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Truthful Revelation Mechanisms for Simultaneous Common Agency Games

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  • Giacomo Calzolari
  • Alessandro Pavan

Abstract

In games in which multiple principals contract simultaneously and non-cooperatively with the same agent, standard direct revelation mechanisms in which the agent reports his type(i.e. his exogenous private information) have been proven inadequate to characterize the entire set of equilibrium outcomes. This paper introduces a more general class of revelation mechanisms in which the agent reports also the contractual decisions he is inducing with the principals. We rst show that such a class has the same nice properties as the class of all unrestricted menus: (i) for any equilibrium of any indirect game with arbitrary communication space for the principals, there exists a truthful equilibrium in the game in which the principals are restricted to o¤er revelation mechanisms that sustains the same outcomes; (ii) any truthful equilibrium is robust in the sense that it remains an equilibrium in any game in which the principalsstrategy space is enlarged. We next show how revelation mechanisms can be put to work in applications such as menu auctions, moral hazard settings, and competition in non-linear tariffs to identify necessary and sufficient conditions for the sustainability of outcomes as common agency equilibria.

Suggested Citation

  • Giacomo Calzolari & Alessandro Pavan, 2007. "Truthful Revelation Mechanisms for Simultaneous Common Agency Games," Discussion Papers 1458, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  • Handle: RePEc:nwu:cmsems:1458
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    References listed on IDEAS

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    1. Attar, Andrea & Piaser, Gwenael & Porteiro, Nicolas, 2007. "Negotiation and take-it or leave-it in common agency with non-contractible actions," Journal of Economic Theory, Elsevier, vol. 135(1), pages 590-593, July.
    2. Attar, Andrea & Majumdar, Dipjyoti & Piaser, Gwenaël & Porteiro, Nicolás, 2008. "Common agency games: Indifference and separable preferences," Mathematical Social Sciences, Elsevier, vol. 56(1), pages 75-95, July.
    3. Dixit, Avinash & Grossman, Gene M & Helpman, Elhanan, 1997. "Common Agency and Coordination: General Theory and Application to Government Policy Making," Journal of Political Economy, University of Chicago Press, vol. 105(4), pages 752-769, August.
    4. Bruno Biais & David Martimort & Jean-Charles Rochet, 2000. "Competing Mechanisms in a Common Value Environment," Econometrica, Econometric Society, vol. 68(4), pages 799-838, July.
    5. B. Douglas Bernheim & Michael D. Whinston, 1985. "Common Marketing Agency as a Device for Facilitating Collusion," RAND Journal of Economics, The RAND Corporation, vol. 16(2), pages 269-281, Summer.
    6. Han, Seungjin, 2006. "Menu theorems for bilateral contracting," Journal of Economic Theory, Elsevier, vol. 131(1), pages 157-178, November.
    7. Peters, Michael & Troncoso-Valverde, Cristián, 2013. "A folk theorem for competing mechanisms," Journal of Economic Theory, Elsevier, vol. 148(3), pages 953-973.
    8. Piaser, Gwenaël, 2007. "Direct Mechanisms, Menus and Latent Contracts," MPRA Paper 7049, University Library of Munich, Germany.
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    Cited by:

    1. Han, Seungjin, 2014. "Implicit collusion in non-exclusive contracting under adverse selection," Journal of Economic Behavior & Organization, Elsevier, vol. 99(C), pages 85-95.
    2. 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.
    3. Andrea Attar & Eloisa Campioni & Gwenaël Piaser & Uday Rajan, 2012. "Competing mechanism games of moral hazard: communication and robustness," Review of Economic Design, Springer;Society for Economic Design, vol. 16(4), pages 283-296, December.
    4. Han, Seungjin, 2012. "On take it or leave it offers in common agency," Economics Letters, Elsevier, vol. 117(3), pages 777-781.
    5. Galperti, Simone, 2015. "Common agency with informed principals: Menus and signals," Journal of Economic Theory, Elsevier, vol. 157(C), pages 648-667.
    6. 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.
    7. Attar, Andrea & Majumdar, Dipjyoti & Piaser, Gwenaël & Porteiro, Nicolás, 2008. "Common agency games: Indifference and separable preferences," Mathematical Social Sciences, Elsevier, vol. 56(1), pages 75-95, July.
    8. Ghosh, Sambuddha & Han, Seungjin, 2012. "Repeated Contracting in Decentralised Markets," Microeconomics.ca working papers seungjin_han-2012-12, Vancouver School of Economics, revised 02 May 2013.
    9. 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.

    More about this item

    Keywords

    mechanism design; contracts; Revelation Principle.;

    JEL classification:

    • D89 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Other
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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