Representing equilibrium aggregates in aggregate games with applications to common agency

► Aggregate games are normal-form games in which each playerʼs payoff depends only upon his own strategy and a strategic aggregate. ► The defining nature of payoffs in an aggregate game allows one to embed the strategic analysis into an aggregate-strategy space. ► When payoffs have a quasi-linear structure, this embedding converts an n-player game into a single-person, self-generating maximization program. ► We illustrate this approach in common-agency games where the playersʼ strategy space is an infinite-dimensional space of nonlinear contracts. ► We derive equilibrium existence and characterization theorems for both the adverse selection and moral hazard variations of these contracting games.