Large Aggregate Games with Heterogeneous Players
Ricardo Serrano-Padial · RePEc: Research Papers in Economics
We study large games played by heterogeneous agents whose payoffs depend on the aggregate action and provide novel equilibrium selection and comparative statics results. Regarding equilibrium selection, we establish the equivalence between potential maximization and the global games selection in supermodular games, and characterize the uniquely selected equilibrium as the strategy profile that maximizes the ex-ante expected payoffs of a player with marginal beliefs. To obtain our equivalence result we show that (i) payoffs in an aggregative potential game must be quasilinear and (ii) beliefs in the global game must satisfy a generalized Laplacian property linking (weighted) average beliefs to the uniform distribution. We present comparative statics results that rely on average rather than pointwise conditions on payoffs and use them to illustrate how heterogeneity affects equilibrium levels of the aggregate action.