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Nash Equilibria In A Model Of Multiproduct Price Competition: An Assignment Problem

  • Ivan Arribas

    ()

    (Universitat de València)

  • Amparo Urbano

    (Universitat de València)

We study the market interaction of a finite number of single-product firms and a representative buyer, where the buyer consumes bundles of these goods. The buyers' value function determines their willingness to pay for subsets of goods. We show that subgame perfect Nash-equilibrium outcomes are solutions of the linear relaxation of an integer programming assignment problem and that they always exits. The (subgame perfect) Nash-equilibrium price set is characterized by the Pareto frontier of the associated dual problem's projection on the firms' price vectors. We identify the Nash-equilibrium prices for monotonic buyers' value functions and, more importantly, we show that some central solution concepts in cooperative game theory are (subgame perfect) equilibrium prices of our strategic game.

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File Function: Fisrt version / Primera version, 2003
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Paper provided by Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie) in its series Working Papers. Serie AD with number 2003-21.

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Length: 48 pages
Date of creation: Jun 2003
Date of revision:
Publication status: Published by Ivie
Handle: RePEc:ivi:wpasad:2003-21
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  1. 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).
  2. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-77, November.
  3. 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.
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  6. d'ASPREMONT, Claude & GABSZEWICZ, Jean J. & THISSE, Jacques-François, . "On Hotelling's "Stability in competition"," CORE Discussion Papers RP -385, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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  8. Bikhchandani, Sushil & Ostroy, Joseph M., 2002. "The Package Assignment Model," Journal of Economic Theory, Elsevier, vol. 107(2), pages 377-406, December.
  9. Jaskold Gabszewicz, J. & Thisse, J. -F., 1979. "Price competition, quality and income disparities," Journal of Economic Theory, Elsevier, vol. 20(3), pages 340-359, June.
  10. Steven C. Salop, 1979. "Monopolistic Competition with Outside Goods," Bell Journal of Economics, The RAND Corporation, vol. 10(1), pages 141-156, Spring.
  11. Perez-Castrillo J. David, 1994. "Cooperative Outcomes through Noncooperative Games," Games and Economic Behavior, Elsevier, vol. 7(3), pages 428-440, November.
  12. 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.
  13. Perez-Castrillo, D. & Sotomayor, M., 1998. "A Simple Selling and Buying Procedure," UFAE and IAE Working Papers 421.98, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  14. Shaked, Avner & Sutton, John, 1983. "Natural Oligopolies," Econometrica, Econometric Society, vol. 51(5), pages 1469-83, September.
  15. GABSZEWICZ, Jean J. & THISSE, Jacques-François, . "Entry (and exit) in a differentiated industry," CORE Discussion Papers RP -400, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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