On the approximate purification of mixed strategies in games with infinite action sets

We consider a game in which the action set of each player is uncountable, and show that, from weak assumptions on the common prior, any mixed strategy has an approximately equivalent pure strategy. The assumption of this result can be further weakened if we consider the purification of a Nash equili...

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Bibliographic Details
Published in:Economic theory bulletin 2022-05, Vol.10 (1), p.69-93
Main Authors: Hosoya, Yuhki, Yu, Chaowen
Format: Article
Language:English
Subjects:
Economic theory
Economic Theory/Quantitative Economics/Mathematical Methods
Economics
Economics and Finance
Equilibrium
Game Theory
Games
Macroeconomics/Monetary Economics//Financial Economics
Public Finance
Purification
Research Article
Social and Behav. Sciences
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Summary:We consider a game in which the action set of each player is uncountable, and show that, from weak assumptions on the common prior, any mixed strategy has an approximately equivalent pure strategy. The assumption of this result can be further weakened if we consider the purification of a Nash equilibrium. Combined with the existence theorem for a Nash equilibrium, we derive an existence theorem for a pure strategy approximated Nash equilibrium under sufficiently weak assumptions. All of the pure strategies we derive in this paper can take a finite number of possible actions.
ISSN:2196-1085
2196-1093
DOI:10.1007/s40505-022-00219-1