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Mixed Bundling Strategies And Multiproduct Price Competition

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  • Ivan Arribas

    ()
    (Universitat de València)

  • Amparo Urbano

    (Universitat de València)

Abstract

This paper deals with price competition among multiproduct firms. We consider a model with n firms and one representative buyer. Each firm produces a set of products that can be different or identical to the other firms' products. The buyer is characterized by her willingness to pay -in monetary terms- for every subset of products. To handle the combinatorial complexity of this general setting we use the linear relaxation of an integer programming package assignment problem. This approach allows to characterize all the equilibrium outcomes. We look for subgame perfect Nash equilibrium prices in mixed bundling strategies, i.e., when firms offer consumers the option of buying goods separately or else packages of them at a discount over the single good prices. We find that a mixed bundling subgame perfect Nash equilibrium price vector always exists. Also, the associated equilibrium outcome is always efficient, in the sense that it maximizes the social surplus. We extend the analysis to a model with m buyers and offer the conditions under which the equilibrium outcome set is non-empty.

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File URL: http://www.ivie.es/downloads/docs/wpasad/wpasad-2004-01.pdf
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Bibliographic Info

Paper provided by Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie) in its series Working Papers. Serie AD with number 2004-01.

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Length: 49 pages
Date of creation: Jan 2004
Date of revision:
Publication status: Published by Ivie
Handle: RePEc:ivi:wpasad:2004-01

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Related research

Keywords: Multiproduct price competition; Integer Programming; Mixed Bundling Strategies; Subgame Perfect Nash Equilibria.;

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References

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  1. Kelso, Alexander S, Jr & Crawford, Vincent P, 1982. "Job Matching, Coalition Formation, and Gross Substitutes," Econometrica, Econometric Society, vol. 50(6), pages 1483-1504, November.
  2. Liao, Chun-Hsiung & Urbano, Amparo, 2002. "Pure Component Pricing in a Duopoly," Manchester School, University of Manchester, vol. 70(1), pages 150-63, January.
  3. Bikhchandani, Sushil & Ostroy, Joseph M., 2002. "The Package Assignment Model," Journal of Economic Theory, Elsevier, vol. 107(2), pages 377-406, December.
  4. Bikhchandani, Sushil & Mamer, John W., 1997. "Competitive Equilibrium in an Exchange Economy with Indivisibilities," Journal of Economic Theory, Elsevier, vol. 74(2), pages 385-413, June.
  5. Ivan Arribas & Amparo Urbano, 2003. "Nash Equilibria In A Model Of Multiproduct Price Competition: An Assignment Problem," Working Papers. Serie AD 2003-21, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  6. Anderson, Simon P. & Leruth, Luc, 1993. "Why firms may prefer not to price discriminate via mixed bundling," International Journal of Industrial Organization, Elsevier, vol. 11(1), pages 49-61, March.
  7. Armstrong, Mark, 1996. "Multiproduct Nonlinear Pricing," Econometrica, Econometric Society, vol. 64(1), pages 51-75, January.
  8. Schmalensee, Richard, 1984. "Gaussian Demand and Commodity Bundling," The Journal of Business, University of Chicago Press, vol. 57(1), pages S211-30, January.
  9. Amparo Urbano Salvador & Junichi Watanabe & Yair Tauman, 1996. "A model of multiproduct price competition," Working Papers. Serie AD 1996-07, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  10. Adams, William James & Yellen, Janet L, 1976. "Commodity Bundling and the Burden of Monopoly," The Quarterly Journal of Economics, MIT Press, vol. 90(3), pages 475-98, August.
  11. Gul, Faruk & Stacchetti, Ennio, 1999. "Walrasian Equilibrium with Gross Substitutes," Journal of Economic Theory, Elsevier, vol. 87(1), pages 95-124, July.
  12. McAfee, R Preston & McMillan, John & Whinston, Michael D, 1989. "Multiproduct Monopoly, Commodity Bundling, and Correlation of Values," The Quarterly Journal of Economics, MIT Press, vol. 104(2), pages 371-83, May.
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