collective Action: A Theory of the Critical Mass. 
III." American Journal of Sociology 94:502-34. 

Olson, Mancur. 1965. The Logic of Collective Action. Cambridge: 
Harvard University Press. 


Phillip Bonacich is a Professor of Sociology at The University of 
California, Los Angeles.  His current research focuses on 
coalitions in exchange networks.

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