Ambiguous Act Equilibria

A novel approach for the study of games with strategic uncertainty is proposed. Games are defined such that players’ strategy spaces do nor only contain pure and mixed strategies but also contain “ambiguous act strategies”, in the sense that players can base their choices on subjective randomization devices. The notions of “independent strategies” as well as “common priors” are relaxed in such a manner that they can be applied to the context of games with strategic uncertainty even though the player’s preferences cannot necessarily be represented by expected utility functions. The concept of “Ambiguous Act Equilibrium” is defined. The main result concerns two player games in which preferences of all players satisfy Schmeidler’s uncertainty aversion as well as transitivity and monotonicity. The ambiguous act equilibria of such a game are observationally equivalent to the mixed strategy equilibria of that game in the sense that a researcher who can only observe equilibrium outcomes is not able to determine whether the players are uncertainty averse or uncertainty neutral.

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