Invited talk: Existence of equilibria in countable games

Although mixed extensions of finite games always admit equilibria, this is not the case for countable games, the best-known example being Wald'€™s pick-the-larger-integer game. Several authors have provided conditions for the existence of equilibria in infinite games. These conditions are typically of topological nature and are not applicable to countable games. Here we establish an existence result for the equilibrium of countable games when the strategy sets are a countable group and the payoff€s are functions of the group operation. In order to obtain the existence of equilibria, finitely additive mixed strategies have to be allowed. This creates a problem of selection of a product measure of mixed strategies. We propose a family of such selections and prove existence of an equilibrium that does not depend on the selection. As a byproduct we show that if finitely additive mixed strategies are allowed, then Wald's game admits an equilibrium. 15: 20 15: 30 Break

Authors

• Marco Scarsini Luiss University

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