Aggregate Representations of Aggregate Games

Abstract. An aggregate game is a normal-form game with the property that each player’s payoff is a function only of his own strategy and an aggregate function of the strategy profile of all players. Aggregate games possess a set of purely algebraic properties that can often provide simple characterizations of equilibrium aggregates without first requiring that one solves for the equilibrium strategy profile. We demon-strate that the defining nature of payoffs in an aggregate game allows one to embed the strategic analysis into the aggregate-strategy space, converting an n-player game to a simpler object – a self-generating single-person maximization program. We apply these techniques to a number of economic settings including competition in supply functions or competitive agency games with nonlinear transfer functions. ∗This paper consolidates many of the results in the previous working papers “A note on aggregate-strategy games, ” 2005 and “Tricks with aggregate games, ” 2007