Ulric B. and Evelyn L. Bray Social Sciences Seminar

Abstract: We develop concepts of conditional equilibria to extend Kreps and Wilson's concept of sequential equilibrium to games where the sets of actions that players can choose and the sets of signals that players may observe are infinite.  A strategy profile is a conditional epsilon-equilibrium if, given any signal event that a player could observe with positive probability, the player's conditionally expected utility would be within epsilon of the best that the player could achieve by deviating.  Fine conditional epsilon-equilibria are defined by testing conditional epsilon-rationality also under nets of small perturbations that can make any finite collection of signal events have positive probability.  With topologies on actions, if a conditional epsilon-equilibrium has full support, then the fine perturbation tests will not be necessary to evaluate epsilon-rationality for a dense class of deviations. For a large class of projective games, we prove existence of fine conditional epsilon-equilibria that have full support.

This talk will be based on a new paper, co-authored with Philip Reny, also in the Department of Economics at the University of Chicago.