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A Bargaining Model of Domestic Politics and the Cost of War
Unformatted Document Text:  the allocations were measured in dollar amounts. The proposer begins by demanding x and offering 1 − x to the “responder.” The responder can either accept the offer, in which case it is implemented, or make a counteroffer to divide the discounted value of the second-stage “pie,” δ, where 0 < δ < 1 is a discount parameter that penalizes delayed settlements. Thus the counteroffer is a split of δ − x 2 for the original proposer and x 2 for the responder. If the responder makes such a counteroffer, then the proposer must decide whether to accept the counteroffer or to engage in conflict to gain control of all of the territory. As before, the proposer will win this conflict with probability p, which was explained to subjects in the experiment in terms of throws of a ten-sided die. The costs of conflict are c P for the proposer and c R for the responder. The expected payoffs with conflict are: δp − c P for the proposer and δ(1 − p) − c R for the responder. Assuming that both the proposer and the responder are fully informed, rational, prospec- tive decision makers, we can solve this game through backward induction. The resulting subgame perfect Nash equilibrium involves an initial demand of x = 1 − δ + δp − c P by the proposer that is immediately accepted. The prediction is that there will be no conflict, but behaviorally, we know conflict does occur. Moreover, our experimental results show that even in this simple setting of complete information, with none of the auxiliary assumptions described above (incomplete information, reputation building) we see out-of-equilibrium con- flict. If this is the case, we need a closer inspection of the simple bargaining model. The problem in crisis bargaining with any equilibrium concept is that actors cannot be fully rational in the sense of completely maximizing, because of their inexperience with bargaining where war is the outside option. Consider this on two dimensions. Even the most belligerent states in war-prone regions rarely fight wars, and also rarely bargain where war is the outside option. Further, belligerent states are often piloted by leaders who have relatively limited experience in conducting international affairs. The result is that decision makers are uncertain about the rationality of their opponents. Imagine playing a bargaining game, for instance, against an opponent who is believed to make choices by tossing a coin. 8

Authors: Clark, David., Holt, Charles., Nordstrom, Timothy., Reed, William. and Sieberg, Katri.
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background image
the allocations were measured in dollar amounts. The proposer begins by demanding x and
offering 1 − x to the “responder.” The responder can either accept the offer, in which case
it is implemented, or make a counteroffer to divide the discounted value of the second-stage
“pie,” δ, where 0 < δ < 1 is a discount parameter that penalizes delayed settlements. Thus
the counteroffer is a split of δ − x
2
for the original proposer and x
2
for the responder. If
the responder makes such a counteroffer, then the proposer must decide whether to accept
the counteroffer or to engage in conflict to gain control of all of the territory. As before,
the proposer will win this conflict with probability p, which was explained to subjects in the
experiment in terms of throws of a ten-sided die. The costs of conflict are c
P
for the proposer
and c
R
for the responder. The expected payoffs with conflict are: δp − c
P
for the proposer
and δ(1 − p) − c
R
for the responder.
Assuming that both the proposer and the responder are fully informed, rational, prospec-
tive decision makers, we can solve this game through backward induction. The resulting
subgame perfect Nash equilibrium involves an initial demand of x = 1 − δ + δp − c
P
by the
proposer that is immediately accepted. The prediction is that there will be no conflict, but
behaviorally, we know conflict does occur. Moreover, our experimental results show that
even in this simple setting of complete information, with none of the auxiliary assumptions
described above (incomplete information, reputation building) we see out-of-equilibrium con-
flict. If this is the case, we need a closer inspection of the simple bargaining model.
The problem in crisis bargaining with any equilibrium concept is that actors cannot
be fully rational in the sense of completely maximizing, because of their inexperience with
bargaining where war is the outside option. Consider this on two dimensions. Even the
most belligerent states in war-prone regions rarely fight wars, and also rarely bargain where
war is the outside option. Further, belligerent states are often piloted by leaders who have
relatively limited experience in conducting international affairs. The result is that decision
makers are uncertain about the rationality of their opponents. Imagine playing a bargaining
game, for instance, against an opponent who is believed to make choices by tossing a coin.
8


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