Best-response equilibrium: an equilibrium in finitely additive mixed strategies

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