Dominance-based Solutions for Strategic Form Games

We model a player’s decision as a choice set based on an abstract concept of dominance, called a dominance structure, and define a choice-theoretic notion of equilibrium. We investigate various properties of dominance structures and provide a general existence result; we give sucient conditions for uniqueness of “maximal” and “minimal” equilibria; and we explore the logical relationships among several well-known and some new dominance structures. Our results explain many regularities observed in the literature on rationalizability, in which specific dominance structures are used to characterize rationalizable strategy profiles under dierent common knowledge assumptions. Our uniqueness result for “minimal” equilibria extends Shapley’s (1964) uniqueness result for the saddle of a two-player zero-sum game.

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