On the Existence of Strong Nash Equilibria

This paper investigates the existence of strong Nashequilibria (SNE) in continuous and convex games. We show that the concavity and an additional condition on payoff functions, together with the compactness of strategy space, permit the existence of strong Nash equilibria. These conditions are satisfied in many economic games and are quite simple to check. We also characterize the existence of SNE by providing a necessary and sufficient condition. Moreover, we suggest a procedure that can be used to efficiently compute strong Nash equilibrium. The result is illustrated with an application to an economy with multilateral environmental externalities and to the simple oligopoly static model.