类数有限的大型博弈和Nash的“改进”证明

International journal of economic research Pub Date : 2012-08-01 DOI:10.17256/JER.2012.17.2.004

S. Kim

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引用次数: 2

摘要

Nash(1951)使用Brouwer的不动点定理而不是Kakutani的不动点定理证明了有限博弈中混合策略纳什均衡的存在性。本文将纳什(1951)的证明应用于类数有限的大型对策，建立了纯策略均衡的存在性。新方法在一定程度上阐明了旧的结果。

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Large Games with a Finite Number of Classes and Nash’s ‘Improved’ Proof

Nash (1951) proved the existence of mixed strategy Nash equilibria for finite games using Brouwer’s, rather than Kakutani’s, fixed point theorem. This paper adapts Nash’s (1951) proof to large games with a finite number of classes to establish the existence of pure strategy equilibria. The new approach sheds some light on the old results.

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International journal of economic research

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