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A Complete Characterization of Equilibria in Two-type Common Agency Screening Games

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  • Martimort, David
  • Semenov, Aggey
  • Stole, Lars

Abstract

We characterize the complete set of equilibrium allocations to a two-type intrinsic common agency screening game as the set of solutions to a self-generating optimization program. The program, in turn, can be thought of as a maximization problem facing a fictional “surrogate” principal with a simple set of incentive constraints that embed the non-cooperative behavior of principals in the underlying game. After providing a complete characterization of equilibrium outcomes, we refine the set by imposing a requirement of biconjugacy on equilibrium tariffs: In biconjugate equilibria, the surrogate principal’s incentive constraints are described by marginal conditions. Biconjugate equilibria always exist, they are simple to compute, and they are robust in the sense that they remain equilibria when “out-of-equilibrium” output-price pairs are pruned. After characterizing the set of biconjugate equilibrium allocations, we ask what is the best equilibrium for the principals from an ex ante perspective. We show that the allocation that maximizes the principals’ ex ante collective payoff among all possible equilibria is distinct from the best allocation in the refined set of biconjugate equilibria, although their qualitative properties remain similar.

Suggested Citation

  • Martimort, David & Semenov, Aggey & Stole, Lars, 2015. "A Complete Characterization of Equilibria in Two-type Common Agency Screening Games," MPRA Paper 66620, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:66620
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    References listed on IDEAS

    as
    1. Martimort, David & Semenov, Aggey, 2008. "Ideological uncertainty and lobbying competition," Journal of Public Economics, Elsevier, vol. 92(3-4), pages 456-481, April.
    2. Alessandro Pavan & Giacomo Calzolari, 2010. "Truthful Revelation Mechanisms for Simultaneous Common Agency Games," American Economic Journal: Microeconomics, American Economic Association, vol. 2(2), pages 132-190, May.
    3. Peters, Michael, 2001. "Common Agency and the Revelation Principle," Econometrica, Econometric Society, vol. 69(5), pages 1349-1372, September.
    4. David Martimort & Lars Stole, 2002. "The Revelation and Delegation Principles in Common Agency Games," Econometrica, Econometric Society, vol. 70(4), pages 1659-1673, July.
    5. Martimort, David & Stole, Lars, 2012. "Representing equilibrium aggregates in aggregate games with applications to common agency," Games and Economic Behavior, Elsevier, vol. 76(2), pages 753-772.
    6. Attar, Andrea & Mariotti, Thomas & Salanié, François, 2019. "On competitive nonlinear pricing," Theoretical Economics, Econometric Society, vol. 14(1), January.
    7. David Martimort, 1992. "Multi-principaux avec anti-sélection," Annals of Economics and Statistics, GENES, issue 28, pages 1-37.
    8. , & , & ,, 2014. "Nonexclusive competition under adverse selection," Theoretical Economics, Econometric Society, vol. 9(1), January.
    9. Jean-Jacques Laffont & Jean Tirole, 1993. "A Theory of Incentives in Procurement and Regulation," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262121743, December.
    10. Martimort, David & Stole, Lars, 2015. "Menu Auctions and Influence Games with Private Information," MPRA Paper 62388, University Library of Munich, Germany.
    11. repec:adr:anecst:y:1992:i:28:p:01 is not listed on IDEAS
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    More about this item

    Keywords

    Intrinsic common agency; aggregate games; screening contracts.;
    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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