A Qualitative Theory of Large Games with Strategic Complementarities

We study the existence and computation of equilibrium in large games with strategic complementarities. Using monotone operators (in stochastic dominance orders) defined on the space of distributions, we first prove existence of the greatest and least distributional Nash equilibrium in the sense of Mas-Colell (1984) under different set of assumptions than those in the existing literature. In addition, we provide results on computable monotone distributional equilibrium comparative statics relative to ordered perturbations of the parameters of our games. We then provide similar results for Nash/Schmeidler (1973) equilibria (defined by strategies) in our large games. We conclude by discussing the question of equilibrium uniqueness, as well as presenting applications of our results to models of Bertrand competition, "beauty contests," and existence of equilibrium in large economies