所有博弈都有均衡
All Games Have Equilibria
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中文总结 AI 辅助
研究无限博弈纳什均衡存在性，通过修正混合策略模型提出统一方案，证明此类博弈存在有限可加混合策略中的纳什均衡，其均衡对应有良好性质，使无限博弈可进行直接均衡分析。
中文摘要 AI 辅助
关于无限博弈的纳什均衡存在性的研究已发展成为一个由技术前提条件和反例拼凑而成的领域。本文通过修正基于可数可加性的混合策略主导模型，提出了一个均衡理论的统一方案。一个博弈由非空的参与者集合、每个参与者的非空行动集和有界的冯·诺依曼 - 摩根斯坦效用函数来确定。证明了每个这样的博弈都存在有限可加混合策略中的纳什均衡。此外，还表明任何此类博弈的均衡对应是非空、紧值且上半连续的，通过有限逼近的极限得到的均衡也是如此。本文所开发的技术表明，长期以来被视为难以处理的无限博弈变得适合进行直接的均衡分析。
英文摘要
Research on Nash equilibrium existence for infinite games has grown into a patchwork of technical preconditions and counterexamples. This paper presents a unified program in equilibrium theory by revising the predominant model of mixed strategies based on countable additivity. A game is specified by a nonempty set of players and, for each player, a nonempty action set and a bounded von Neumann-Morgenstern utility function. Every such game is shown to admit a Nash equilibrium in finitely additive mixed strategies. In addition, the equilibrium correspondence for any such game is shown to be nonempty, compact-valued, and upper hemicontinuous, and the same is true for equilibria obtained as limits of finite approximations. Techniques developed in this paper show that infinite games long treated as intractable become amenable to direct equilibrium analysis.
