Ania (J Econ Behav Organ 65:472–488, 2008) shows that in the class of symmetric games with weak payoff externalities, symmetric Nash equilibria are equivalent to symmetric evolutionary equilibria (Schaffer in J Econ Behav Organ 12:29–45, 1989). We introduce a notion of a game with partial weak payoff externalities. We show that the class of games with partial weak payoff externalities includes most of previously known classes of games in which the equivalence prevails. We also establish a number of pure strategy Nash equilibrium existence results for a game with weak payoff externalities, and for a class of games that includes games with partial weak payoff externalities. The results include, in particular, the existence of pure strategy Nash equilibrium in some finite games.
Existence of equilibrium Evolutionary equilibrium Weak payoff externalities Weakly unilaterally competitive games Weakly competitive games Potential games
Yuan, G.X.-Z.: The Study of Minimax Inequalities and Applications to Economics and Variational Inequalities, Memoirs of the American Mathematical Society No. 625, American Mathematical Society (1998)Google Scholar