Monotone equilibria in nonatomic supermodular games. A comment

Recently Yang and Qi (2013) stated an interesting theorem on existence of complete lattice of equilibria in a particular class of large nonatomics supermodular games for general action and types spaces. Unfortunately, their result is incorrect. In this note, we detail the nature of the problem with the stated theorem, provide a counterexample, and then correct the result under additional assumptions. We also provide a number of new results per existence of equilibria in more general classes of games of strategic complementarities that are monotone in players’ types, as well as provide a class of constructive methods for computing monotone equilibrium comparative statics. keywords: large games, supermodular games, games with strategic complementarities, distributional equilibria, JEL codes: C72