Existence of equilibria in countable games: An algebraic approach

• 成果类型: Article
• 署名作者: Capraro, Valerio; Scarsini, Marco
• 署名单位: University of Southampton; Singapore University of Technology & Design
• 刊物名称: GAMES AND ECONOMIC BEHAVIOR
• ISSN/ISSBN: 0899-8256
• DOI: 10.1016/j.geb.2013.01.010
• 发表日期: 2013
• 页码: 163-180
• 关键词: Amenable groups; infinite games; Existence of equilibria; Invariant means; Wald's game

摘要

Although mixed extensions of finite 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 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 sigma-additive. As a byproduct we show that if finitely additive mixed strategies are allowed, then Wald's game admits an equilibrium. Finally we extend the main results to uncountable games. (c) 2013 Elsevier Inc. All rights reserved.