IDEAS home Printed from https://ideas.repec.org/a/the/publsh/2266.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://econtheory.org/ojs/index.php/te/article/viewFile/20181151/21822/650
    Download Restriction: no
    ---><---

    Other versions of this item:

    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. Laussel, Didier & Le Breton, Michel, 2001. "Conflict and Cooperation: The Structure of Equilibrium Payoffs in Common Agency," Journal of Economic Theory, Elsevier, vol. 100(1), pages 93-128, September.
    3. Peters, Michael, 2001. "Common Agency and the Revelation Principle," Econometrica, Econometric Society, vol. 69(5), pages 1349-1372, September.
    4. David Martimort, 1992. "Multi-principaux avec anti-sélection," Annals of Economics and Statistics, GENES, issue 28, pages 1-37.
    5. Myerson, Roger B., 1982. "Optimal coordination mechanisms in generalized principal-agent problems," Journal of Mathematical Economics, Elsevier, vol. 10(1), pages 67-81, June.
    6. Hoernig Steffen & Valletti Tommaso M., 2011. "When Two-Part Tariffs are Not Enough: Mixing with Nonlinear Pricing," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 11(1), pages 1-20, October.
    7. Laussel, Didier & Le Breton, Michel, 1998. "Efficient Private Production of Public Goods under Common Agency," Games and Economic Behavior, Elsevier, vol. 25(2), pages 194-218, November.
    8. Paul Milgrom & Ilya Segal, 2002. "Envelope Theorems for Arbitrary Choice Sets," Econometrica, Econometric Society, vol. 70(2), pages 583-601, March.
    9. Martimort, David & Stole, Lars, 2015. "Menu Auctions and Influence Games with Private Information," MPRA Paper 62388, University Library of Munich, Germany.
    10. Martimort, David & Semenov, Aggey, 2006. "Continuity in mechanism design without transfers," Economics Letters, Elsevier, vol. 93(2), pages 182-189, November.
    11. 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.
    12. Manuel Amador & Kyle Bagwell, 2013. "The Theory of Optimal Delegation With an Application to Tariff Caps," Econometrica, Econometric Society, vol. 81(4), pages 1541-1599, July.
    13. Mark Bagnoli & Ted Bergstrom, 2006. "Log-concave probability and its applications," Studies in Economic Theory, in: Charalambos D. Aliprantis & Rosa L. Matzkin & Daniel L. McFadden & James C. Moore & Nicholas C. Yann (ed.), Rationality and Equilibrium, pages 217-241, Springer.
    14. Giacomo Calzolari & Vincenzo Denicol?, 2013. "Competition with Exclusive Contracts and Market-Share Discounts," American Economic Review, American Economic Association, vol. 103(6), pages 2384-2411, October.
    15. David Martimort & Lars Stole, 2002. "The Revelation and Delegation Principles in Common Agency Games," Econometrica, Econometric Society, vol. 70(4), pages 1659-1673, July.
    16. repec:hal:pseose:hal-00813181 is not listed on IDEAS
    17. Szentes, Balázs, 2015. "Contractible contracts in common agency problems," LSE Research Online Documents on Economics 66071, London School of Economics and Political Science, LSE Library.
    18. Balázs Szentes, 2015. "Contractible Contracts in Common Agency Problems," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 82(1), pages 391-422.
    19. Nahum D. Melumad & Toshiyuki Shibano, 1991. "Communication in Settings with No. Transfers," RAND Journal of Economics, The RAND Corporation, vol. 22(2), pages 173-198, Summer.
    20. Chiesa, Gabriella & Denicolò, Vincenzo, 2009. "Trading with a common agent under complete information: A characterization of Nash equilibria," Journal of Economic Theory, Elsevier, vol. 144(1), pages 296-311, January.
    21. 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, April.
    22. Carlier, Guillaume, 2001. "A general existence result for the principal-agent problem with adverse selection," Journal of Mathematical Economics, Elsevier, vol. 35(1), pages 129-150, February.
    23. repec:adr:anecst:y:1992:i:28:p:01 is not listed on IDEAS
