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Aggregation and Imperfect Competition: On the Existence of Equilibrium

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Author Info
Caplin, Andrew
Nalebuff, Barry

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Abstract

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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Publisher Info
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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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. 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. [Downloadable!] (restricted)
  2. Grandmont, Jean-Michel, 1978. "Intermediate Preferences and the Majority Rule," Econometrica, Econometric Society, vol. 46(2), pages 317-30, March. [Downloadable!] (restricted)
  3. Feenstra, R.C. & Levinsohn, J.A., 1989. "Distance, Demand, And Oligopoly Pricing," Working Papers 245, Research Seminar in International Economics, University of Michigan.
    Other versions:
  4. Caplin, A. & Nalebuff, B., 1989. "Aggregation And Imperfect Competition: On The Existence Of Equilibrium," Discussion Papers 1989_30, Columbia University, Department of Economics.
    Other versions:
  5. 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. [Downloadable!] (restricted)
  6. 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. [Downloadable!] (restricted)
  7. Andrew Caplin & Barry Nalebuff, 1990. "Aggregation and Social Choice: A Mean Voter Theorem," Cowles Foundation Discussion Papers 938, Cowles Foundation, Yale University. [Downloadable!]
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  8. 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. [Downloadable!] (restricted)
  9. Steven C. Salop, 1979. "Monopolistic Competition with Outside Goods," Bell Journal of Economics, The RAND Corporation, vol. 10(1), pages 141-156, Spring. [Downloadable!] (restricted)
  10. Anderson, Simon P & de Palma, Andre, 1988. "Spatial Price Discrimination with Heterogeneous Products," Review of Economic Studies, Blackwell Publishing, vol. 55(4), pages 573-92, October. [Downloadable!] (restricted)
  11. B. Curtis Eaton, 1972. "Spatial Competition Revisited," Canadian Journal of Economics, Canadian Economics Association, vol. 5(2), pages 268-78, May. [Downloadable!] (restricted)
  12. 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. [Downloadable!] (restricted)
  13. Osborne, Martin J & Pitchik, Carolyn, 1987. "Equilibrium in Hotelling's Model of Spatial Competition," Econometrica, Econometric Society, vol. 55(4), pages 911-22, July. [Downloadable!] (restricted)
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  14. Perloff, Jeffrey M & Salop, Steven C, 1985. "Equilibrium with Product Differentiation," Review of Economic Studies, Blackwell Publishing, vol. 52(1), pages 107-20, January. [Downloadable!] (restricted)
  15. 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. [Downloadable!] (restricted)
  16. Greenberg, Joseph, 1979. "Consistent Majority Rules over Compact Sets of Alternatives," Econometrica, Econometric Society, vol. 47(3), pages 627-36, May. [Downloadable!] (restricted)
  17. 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. [Downloadable!] (restricted)
  18. Economides, Nicholas, 1989. "Symmetric equilibrium existence and optimality in differentiated product markets," Journal of Economic Theory, Elsevier, vol. 47(1), pages 178-194, February. [Downloadable!] (restricted)
  19. Spence, Michael, 1976. "Product Selection, Fixed Costs, and Monopolistic Competition," Review of Economic Studies, Blackwell Publishing, vol. 43(2), pages 217-35, June. [Downloadable!] (restricted)
  20. Egbert Dierker, 1989. "Competition for Customers," Discussion Paper Serie A 244, University of Bonn, Germany.
  21. 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. [Downloadable!] (restricted)
  22. 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. [Downloadable!] (restricted)
  23. repec:fth:michin:245 is not listed on IDEAS
  24. Caplin, Andrew S & Nalebuff, Barry J, 1988. "On 64%-Majority Rule," Econometrica, Econometric Society, vol. 56(4), pages 787-814, July. [Downloadable!] (restricted)
  25. 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. [Downloadable!] (restricted)
  26. 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. [Downloadable!] (restricted)
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  27. 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. [Downloadable!]
  28. 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. [Downloadable!]
  29. David M. Kreps & Jose A. Scheinkman, 1983. "Quantity Precommitment and Bertrand Competition Yield Cournot Outcomes," Bell Journal of Economics, The RAND Corporation, vol. 14(2), pages 326-337, Autumn. [Downloadable!] (restricted)
  30. de Palma, A, et al, 1985. "The Principle of Minimum Differentiation Holds under Sufficient Heterogeneity," Econometrica, Econometric Society, vol. 53(4), pages 767-81, July. [Downloadable!] (restricted)
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