Roy Seminar (ADRES)

Du 15/04/2019 de 17:00 à 18:30

Salle R1-09, Campus Jourdan, 48 boulevard Jourdan, 75014 Paris

RENY Philip (University of Chicago)

Conditional ?-Equilibria of Multi-Stage Games with Infinite Sets of Signals and Actions

We extend Kreps and Wilson's concept of sequential equilibrium to games where the sets of actions that players can choose from and the sets of signals that players may observe are infinite. A strategy profile is a conditional ?-equilibrium if, for any player and for any of his positive probability signal events, the player's conditional expected utility is within ? of the best that the player can achieve by deviating. Perfect conditional ?-equilibria are defined by testing conditional ?-rationality also under nets of small perturbations of the players' strategies and of nature's probability function that can make any finite collection of signals outside a negligible set have positive probability. Every perfect conditional ?-equilibrium strategy profile is a subgame perfect ?-equilibrium, and, in finite games, limits of perfect conditional ?-equilibria as ??0 are sequential equilibrium strategy profiles. Because such limit strategies need not exist even in very "nice" infinite games, we consider instead their limit distributions over outcomes. We call such outcome distributions perfect conditional equilibrium distributions and establish their existence for a large class of regular projective games. Nature's perturbations can produce equilibria that seem unintuitive and so we consider two ways to limit the effects of those perturbations, using topologies on nature's states and on players' actions.