Equilibria in Large Games with Strategic Complementarities∗

We study a class of static games with a continuum of players and complementarites. Using monotone operators on the space of distributions, we prove existence of the greatest and least distributional Nash equilibrium under different set of assumptions than one stemming from Mas-Colell (1984) original work, via constructive methods. In addition, we provide computable monotone comparative statics results for ordered perturbations of the space of our games. We complement our paper with results concerning equilibria on strategies as introduced by Schmeidler (1973). Finally we discuss the equilibrium uniqueness and present applications for Bertrand competition, general equilibrium models, and so called ”beauty contests”. keywords: large games, distributional equilibria, supermodular games, computation JEL codes: C72