Random belief equilibrium in normal form games
نویسندگان
چکیده
We de ̄ne Random Belief Equilibrium (RBE) in ̄nite, normal form games. We assume that a player's beliefs about the strategy choices of others are randomly drawn from a belief distribution. This distribution is dispersed around a central strategy pro ̄le, the focus. At an RBE: (1) Each player chooses a best response relative to her drawn beliefs. (2) The expected choice of each player coincides with the focus of the other players' belief distributions. RBE provides a statistical framework for estimation which we apply to data from three experimental games. We provide a characterization of the limit-RBE as players' beliefs converge to certainty. Let Di(si) be the set of mixed strategies of player i's opponents to which si is a best reply. When atoms in the belief distributions vanish in the limit, all pure strategies si used with positive probability by player i in a limit-RBE (called a Robust Equilibrium) must have the following property. The intersection of Di(si) with any ball around the equilibrium mixed strategies of player i's opponents must have positive Lebesgue measure. We show that this implies that not all trembling hand perfect Nash equilibria are robust and not all robust equilibria are perfect.
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عنوان ژورنال:
- Games and Economic Behavior
دوره 51 شماره
صفحات -
تاریخ انتشار 2005