Pure strategy Nash equilibrium in a group formation game with positive externalities

This paper identifies a domain of payoff functions in no spillover noncooperative games with Positive externality which admit a pure strategy Nash equilibrium. Since in general a Nash equilibrium may fail to exist, in order to guarantee the existence of an equilibrium, we impose two additional assumptions, Anonymity and Order presentation. The proof of our main result is carried out by constructing, for a given game G, a potential function Psi over the set of strategy profiles in such a way that the maximum of Psi yields a Nash equilibrium in pure strategies of G. Journal of Economics Literature Classification Numbers: C72, D62, H73. (C) 1997 Academic Press.