On the Existence of Strong Nash Equilibria

This paper investigates the existence of strong Nash equilibria (SNE) in continuous and concave games. We show that the coalition consistence property introduced in the paper, together with the concavity and continuity of payoffs, permits the existence of strong Nash equilibria in games with compact and convex strategy spaces. The coalition consistency property is a general condition that cannot be dispensed with for the existence of strong Nash equilibrium. It is satisfied in many economic games and can be checked with a similar way as finding weak Pareto efficient outcomes. We also characterize the existence of SNE by providing necessary and sufficient conditions. Moreover, we suggest an algorithm for efficiently computing strong Nash equilibrium. The results are illustrated with applications to economies with multilateral environmental externalities and to the simple oligopoly static model.