Representing Equilibrium Aggregates in Aggregate Games with Applications to Common Agency
36 Pages Posted: 15 Feb 2014 Last revised: 3 Mar 2015
Date Written: October 5, 1012
An aggregate game is a normal-form game with the property that each player’s payoff is a function of only his own strategy and an aggregate of the strategy profile of all players. Such games possess properties that can often yield simple characterizations of equilibrium aggregates without re- quiring that one solves for the equilibrium strategy profile. When payoffs have a quasi-linear structure and a degree of symmetry, we construct a self- generating maximization program over the space of aggregates with the property that the solution set corresponds to the set of equilibrium aggre- gates of the original n-player game. We illustrate the value of this approach in common-agency games where the players’ strategy space is an infinite- dimensional space of nonlinear contracts. We derive equilibrium existence and characterization theorems for both the adverse selection and moral haz- ard versions of these games.
Keywords: game theory, aggregate games, common agency
JEL Classification: C70, D82
Suggested Citation: Suggested Citation