Characterizations of the Existence of Nash Equilibria with Non-convex Strategy Sets

A sufficient and necessary condition is presented for the existence of a Nash equilibrium in n-person noncooperative games in normal form where strategy sets are not necessarily convex. Under the convexity condition, we show that this new sufficient and necessary condition is a particular case of diagonal transfer quasiconcavity. The result is illustrated with an application to an economy with multilateral environmental externalities and to the existence of a Cournot equilibrium.