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Aggregation and Imperfect Competition: On the Existence of Equilibrium

  • Caplin, Andrew
  • Nalebuff, Barry

The authors present a new approach to the theory of imperfect competition and apply it to study price competition among differentiated products. The central result provides general conditions for existence and uniqueness of a pure-strategy price equilibrium given any number of firms producing any set of products. This includes products with multidimensional attributes. The authors' analysis covers location models, the characteristics approach, and probabilistic choice in a unified framework. To prove existence, they employ aggregation theorems due to A. Pr$8Ekopa (1971) and C. Borell (1975). A companion paper introduces these theorems and develops the application to super-majority voting rules. Copyright 1991 by The Econometric Society.

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Article provided by Econometric Society in its journal Econometrica.

Volume (Year): 59 (1991)
Issue (Month): 1 (January)
Pages: 25-59

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Handle: RePEc:ecm:emetrp:v:59:y:1991:i:1:p:25-59
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  1. Lederer, Phillip J & Hurter, Arthur P, Jr, 1986. "Competition of Firms: Discriminatory Pricing and Location," Econometrica, Econometric Society, vol. 54(3), pages 623-40, May.
  2. Robert C. Feenstra & James A. Levinsohn, 1989. "Distance, Demand, and Oligopoly Pricing," NBER Working Papers 3076, National Bureau of Economic Research, Inc.
  3. Victor Ginsburgh & André De Palma & Yorgo Papageorgiou & Jacques-François Thisse, 1999. "The principle of minimum differentiation holds under sufficient heterogeneity," ULB Institutional Repository 2013/3319, ULB -- Universite Libre de Bruxelles.
  4. Caplin, A. & Nalebuff, B., 1989. "Aggregation And Social Choice: A Mean Voter Theorem," Discussion Papers 1989_31, Columbia University, Department of Economics.
  5. Dixit, Avinash K & Stiglitz, Joseph E, 1977. "Monopolistic Competition and Optimum Product Diversity," American Economic Review, American Economic Association, vol. 67(3), pages 297-308, June.
  6. Hauser, John R., 1987. "Existence and uniqueness of price equilibria in Defender," Working papers 1878-87., Massachusetts Institute of Technology (MIT), Sloan School of Management.
  7. Osborne, Martin J & Pitchik, Carolyn, 1987. "Equilibrium in Hotelling's Model of Spatial Competition," Econometrica, Econometric Society, vol. 55(4), pages 911-22, July.
  8. Christensen, Laurits R & Jorgenson, Dale W & Lau, Lawrence J, 1975. "Transcendental Logarithmic Utility Functions," American Economic Review, American Economic Association, vol. 65(3), pages 367-83, June.
  9. Grandmont, Jean-Michel, 1978. "Intermediate Preferences and the Majority Rule," Econometrica, Econometric Society, vol. 46(2), pages 317-30, March.
  10. B. Curtis Eaton, 1972. "Spatial Competition Revisited," Canadian Journal of Economics, Canadian Economics Association, vol. 5(2), pages 268-78, May.
  11. Spence, Michael, 1976. "Product Selection, Fixed Costs, and Monopolistic Competition," Review of Economic Studies, Wiley Blackwell, vol. 43(2), pages 217-35, June.
  12. GABSZEWICZ, Jean J. & THISSE, Jacques-François, . "Price competition, quality and income disparities," CORE Discussion Papers RP -370, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  13. Perloff, Jeffrey M & Salop, Steven C, 1985. "Equilibrium with Product Differentiation," Review of Economic Studies, Wiley Blackwell, vol. 52(1), pages 107-20, January.
  14. d'Aspremont, C & Gabszewicz, Jean Jaskold & Thisse, J-F, 1979. "On Hotelling's "Stability in Competition"," Econometrica, Econometric Society, vol. 47(5), pages 1145-50, September.
  15. Egbert Dierker, 1989. "Competition for Customers," Discussion Paper Serie A 244, University of Bonn, Germany.
  16. Anderson, Simon P & de Palma, Andre, 1988. "Spatial Price Discrimination with Heterogeneous Products," Review of Economic Studies, Wiley Blackwell, vol. 55(4), pages 573-92, October.
  17. Caplin, Andrew S & Nalebuff, Barry J, 1986. "Multi-dimensional Product Differentiation and Price Competition," Oxford Economic Papers, Oxford University Press, vol. 38(0), pages 129-45, Suppl. No.
  18. Levitan, Richard & Shubik, Martin, 1972. "Price Duopoly and Capacity Constraints," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 13(1), pages 111-22, February.
  19. Schulz, Norbert & Stahl, Konrad, 1985. "On the non-existence of oligopolistic equilibria in differentiated products spaces," Regional Science and Urban Economics, Elsevier, vol. 15(2), pages 229-243, June.
  20. Economides, Nicholas, 1989. "Symmetric equilibrium existence and optimality in differentiated product markets," Journal of Economic Theory, Elsevier, vol. 47(1), pages 178-194, February.
  21. W.J. Lane, 1980. "Product Differentiation in a Market with Endogenous Sequential Entry," Bell Journal of Economics, The RAND Corporation, vol. 11(1), pages 237-260, Spring.
  22. repec:fth:inseep:8801 is not listed on IDEAS
  23. Edward C. Prescott & Michael Visscher, 1977. "Sequential Location among Firms with Foresight," Bell Journal of Economics, The RAND Corporation, vol. 8(2), pages 378-393, Autumn.
  24. Caplin, Andrew S & Nalebuff, Barry J, 1988. "On 64%-Majority Rule," Econometrica, Econometric Society, vol. 56(4), pages 787-814, July.
  25. John R. Hauser, 1988. "Note—Competitive Price and Positioning Strategies," Marketing Science, INFORMS, vol. 7(1), pages 76-91.
  26. Greenberg, Joseph, 1979. "Consistent Majority Rules over Compact Sets of Alternatives," Econometrica, Econometric Society, vol. 47(3), pages 627-36, May.
  27. Milgrom, Paul & Roberts, John, 1990. "The Economics of Modern Manufacturing: Technology, Strategy, and Organization," American Economic Review, American Economic Association, vol. 80(3), pages 511-28, June.
  28. Archibald, G C & Rosenbluth, Gideon, 1975. "The "New" Theory of Consumer Demand and Monopolistic Competition," The Quarterly Journal of Economics, MIT Press, vol. 89(4), pages 569-90, November.
  29. Simon P. Anderson & Andre de Palma & Jacques-Francois Thisse, 1987. "Demand for Differentiated Products," Discussion Papers 726, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
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