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Endogenous mechanisms and Nash equilibrium in competitive contracting games

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  • Monteiro, Paulo K.
  • Page Jr., Frank H.

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.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Mathematical Economics.

Volume (Year): 45 (2009)
Issue (Month): 9-10 (September)
Pages: 664-678

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Handle: RePEc:eee:mateco:v:45:y:2009:i:9-10:p:664-678

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Web page: http://www.elsevier.com/locate/jmateco

Related research

Keywords: Common agency with adverse selection Endogenous contracting mechanisms Discontinuous games Catalog games Existence of Nash equilibrium Competitive contracting;

References

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  1. 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.
  2. Yang, Huanxing & Ye, Lixin, 2008. "Nonlinear pricing, market coverage, and competition," Theoretical Economics, Econometric Society, vol. 3(1), March.
  3. Guilherme Carmona & José Fajardo, 2006. "Existence of Equilibrium in Common Agency Games with Adverse Selection," IBMEC RJ Economics Discussion Papers 2006-05, Economics Research Group, IBMEC Business School - Rio de Janeiro.
  4. Frank H. Page & Paulo Klinger Monteiro, 2002. "Three principles of competitive nonlinear pricing," Game Theory and Information 0204001, EconWPA.
  5. 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.
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  7. Page, Frank H, Jr, 1992. "Mechanism Design for General Screening Problems with Moral Hazard," Economic Theory, Springer, vol. 2(2), pages 265-81, April.
  8. 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.
  9. Dasgupta, Partha & Maskin, Eric, 1986. "The Existence of Equilibrium in Discontinuous Economic Games, I: Theory," Review of Economic Studies, Wiley Blackwell, vol. 53(1), pages 1-26, January.
  10. David Martimort & Lars Stole, 2001. "The Revelation and Delegation Principles in Common Agency Games," CESifo Working Paper Series 575, CESifo Group Munich.
  11. 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.
  12. Paulo Monteiro & Frank Page, 2008. "Catalog competition and Nash equilibrium in nonlinear pricing games," Economic Theory, Springer, vol. 34(3), pages 503-524, March.
  13. Michael Peters, 1999. "Common Agency and the Revelation Principle," Working Papers peters-99-01, University of Toronto, Department of Economics.
  14. Dasgupta, Partha & Maskin, Eric, 1986. "The Existence of Equilibrium in Discontinuous Economic Games, II: Applications," Review of Economic Studies, Wiley Blackwell, vol. 53(1), pages 27-41, January.
  15. Simon, Leo K, 1987. "Games with Discontinuous Payoffs," Review of Economic Studies, Wiley Blackwell, vol. 54(4), pages 569-97, October.
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