Strategic uncertainty and the ex-post Nash property in large games

, (), , P. (), , () and , ()
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,: Department of Economics, Johns Hopkins University
, P.: Department of Economics, University of Notre Dame
,: Department of Economics, National University of Singapore
,: Department of Economics, Ryerson University
Authors registered in the RePEc Author Service: M. Ali Khan and Haomiao Yu

Theoretical Economics, 2015, vol. 10, issue 1

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 {\it induces} a RSED, and any RSED can be {\it 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 {\it exact} law of large numbers (ELLN) that can be formalized in the analytic framework of a Fubini extension. We discuss how the \lq 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.

Keywords: Large game; pure strategy; mixed strategy; randomized strategy in distributional form; Nash equilibrium; ex-post Nash property; saturated probability space; rich Fubini extension; exact law of large numbers (ELLN); asymptotic implementation (search for similar items in EconPapers)
JEL-codes: C65 C72 D84 (search for similar items in EconPapers)
Date: 2015-01-30
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (7)

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