    24. Rochet, Jean-Charles, 1987. "A necessary and sufficient condition for rationalizability in a quasi-linear context," Journal of Mathematical Economics, Elsevier, vol. 16(2), pages 191-200, April.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. David Martimort & Aggey Semenov & Lars Stole, 2016. "A Complete Characterization of Equilibria in Common Agency Screening Games," Working Papers 1618E, University of Ottawa, Department of Economics.
    2. Martimort, David & Stole, Lars, 2011. "Public Contracting in Delegated Agency Games," MPRA Paper 32874, University Library of Munich, Germany.
    3. Martimort, David & Stole, Lars, 2015. "Menu Auctions and Influence Games with Private Information," MPRA Paper 62388, University Library of Munich, Germany.
    4. 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.
    5. David Martimort & Jérôme Pouyet & Carine Staropoli, 2020. "Use and abuse of regulated prices in electricity markets: “How to regulate regulated prices?”," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 29(3), pages 605-634, July.
    6. Martimort, David & Stole, Lars A., 2022. "Participation constraints in discontinuous adverse selection models," Theoretical Economics, Econometric Society, vol. 17(3), July.
    7. Attar, Andrea & Campioni, Eloisa & Mariotti, Thomas & Pavan, Alessandro, 2021. "Keeping the Agents in the Dark: Private Disclosures in Competing Mechanisms," TSE Working Papers 21-1227, Toulouse School of Economics (TSE), revised Dec 2023.
    8. Attar, Andrea & Campioni, Eloisa & Piaser, Gwenaël, 2018. "On competing mechanisms under exclusive competition," Games and Economic Behavior, Elsevier, vol. 111(C), pages 1-15.
    9. Martimort David & Stole Lars, 2003. "Contractual Externalities and Common Agency Equilibria," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 3(1), pages 1-40, July.
    10. Martimort, David, 2019. ""When Olson Meets Dahl": From Inefficient Groups Formation to Inefficient Policy-Making," CEPR Discussion Papers 13843, C.E.P.R. Discussion Papers.
    11. Kolotilin, Anton & Li, Hongyi, 2021. "Relational communication," Theoretical Economics, Econometric Society, vol. 16(4), November.
    12. Attar, Andrea & Campioni, Eloisa & Piaser, Gwenaël, 2019. "Private communication in competing mechanism games," Journal of Economic Theory, Elsevier, vol. 183(C), pages 258-283.
    13. Martimort, David & Semenov, Aggey, 2008. "Ideological uncertainty and lobbying competition," Journal of Public Economics, Elsevier, vol. 92(3-4), pages 456-481, April.
    14. Attar, Andrea & Campioni, Eloisa & Mariotti, Thomas & Piaser, Gwenaël, 2021. "Competing mechanisms and folk theorems: Two examples," Games and Economic Behavior, Elsevier, vol. 125(C), pages 79-93.
    15. Semenov, Aggey, 2010. "Common agency with risk-averse agent," Journal of Mathematical Economics, Elsevier, vol. 46(1), pages 38-49, January.
    16. Martimort, David & Stole, Lars, 2009. "Selecting equilibria in common agency games," Journal of Economic Theory, Elsevier, vol. 144(2), pages 604-634, March.
    17. Ales, Laurence & Maziero, Pricila, 2016. "Non-exclusive dynamic contracts, competition, and the limits of insurance," Journal of Economic Theory, Elsevier, vol. 166(C), pages 362-395.
    18. Hernández-Murillo, Rubén, 2019. "Interjurisdictional competition with adverse selection," Journal of Public Economics, Elsevier, vol. 173(C), pages 85-95.
    19. Iossa, Elisabetta & Martimort, David, 2016. "Corruption in PPPs, incentives and contract incompleteness," International Journal of Industrial Organization, Elsevier, vol. 44(C), pages 85-100.
    20. Navin Kartik & Andreas Kleiner & Richard Van Weelden, 2021. "Delegation in Veto Bargaining," American Economic Review, American Economic Association, vol. 111(12), pages 4046-4087, December.

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:the:publsh:2266. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Martin J. Osborne (email available below). General contact details of provider: http://econtheory.org .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.