Con Games with Payo¤ Uncertainty1 ict
Sandeep Baliga Northwestern University Tomas Sjstrm Rutgers University
August 2009
paper has bene…tted from insightful comments by Stephen Morris and Alessandro Pavan. Kane Sweeney provided excellent research assitance.
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Abstract Stag hunt and chicken games are canonical representations of two kinds of strategic interactions. In stag hunt, aggression feeds on itself, and mutual fear escalates into con ict. Chicken is a model of preemption and deterrence. With complete information, these games have multiple Nash equilbria. Using standard arguments from the Industrial Organization literature, we …nd su cient conditions for payo¤ uncertainty to generate a unique Bayesian Nash equilibrium. These conditions encompass information structures ranging from independent types (as in our previous work) to highly correlated types (as in global games). Keywords: con global games, strategic comict, plements, strategic substitutes.
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Introduction
Simple two-by-two games are frequently used to represent strategic interactions in political science and international relations (see, for example, Jervis [12]). In this literature, the prisoner' dilemma plays a prominent role. But s in many instances, stag hunt and chicken games seem more apt metaphors. Stag hunt captures Hobbes' "state of nature" where con is caused by s , ict 1 lack of trust. Chicken is a model of preemption and deterrence. The prominence of prisoner' dilemma games in the literature may be due to analytical s convenience: the prisoner' dilemma has a unique Nash equilibrium, whereas s stag hunt and chicken have multiple equilibria. The prisoner' dilemma can be thought of as a degenerate stag hunt or s chicken game, where extreme levels of hostility have made "war"a dominant strategy. And even if this scenario is not very likely, a player who is himself not intrinsically hostile may be unable to completely rule out the possibility that the opponent is extremely hostile, or that the opponent thinks he is very hostile... As is well known, this type of reasoning may produce "spirals" of fear and aggression. The most useful way to think about these spirals is to formally introduce payo¤ uncertainty. This not only makes the model more realistic, but it may also generate a unique equilibrium. Consider a two-player game, where each player must choose either hawk (H) or dove (D). The hawkish action H might represent an act of war, accumulation of weapons, or some other aggressive action. In the payo¤ matrix, the row represents the choice of player i; and the column the choice of player j. Only player i' payo¤ is indicated. s D H hi c hi D d 0 The payo¤ from the peaceful outcome (D; D) is, without loss of generality,

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