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

Artikel

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.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Journal: Theoretical Economics ; ISSN: 1555-7561 ; Volume: 10 ; Year: 2015 ; Issue: 1 ; Pages: 103-129 ; New Haven, CT: The Econometric Society

Classification and Topics

• Classification: Wirtschaft ; Noncooperative Games ; Expectations; Speculations ; Miscellaneous Mathematical Tools
• Subject: 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

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Yu, Haomiao ; Khan, M. Ali ; Rath, Kali P. ; Sun, Yeneng
• Event: Veröffentlichung
• (who): The Econometric Society
• (where): New Haven, CT
• (when): 2015

Further information

• DOI: doi:10.3982/TE1492
• Handle: http://hdl.handle.net/10419/150245
• Last update: 10.03.2025, 11:42 AM CET