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Aggregation And Imperfect Competition: On The Existence Of Equilibrium

  • CAPLIN, A.
  • NALEBUFF, B.

We 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 under which there exists a pure strategy price equilibrium for any number of firms producing any set of products. This includes products with multi-dimensional attributes. In addition to the proof of existence, we provide conditions for uniqueness. Our analysis covers location models, the characteristic approach, and probabilistic choice together in a unified framework. To prove existence, we employ aggregation theorems due to Prekopa (1971) and Borell (1975). Our companion paper [CFDP 938] introduces these theorems and develops the application to super-majority voting rules.

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Paper provided by Columbia University, Department of Economics in its series Discussion Papers with number 1989_30.

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Length: 36 pages
Date of creation: 1989
Date of revision:
Handle: RePEc:clu:wpaper:1989_30
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  1. Feenstra, R.C. & Levinsohn, J.A., 1989. "Distance, Demand And Oligopoly Pricing," Papers 342, California Davis - Institute of Governmental Affairs.
  2. 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).
  3. 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.
  4. Greenberg, Joseph, 1979. "Consistent Majority Rules over Compact Sets of Alternatives," Econometrica, Econometric Society, vol. 47(3), pages 627-36, May.
  5. Spence, Michael, 1976. "Product Selection, Fixed Costs, and Monopolistic Competition," Review of Economic Studies, Wiley Blackwell, vol. 43(2), pages 217-35, June.
  6. Perloff, Jeffrey M & Salop, Steven C, 1985. "Equilibrium with Product Differentiation," Review of Economic Studies, Wiley Blackwell, vol. 52(1), pages 107-20, January.
  7. 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.
  8. Osborne, Martin J & Pitchik, Carolyn, 1987. "Equilibrium in Hotelling's Model of Spatial Competition," Econometrica, Econometric Society, vol. 55(4), pages 911-22, July.
  9. Caplin, Andrew S & Nalebuff, Barry J, 1988. "On 64%-Majority Rule," Econometrica, Econometric Society, vol. 56(4), pages 787-814, July.
  10. de PALMA, A. & GINSBURGH, V. & PAPAGEOGIOU, Y.Y. & THISSE, J-F., . "The principle of minimum differentiation holds under sufficient heterogeneity," CORE Discussion Papers RP -640, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  11. Andrew Caplin & Barry Nalebuff, 1990. "Aggregation and Social Choice: A Mean Voter Theorem," Cowles Foundation Discussion Papers 938, Cowles Foundation for Research in Economics, Yale University.
  12. 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.
  13. 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.
  14. 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.
  15. Richard E. Levitan & Martin Shubik, 1970. "Price Duopoly and Capacity Constraints," Cowles Foundation Discussion Papers 287, Cowles Foundation for Research in Economics, Yale University.
  16. 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.
  17. 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.
  18. Egbert Dierker, 1989. "Competition for Customers," Discussion Paper Serie A 244, University of Bonn, Germany.
  19. 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.
  20. repec:fth:inseep:8801 is not listed on IDEAS
  21. 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.
  22. Grandmont, Jean-Michel, 1978. "Intermediate Preferences and the Majority Rule," Econometrica, Econometric Society, vol. 46(2), pages 317-30, March.
  23. B. Curtis Eaton, 1972. "Spatial Competition Revisited," Canadian Journal of Economics, Canadian Economics Association, vol. 5(2), pages 268-78, May.
  24. 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.
  25. John R. Hauser, 1988. "Note—Competitive Price and Positioning Strategies," Marketing Science, INFORMS, vol. 7(1), pages 76-91.
  26. 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.
  27. 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.
  28. 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.
  29. Economides, Nicholas, 1989. "Symmetric equilibrium existence and optimality in differentiated product markets," Journal of Economic Theory, Elsevier, vol. 47(1), pages 178-194, February.
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