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.

Existence of equilibria in countable games: an algebraic approach / V., Capraro; Scarsini, Marco. - In: GAMES AND ECONOMIC BEHAVIOR. - ISSN 0899-8256. - 79:(2013), pp. 163-180. [10.1016/j.geb.2013.01.010]

Existence of equilibria in countable games: an algebraic approach

SCARSINI, MARCO
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.
Amenable groups; Infinite games; Existence of equilibria; Invariant means; Wald’s game
Existence of equilibria in countable games: an algebraic approach / V., Capraro; Scarsini, Marco. - In: GAMES AND ECONOMIC BEHAVIOR. - ISSN 0899-8256. - 79:(2013), pp. 163-180. [10.1016/j.geb.2013.01.010]
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11385/64656
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