Robust comparative statics in large static games

We provide general comparative static results for large finite and infinite-dimensional aggregative games. In aggregative games, each player's payoff depends on her own actions and an aggregate of the actions of all the players (for example, the average of the actions among the players). In large games, players take these aggregates as given. We derive comparative static results for large aggregative games, showing both how equilibrium aggregates and the behavior of each player change in response to various different types of changes in parameters. Our results can also be interpreted as comparative statics of ∈-equilibria in games in which there is a large but finite number of players, who still take their impact on aggregates into account in choosing their strategies. We illustrate how these results can be applied easily using two examples: (1) large single or multi-dimensional contests; (2) large beauty contests where each player's strategy is a probability distribution.