Best-Response Equilibrium: An Equilibrium in Finitely Additive Mixed Strategies

Igal Milchtaich


A generalization of mixed strategy equilibrium is proposed, where mixed strategies need only be finitely additive and payoff functions need not be integrable or bounded. It is based on an extension of the idea that an equilibrium strategy is supported in the set of bestresponse actions of the player, but is applicable also when no best-response actions exist. This notion of best-response equilibrium yields simple, natural mixed equilibria in a number of well-known games where other kinds of mixed equilibrium are complicated, are not compelling or do not existent.

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