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A complete characterization of equilibria in an intrinsic common agency screening game

Author

Listed:
  • Martimort, David

    (Paris School of Economics)

  • Semenov, Aggey

    (Department of Economics, University of Ottawa)

  • Stole, Lars A.

    (Booth School of Business, University of Chicago)

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 include those with non-differentiable 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 bi-conjugate (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 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 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 with 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.

Suggested Citation

  • Martimort, David & Semenov, Aggey & Stole, Lars A., 2018. "A complete characterization of equilibria in an intrinsic common agency screening game," Theoretical Economics, Econometric Society, vol. 13(3), September.
    • Handle: RePEc:the:publsh:2266
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    1. Didier Laussel & Joana Resende, 2020. "Complementary Monopolies with asymmetric information," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 70(4), pages 943-981, November.

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    More about this item

    Keywords

    Intrinsic common agency; aggregate games; mechanism design for delegated decision-making; duality; equilibrium selection;
    All these keywords.

    JEL classification:

    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • D86 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Economics of Contract Law

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