Strategic uncertainty and the ex post Nash property in large games
澄清了独立随机化在非合作博弈理论中的概念作用，针对大型（无原子）正则博弈，形式化了混合策略均衡和分布形式随机策略均衡，并解决了两个长期未决问题：任何混合策略均衡都诱导一个分布形式随机策略均衡，反之亦然；混合策略剖面是混合策略均衡当且仅当它具有事后纳什性质。
Abstract: This paper elucidates the conceptual role that independent randomization plays in non-cooperative game theory. In the context of large (atomless) games in normal form, we present precise formalizations of the notions of a mixed strategy equilibrium (MSE), and of a randomized strategy equilibrium in distributional form (RSED). We offer a resolution of two long-standing open problems and show: (i) any MSE induces a RSED, and any RSED can be lifted to a MSE, (ii) a mixed strategy profile is a MSE if and only if it has the ex-post Nash property. Our substantive results are a direct consequence of an exact law of large numbers (ELLN) that can be formalized in the analytic framework of a Fubini extension. We discuss how the ‘measurability ’ problem associated with a MSE of a large game is automatically resolved in such a framework. We also illustrate our ideas by an approximate result pertaining to a sequence of large but finite games.