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Endogenous Mechanisms and Nash Equilibrium in Competitive Contracting

Author

Listed:
  • Frank H. Page, Jr.

    () (Indiana University Bloomington)

  • Paulo K. Monteiro

    () (EPGE/FGV)

Abstract

We model strategic competition in a market with asymmetric information as a noncooperative game in which each firm competes for the business of a buyer of unknown type by offering the buyer a catalog of products and prices. The timing in our model is Stackelberg: in the first stage, given the distribution of buyer types known to all firms and the deducible, type-dependent best responses of the agent, firms simultaneously and noncooperatively choose their catalog offers. In the second stage the buyer, knowing his type, chooses a single firm and product-price pair from that firm's catalog. By backward induction, this Stackelberg game with asymmetric information reduces to a game over catalogs with payoff indeterminacies. In particular, due to ties within catalogs and/or across catalogs, corresponding to any catalog profile offered by firms there may be multiple possible expected firm payoffs, all consistent with the rational optimizing behavior of the agent for each of his types. The resolution of these indeterminacies depends on the tie-breaking mechanism which emerges in the market. Because each tie-breaking mechanism induces a particular game over catalogs, a reasonable candidate would be a tie-breaking mechanism which supports a Nash equilibrium in the corresponding catalog game. We call such a mechanism an endogenous Nash mechanism. The fundamental question we address in this paper is, does there exist an endogenous Nash mechanism - and therefore, does there exist a Nash equilibrium for the catalog game? We show under fairly mild conditions on primitives that catalog games naturally possess tie-breaking mechanisms which support Nash equilibria.

Suggested Citation

  • Frank H. Page, Jr. & Paulo K. Monteiro, 2007. "Endogenous Mechanisms and Nash Equilibrium in Competitive Contracting," Caepr Working Papers 2007-025, Center for Applied Economics and Policy Research, Economics Department, Indiana University Bloomington.
  • Handle: RePEc:inu:caeprp:2007025
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    File URL: http://www.iub.edu/~caepr/RePEc/PDF/2007/CAEPR2007-025.pdf
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    References listed on IDEAS

    as
    1. Page, Frank H, Jr, 1992. "Mechanism Design for General Screening Problems with Moral Hazard," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 2(2), pages 265-281, April.
    2. Simon, Leo K & Zame, William R, 1990. "Discontinuous Games and Endogenous Sharing Rules," Econometrica, Econometric Society, vol. 58(4), pages 861-872, July.
    3. 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.
    4. Peters, Michael, 2001. "Common Agency and the Revelation Principle," Econometrica, Econometric Society, vol. 69(5), pages 1349-1372, September.
    5. David Martimort & Lars Stole, 2002. "The Revelation and Delegation Principles in Common Agency Games," Econometrica, Econometric Society, vol. 70(4), pages 1659-1673, July.
    6. 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.
    7. 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), vol. 34(3), pages 503-524, March.
    8. Artstein, Zvi, 1979. "A note on fatou's lemma in several dimensions," Journal of Mathematical Economics, Elsevier, vol. 6(3), pages 277-282, December.
    9. Mertens, J.-F., 1987. "A measurable “measurable choice” theorem," CORE Discussion Papers 1987049, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    10. Philip J. Reny, 1999. "On the Existence of Pure and Mixed Strategy Nash Equilibria in Discontinuous Games," Econometrica, Econometric Society, vol. 67(5), pages 1029-1056, September.
    11. Monteiro, Paulo Klinger & Page Jr, Frank H., 2007. "Uniform payoff security and Nash equilibrium in compact games," Journal of Economic Theory, Elsevier, vol. 134(1), pages 566-575, May.
    12. Leo K. Simon, 1987. "Games with Discontinuous Payoffs," Review of Economic Studies, Oxford University Press, vol. 54(4), pages 569-597.
    13. Matthew O. Jackson & Leo K. Simon & Jeroen M. Swinkels & William R. Zame, 2002. "Communication and Equilibrium in Discontinuous Games of Incomplete Information," Econometrica, Econometric Society, vol. 70(5), pages 1711-1740, September.
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    Cited by:

    1. Braido, Luis H.B., 2009. "Multiproduct price competition with heterogeneous consumers and nonconvex costs," Journal of Mathematical Economics, Elsevier, vol. 45(9-10), pages 526-534, September.

    More about this item

    Keywords

    common agency with adverse selection; endogenous contracting mechanisms; discontinuous games; catalog games; existence of Nash equilibrium; competitive contracting;

    JEL classification:

    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D4 - Microeconomics - - Market Structure, Pricing, and Design

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