Aggregate Representations of Aggregate Games

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 demonstrate 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 aggregatestrategy games,” 2005 and “Tricks with aggregate games,” 2007. †Toulouse School of Economics (EHESS). Email: [email protected]. ‡University of Chicago Booth School of Business. Email: [email protected]. The authors thank Karen Bernhardt-Walther, John Birge, Emir Kamenica, Dan Levin, David Myatt, David Rahman, Michael Schwarz and seminar participants at the University of Chicago and Ohio State University for helpful conversations and suggestions.