Large Games with Heterogeneous Players

Abstract

We study large games played by heterogeneous agents whose payoffs depend on the aggregate action and provide novel equilibrium selection and comparative statics results. We prove the equivalence between the global games selection and potential maximization in games with strategic complementarities, and characterize the selected equilibrium as the solution to maximizing the ex-ante expected payoffs of a player with pessimistic beliefs. To obtain our results we uncover two key properties. First, we show that potential games exhibit quasilinear payoffs, which include as examples Cournot competition, public goods and externalities, search models and coordination games. Second, we show that beliefs in the global game satisfy a generalized Laplacian property, which links average beliefs about the aggregate action to the uniform distribution. Our comparative statics results rely on average rather than pointwise conditions on payoffs and can be used to analyze both parameter changes and the impact of heterogeneity.