A complete characterization of equilibria in an intrinsic common agency screening game. Issue 3 (18th October 2018) - Martimort, David; Semenov, Aggey; Stole, Lars A.
Abstract : We characterize the complete set of equilibrium allocations to an intrinsic common agency screening game as the set of solutions to self‐generating optimization programs. We provide a complete characterization of equilibrium outcomes for regular environments by relying on techniques developed elsewhere for aggregate games and for the mechanism design delegation literature. The set of equilibria includes those with nondifferentiable payoffs and discontinuous choices, as well as equilibria that are smooth and continuous in types. We identify one equilibrium, the maximal equilibrium, which is the unique solution to a self‐generating optimization program with the largest (or "maximal") domain, and the only equilibrium that is supported with biconjugate (i.e., least‐concave) tariffs. The maximal equilibrium exhibits a n ‐fold distortion caused by each of the n principal's non‐cooperative behavior in overharvesting the agent's information rent. Furthermore, in any equilibrium, over any interval of types in which there is full separation, the agent's equilibrium action corresponds to the allocation in the maximal equilibrium. Under reasonable conditions, the maximal equilibrium maximizes the agent's information rent within the class of equilibrium allocations. When the principals' most‐preferred equilibrium allocation differs from the maximal equilibrium, we demonstrate that the agent's choice function exhibits an interval of bunching over the worst agent types, and elsewhere corresponds to the maximal allocation. The optimal region of bunching trades off the principals' desire to constrain inefficient n ‐fold marginalizations of the agent's rent against the inefficiency of pooling agent types.