Equilibrium selection in aggregative games with strategic complementarities

We study large games played by heterogeneous agents whose payoffs depend on their type and on the aggregate action. We show that when player actions and the aggregate action are complements the global games equilibrium selection yields a unique equilibrium. We characterize the selected equilibrium as the strategy profile that maximizes average expected payoffs when players have pessimistic beliefs about the aggregate action. In particular, each agent believes to be the lowest type to contribute to the aggregate action. To obtain our result we prove that beliefs about the distribution of the aggregate action in the global game satisfy a generalized Laplacian property , which states that the (weighted) average belief is the uniform distribution.