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Existence of equilibrium in common agency games with adverse selection

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  • Carmona, Guilherme
  • Fajardo, José

Abstract

We establish the existence of subgame perfect equilibria in general menu games, known to be sufficient to analyze common agency problems. Our main result states that every menu game satisfying enough continuity properties has a subgame perfect equilibrium. Despite the continuity assumptions that we make, discontinuities naturally arise due to the absence, in general, of continuous optimal choices for the agent. Our approach, then, is based on (and generalizes) the existence theorem of [Simon, L., Zame, W., 1990. Discontinuous games and endogenous sharing rules. Econometrica 58 (4), 861-872] designed for discontinuous games.

Suggested Citation

  • Carmona, Guilherme & Fajardo, José, 2009. "Existence of equilibrium in common agency games with adverse selection," Games and Economic Behavior, Elsevier, vol. 66(2), pages 749-760, July.
  • Handle: RePEc:eee:gamebe:v:66:y:2009:i:2:p:749-760
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    References listed on IDEAS

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    1. Kreps, David M & Wilson, Robert, 1982. "Sequential Equilibria," Econometrica, Econometric Society, pages 863-894.
    2. Maskin, Eric & Tirole, Jean, 1990. "The Principal-Agent Relationship with an Informed Principal: The Case of Private Values," Econometrica, Econometric Society, vol. 58(2), pages 379-409, March.
    3. Simon, Leo K & Zame, William R, 1990. "Discontinuous Games and Endogenous Sharing Rules," Econometrica, Econometric Society, pages 861-872.
    4. Martimort, David & Semenov, Aggey, 2008. "Ideological uncertainty and lobbying competition," Journal of Public Economics, Elsevier, pages 456-481.
    5. Page, Frank Jr. & Monteiro, Paulo K., 2003. "Three principles of competitive nonlinear pricing," Journal of Mathematical Economics, Elsevier, vol. 39(1-2), pages 63-109, February.
    6. Martimort David & Stole Lars, 2003. "Contractual Externalities and Common Agency Equilibria," The B.E. Journal of Theoretical Economics, De Gruyter, pages 1-40.
    7. Peters, Michael, 2001. "Common Agency and the Revelation Principle," Econometrica, Econometric Society, vol. 69(5), pages 1349-1372, September.
    8. David Martimort & Lars Stole, 2002. "The Revelation and Delegation Principles in Common Agency Games," Econometrica, Econometric Society, vol. 70(4), pages 1659-1673, July.
    9. Paulo Monteiro & Frank Page, 2008. "Catalog competition and Nash equilibrium in nonlinear pricing games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), pages 503-524.
    10. Fabrice Collard & Patrick Feve & François Langot, 2002. "Structural Inference and the Lucas Critique," Annals of Economics and Statistics, GENES, issue 67-68, pages 183-206.
    11. Martimort David & Stole Lars, 2003. "Contractual Externalities and Common Agency Equilibria," The B.E. Journal of Theoretical Economics, De Gruyter, pages 1-40.
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    Cited by:

    1. Attar, Andrea & Mariotti, Thomas & Salanié, François, 2016. "On Competitive Nonlinear Pricing," TSE Working Papers 16-737, Toulouse School of Economics (TSE).
    2. Ronald J. Baker II & Susan K. Laury & Arlington W. Williams, 2008. "Comparing Small-Group and Individual Behavior in Lottery-Choice Experiments," Southern Economic Journal, Southern Economic Association, vol. 75(2), pages 367-382, October.
    3. Gwenaël Piaser, 2014. "Common Agency Games with Common Value Exclusion, Convexity and Existence," Working Papers 2014-420, Department of Research, Ipag Business School.
    4. Graham Mallard, 2014. "Static Common Agency And Political Influence: An Evaluative Survey," Journal of Economic Surveys, Wiley Blackwell, vol. 28(1), pages 17-35, February.
    5. Arribas, I. & Urbano, A., 2017. "Multiproduct trading with a common agent under complete information: Existence and characterization of Nash equilibrium," Journal of Economic Theory, Elsevier, pages 14-38.
    6. Attar, Andrea & Mariotti, Thomas & Salanié, François, 2016. "On Competitive Nonlinear Pricing," IDEI Working Papers 866, Institut d'Économie Industrielle (IDEI), Toulouse.
    7. Monteiro, Paulo K. & Page Jr., Frank H., 2009. "Endogenous mechanisms and Nash equilibrium in competitive contracting games," Journal of Mathematical Economics, Elsevier, vol. 45(9-10), pages 664-678, September.
    8. Robert Becker & Ram Dubey & Tapan Mitra, 2014. "On Ramsey equilibrium: capital ownership pattern and inefficiency," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 55(3), pages 565-600, April.
    9. Ales, Laurence & Sleet, Christopher, 2014. "Revision proofness," Journal of Economic Theory, Elsevier, pages 324-355.
    10. Ulrich Horst & Santiago Moreno-Bromberg, 2010. "Efficiency and Equilibria in Games of Optimal Derivative Design," SFB 649 Discussion Papers SFB649DP2010-035, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    11. Martimort, David & Stole, Lars, 2012. "Representing equilibrium aggregates in aggregate games with applications to common agency," Games and Economic Behavior, Elsevier, pages 753-772.
    12. Andrea Attar & Thomas Mariotti & François Salanié, 2014. "On Competitive Nonlinear Pricing," CEIS Research Paper 314, Tor Vergata University, CEIS, revised 18 Apr 2014.
    13. Galperti, Simone, 2015. "Common agency with informed principals: Menus and signals," Journal of Economic Theory, Elsevier, pages 648-667.
    14. Laurence Ales, 2009. "Adverse Selection and Non-exclusive Contracts," 2009 Meeting Papers 854, Society for Economic Dynamics.
    15. Simone Galperti, 2011. "Common Agency with Informed Principals: Menus and Signals," Discussion Papers 1541, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    16. repec:inu:caeprp:2012-008 is not listed on IDEAS
    17. Martimort, David & Stole, Lars, 2012. "Representing equilibrium aggregates in aggregate games with applications to common agency," Games and Economic Behavior, Elsevier, pages 753-772.

    More about this item

    Keywords

    Common agency Menu games Subgame perfect equilibrium;

    JEL classification:

    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • D89 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Other

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