Best-reply sets

Jonathan Weinstein ()
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Jonathan Weinstein: Washington University in St. Louis

Economic Theory Bulletin, 2020, vol. 8, issue 1, No 9, 105-112

Abstract: Abstract We provide results concerning, in a given normal-form game, which sets of actions are best replies to some belief. Proposition 1 states that for any set S of actions, there is a belief under which all actions in S are simultaneously best replies if and only if no mixture of actions in S is strictly dominated. Similarly, Proposition 2 states that for any set S of actions, there is a full-support belief under which all actions in S are best replies if and only if no mixture of actions in S is weakly dominated. One important consequence is Corollary 1: a two-player game has a totally mixed Nash equilibrium if and only if neither player has a pair of mixed strategies such that one weakly dominates the other.

Keywords: Game theory; Normal-form games; Best replies; Rationalizability (search for similar items in EconPapers)
JEL-codes: C72 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s40505-019-00169-1

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