Events at CERGE-EI

Prof. Philip Reny

The University of Chicago, USA

Author: Philip J. Reny

Abstract: We extend Kreps and Wilson's 1982 definition of sequential equilibrium to multi-stage games with infinite sets of signals and actions. We define a strategy profile to be a full conditional ε-equilibrium if it has full support and players are ε-optimizing conditional on every positive probability event. Full conditional ε-equilibria need not be subgame perfect ε-equilibria. A strategy profile is a perfect conditional ε-equilibrium if it has full support and for any finite set of signals the strategies and nature's probability function can be perturbed to give all signals in the finite set positive probability and so that players are ε-optimizing conditional on every positive probability event. Perfect conditional ε-equilibria are shown to be full conditional ε-equilibria and to be subgame perfect ε-equilibria, and are shown to exist for a large class of regular projective games. Examples illustrate properties of perfect conditional ε-equilibria and the difficulties of alternative approaches to the problem of extending sequential equilibrium to infinite games.

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