Martimort, David and Semenov, Aggey and Stole, Lars (2017): A Complete Characterization of Equilibria in a Common Agency Screening Game.

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Abstract
We characterize the complete set of equilibrium allocations to an intrinsic common agency screening game as the set of solutions to selfgenerating 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 include 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 selfgenerating optimization program with the largest (or “maximal”) domain, and the only equilibrium that is supported with biconjugate (i.e., leastconcave) tariffs. The maximal equilibrium exhibits a nfold distortion caused by each of the n principal’s noncooperative behavior in over harvesting 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 mild conditions, the maximal equilibrium maximizes the agent’s information rent within the class of equilibrium allocations. When the principals’ mostpreferred 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 with the maximal allocation. The optimal region of bunching trades off the principals’ desire to constrain inefficient nfold marginalizations of the agent’s rent against the inefficiency of pooling agent types.
Item Type:  MPRA Paper 

Original Title:  A Complete Characterization of Equilibria in a Common Agency Screening Game 
Language:  English 
Keywords:  Intrinsic common agency, aggregate games, mechanism design for delegated decisionmaking, duality, equilibrium selection. 
Subjects:  D  Microeconomics > D8  Information, Knowledge, and Uncertainty > D82  Asymmetric and Private Information ; Mechanism Design D  Microeconomics > D8  Information, Knowledge, and Uncertainty > D86  Economics of Contract: Theory 
Item ID:  80870 
Depositing User:  Lars A. Stole 
Date Deposited:  19 Aug 2017 14:12 
Last Modified:  06 Oct 2019 00:51 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/80870 