Nash equilibria of games with monotonic best replies

Abstract

We introduce notions of increasingness for the best reply of a game that capture properly the intuitive idea of complementarity among players’ strategies. We show, by generalizing the fixpoint theorems of Veinott and Zhou, that the Nash sets of our games with increasing best replies are nonempty complete lattices. Hence we extend the class of games with strategic complementarities.Complementarity, supermodular games, fixpoint theorem, Nash equilibria