EQUIVALENCE OF STRONG AND COALITION-PROOF NASH EQUILIBRIA IN GAMES WITHOUT SPILLOVERS

This paper examines the conditions which guarantee that the set of coa lition-proof Nash equilibria coincides with the set of strong Nash equ ilibria in the normal form games without spillovers. We find that popu lation monotonicity properties of the payoff functions, when the payof f of a player changes monotonically when the size of the group of play ers choosing the same strategy increases, are crucial to obtain the eq uivalence of these two solution concepts, We identify the classes of g ames, satisfying population monotonicity properties, which yield the e quivalence of the set of coalition-proof Nash equilibria and the set o f strong Nash equilibria. We also provide sufficient conditions for th e equivalence result even when the population monotonicity assumptions are relaxed.