Existence of Equilibria in Countable Games: An Algebraic Approach

Posted: 15 Jul 2013

See all articles by Valerio Capraro

Valerio Capraro

Università degli Studi di Milano-Bicocca - Department of Psychology

Marco Scarsini

Luiss University Dipartimento di Economia e Finanza

Date Written: July 13, 2013

Abstract

Although mixed extensions of finite games always admit equilibria, this is not the case for countable games, the best-known example being Waldʼs pick-the-larger-integer game. Several authors have provided conditions for the existence of equilibria in infinite games. These conditions are typically of topological nature and are rarely applicable to countable games. Here we establish an existence result for the equilibrium of countable games when the strategy sets are a countable group, the payoffs are functions of the group operation, and mixed strategies are not requested to be σ-additive. As a byproduct we show that if finitely additive mixed strategies are allowed, then Waldʼs game admits an equilibrium. Finally we extend the main results to uncountable games.

Keywords: Amenable groups, Infinite games, Existence of equilibria, Invariant means, Waldʼs game

JEL Classification: C72

Suggested Citation

Capraro, Valerio and Scarsini, Marco, Existence of Equilibria in Countable Games: An Algebraic Approach (July 13, 2013). Games and Economic Behavior, Vol. 79, 2013, Available at SSRN: https://ssrn.com/abstract=2293437

Valerio Capraro

Università degli Studi di Milano-Bicocca - Department of Psychology ( email )

Marco Scarsini (Contact Author)

Luiss University Dipartimento di Economia e Finanza ( email )

Viale Romania 32
Rome, RM 00197
Italy

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