We present a set of necessary and sufficient conditions for a class of optimal control problems with pure state constraints for which the objective function is linear in the state variable but the objective function is otherwise only restricted to be upper semicontinuous in the control variable.

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...

We study games of public delegated common agency under asymmetric information. Us- ing tools from non-smooth analysis and optimal control, we derive best responses and characterize equilibria (both continuous and discontinuous) using self-generating opti- mization programs of which any...

This note uses techniques developed for aggregate games to characterize the set of equilib- ria for a beauty contest or prediction game in which the experts’ preferences are quadratic, but with an otherwise unrestricted information structure for private signals and the state variable. We show...

We present a Theory of Contracts under costly enforcement in the context of a dynamic relationship between an uninformed buyer and a seller who is privately informed on his persistent cost at the outset. Public enforcement relies on remedies for breach. Private enforcement comes from severing...

An aggregate game is a normal-form game with the property that each playerʼs 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...

We study games in which multiple principals influence the choice of a privately-informed agent by offering action-contingent payments. We characterize the equilibrium allocation set as the maximizers of an endogenous aggregate virtual-surplus program. The aggregate maximand for every equilibrium...

We present a Theory of Contracts under costly enforcement in the context of a dynamic relationship between an uninformed buyer and a seller who is privately informed on his persistent cost at the outset. Public enforcement relies on remedies for breach. Private enforcement comes from severing...

We study how competition in nonlinear pricing between two principals (sellers) affects market participation by a privately informed agent (consumer). When participation is restricted to all or nothing (intrinsic agency), the agent must choose between both principals' contracts and selecting her...

This paper characterizes the equilibrium sets of an intrinsic common agency game with direct exter-nalities between principals both under complete and asymmetric information. Direct externalities arise when the contracting variable of one principal affects directly the other principal's payoff....