Pure Strategy Nash Equilibrium in a Group Formation Game with Positive Externalities

Abstract 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 preservation . The proof of our main result is carried out by constructing, for a given game G , a potential function Ψ over the set of strategy profiles in such a way that the maximum of Ψ yields a Nash equilibrium in pure strategies of G . Journal of Economics Literature Classification Numbers: C72, D62, H73.

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