Legitimate equilibrium

Abstract We present a general existence result for type of equilibrium in normal-form games, which extends the concept Nash equilibrium. consider nonzero-sum games with an arbitrary number players and action spaces. impose merely one condition: payoff function each player is bounded. allow to use finitely additive probability measures as mixed strategies. Since we do not assume any measurability conditions, given strategy profile expected generally uniquely defined, integration theory only provides upper bound, integral, lower integral. A called legitimate if evaluates this by all his possible deviations show that always exists. Our are motivated Vasquez (2017), who defines conceptually related notion, shows its under conditions many players, separable metric spaces bounded Borel measurable functions. proof borrows several ideas from (Vasquez (2017)), but more direct it does make countably representations (Yosida Hewitt (1952)).