Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/150245
Title:

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

Authors:
Yu, Haomiao
Khan, M. Ali
Rath, Kali P.
Sun, Yeneng
Year of Publication:
2015
Citation:
[Journal:] Theoretical Economics [ISSN:] 1555-7561 [Volume:] 10 [Year:] 2015 [Issue:] 1 [Pages:] 103-129
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.
Subjects:
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
JEL:
C72
D84
C65
Persistent Identifier of the first edition:
Document Type:
Article
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