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CURRENT RESEARCH IN SOCIAL PSYCHOLOGY
CURRENT RESEARCH IN SOCIAL PSYCHOLOGY
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
ABSTRACT
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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INTRODUCTION
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.
THE EXCHANGE SITUATION
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
networks.
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I Solidarity of the weak against the strong - a prisoner's dilemma
A C
\ /
B
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
\ /
C
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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
nothing.
Player B
Cooperation Non-cooperation
----------------------------------
Cooperation .5, .5 | .1, .9
Player A ----------------|-----------------
Non-cooperation .9, .1 | 0, 0
----------------------------------
IV Irrational Patterns - a coordination game
A
/ \
B F
| |
C E
\ /
D
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
position.
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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CONCLUSION
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.
REFERENCES
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
58:768-796.
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.
ABOUT THE AUTHOR
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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