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Competitive selling mechanisms: the delegation principle and farsighted stability

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  • PAGE, Frank

Abstract

We analyze the problem of competitive mechanism design within the context of a model of product differentiated oligopoly. In our model, firms compete via their catalogs, that is, via the sets of products (broadly defined) and prices firms offer to the market (i.e., catalogs are the primitives, while selling mechanisms are derived). In an oligopoly setting, participation by an agent in any one firm’s catalog is endogenously determined. This fact leads naturally to a modification of the classical notion of incentive compatibility for mechanisms. We extend the classical notion of incentive compatibility to take into account endogenous participation, introducing the notion of participation incentive compatibility (PIC). Our main contribution is a characterization of all PIC selling mechanisms in terms of catalogs. In particular, we show that a selling mechanism is PIC if and only if there exists a unique, minimal catalog profile which implements the mechanisms. We call this characterization the delegation principle (Theorem 4). Using the delegation principle, we conclude that in order to solve the problem of competitive mechanism design, an essentially cooperative problem, it is sufficient to consider only the underlying noncooperative problem of catalog choice by firms. Moreover, using the delegation principle we show that corresponding to each PIC mechanism there is a unique profile of nonlinear pricing schedules which implements the mechanism - thus, extending the taxation principle to problems of competitive nonlinear pricing (Theorem 5). A second contribution is our application of the notion of farsighted stability to the problem of competitive mechanism design. We show that for any approximating finite subgame (of catalog choice), the farsightedly stable set of catalog profiles (and hence the farsightedly stable set of nonlinear pricing schedules) is nonempty (Theorem 10).

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Paper provided by Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) in its series CORE Discussion Papers with number 2000021.

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Date of creation: 00 Mar 2000
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Handle: RePEc:cor:louvco:2000021

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  1. Berliant, M. & Page, F.H., 2001. "Income Taxes and Provision of Public Goods: Optima with Balanced Goverment Budgets," Papiers d'Economie Mathématique et Applications 2001.37, Université Panthéon-Sorbonne (Paris 1).
  2. Artstein, Zvi, 1979. "A note on fatou's lemma in several dimensions," Journal of Mathematical Economics, Elsevier, vol. 6(3), pages 277-282, December.
  3. Hans M. Amman & David A. Kendrick, . "Computational Economics," Online economics textbooks, SUNY-Oswego, Department of Economics, number comp1, Spring.
  4. KLINGER MONTEIRO , Paulo & PAGE, Frank H. Jr., 1997. "Optimal selling mechanisms for multiproduct monopolists : incentive compatibility in the presence of budget constraints," CORE Discussion Papers 1997011, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  5. Wilson, Robert, 1996. "Nonlinear pricing and mechanism design," Handbook of Computational Economics, in: H. M. Amman & D. A. Kendrick & J. Rust (ed.), Handbook of Computational Economics, edition 1, volume 1, chapter 5, pages 253-293 Elsevier.
  6. Myerson, Roger B., 1982. "Optimal coordination mechanisms in generalized principal-agent problems," Journal of Mathematical Economics, Elsevier, vol. 10(1), pages 67-81, June.
  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. Konishi, Hideo & Le Breton, Michel & Weber, Shlomo, 1999. "On Coalition-Proof Nash Equilibria in Common Agency Games," Journal of Economic Theory, Elsevier, vol. 85(1), pages 122-139, March.
  9. Eric Maskin & John Riley, 1984. "Monopoly with Incomplete Information," RAND Journal of Economics, The RAND Corporation, vol. 15(2), pages 171-196, Summer.
  10. Mirrlees, James A, 1971. "An Exploration in the Theory of Optimum Income Taxation," Review of Economic Studies, Wiley Blackwell, vol. 38(114), pages 175-208, April.
  11. David Martimort, 1996. "Exclusive Dealing, Common Agency, and Multiprincipals Incentive Theory," RAND Journal of Economics, The RAND Corporation, vol. 27(1), pages 1-19, Spring.
  12. 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.
  13. Bernheim, B Douglas & Whinston, Michael D, 1986. "Common Agency," Econometrica, Econometric Society, vol. 54(4), pages 923-42, July.
  14. Hammond, Peter J, 1979. "Straightforward Individual Incentive Compatibility in Large Economies," Review of Economic Studies, Wiley Blackwell, vol. 46(2), pages 263-82, April.
  15. Page, Frank H, Jr, 1992. "Mechanism Design for General Screening Problems with Moral Hazard," Economic Theory, Springer, vol. 2(2), pages 265-81, April.
  16. Didier Laussel & Thomas R. Palfrey, 2003. "Efficient Equilibria in the Voluntary Contributions Mechanism with Private Information," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 5(3), pages 449-478, 07.
  17. Rochet, J. C., 1985. "The taxation principle and multi-time Hamilton-Jacobi equations," Journal of Mathematical Economics, Elsevier, vol. 14(2), pages 113-128, April.
  18. Wilson, Robert, 1997. "Nonlinear Pricing," OUP Catalogue, Oxford University Press, number 9780195115826, October.
  19. Xue, Licun, 1997. "Nonemptiness of the Largest Consistent Set," Journal of Economic Theory, Elsevier, vol. 73(2), pages 453-459, April.
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