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

, (), , P. (), , () and , ()
Additional contact information
,: 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: Haomiao Yu and M. Ali Khan

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)

Downloads: (external link)
http://econtheory.org/ojs/index.php/te/article/viewFile/20150103/12317/371 (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:the:publsh:1492

Access Statistics for this article

Theoretical Economics is currently edited by Federico Echenique, Mira Frick, Pablo Kurlat, Juuso Toikka, Rakesh Vohra

More articles in Theoretical Economics from Econometric Society
Bibliographic data for series maintained by Martin J. Osborne ().