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Aggregation and Imperfect Competition: On the Existence of Equilibrium

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  • Caplin, Andrew
  • Nalebuff, Barry

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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Bibliographic 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

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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. 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.
  3. John R. Hauser, 1988. "Note—Competitive Price and Positioning Strategies," Marketing Science, INFORMS, vol. 7(1), pages 76-91.
  4. Perloff, Jeffrey M & Salop, Steven C, 1985. "Equilibrium with Product Differentiation," Review of Economic Studies, Wiley Blackwell, vol. 52(1), pages 107-20, January.
  5. 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).
  6. Caplin, A. & Nalebuff, B., 1989. "Aggregation And Social Choice: A Mean Voter Theorem," Discussion Papers 1989_31, Columbia University, Department of Economics.
  7. 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.
  8. Egbert Dierker, 1989. "Competition for Customers," Discussion Paper Serie A 244, University of Bonn, Germany.
  9. 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.
  10. Osborne, Martin J & Pitchik, Carolyn, 1987. "Equilibrium in Hotelling's Model of Spatial Competition," Econometrica, Econometric Society, vol. 55(4), pages 911-22, July.
  11. 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.
  12. 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.
  13. B. Curtis Eaton, 1972. "Spatial Competition Revisited," Canadian Journal of Economics, Canadian Economics Association, vol. 5(2), pages 268-78, May.
  14. 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.
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  16. Spence, Michael, 1976. "Product Selection, Fixed Costs, and Monopolistic Competition," Review of Economic Studies, Wiley Blackwell, vol. 43(2), pages 217-35, June.
  17. 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.
  18. 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.
  19. Dixit, Avinash K & Stiglitz, Joseph E, 1975. "Monopolistic Competition and Optimum Product Diversity," The Warwick Economics Research Paper Series (TWERPS) 64, University of Warwick, Department of Economics.
  20. 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.
  21. 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.
  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.
  23. Greenberg, Joseph, 1979. "Consistent Majority Rules over Compact Sets of Alternatives," Econometrica, Econometric Society, vol. 47(3), pages 627-36, May.
  24. Economides, Nicholas, 1989. "Symmetric equilibrium existence and optimality in differentiated product markets," Journal of Economic Theory, Elsevier, vol. 47(1), pages 178-194, February.
  25. 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.
  26. 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.
  27. Grandmont, Jean-Michel, 1978. "Intermediate Preferences and the Majority Rule," Econometrica, Econometric Society, vol. 46(2), pages 317-30, March.
  28. 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.
  29. Caplin, Andrew S & Nalebuff, Barry J, 1988. "On 64%-Majority Rule," Econometrica, Econometric Society, vol. 56(4), pages 787-814, July.
  30. repec:fth:michin:245 is not listed on IDEAS
  31. repec:fth:coluec:450 is not listed on IDEAS
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