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

Yuhki Hosoya () and Chaowen Yu
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Yuhki Hosoya: Chuo University
Chaowen Yu: Rissho University

Economic Theory Bulletin, 2022, vol. 10, issue 1, No 6, 69-93

Abstract: Abstract 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.

Keywords: Mixed strategy; Approximate purification; Uncountable action set; Conditionally atomless; Nash equilibrium (search for similar items in EconPapers)
JEL-codes: C62 C65 C72 C73 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s40505-022-00219-1

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