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Multiproduct price competition with heterogeneous consumers and nonconvex costs

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Author Info

  • Braido, Luis H.B.

Abstract

This paper extends the oligopolistic model of price competition to environments with multiple goods, heterogeneous consumers, and arbitrary continuous cost functions. A Nash equilibrium in mixed strategies with an endogenous sharing rule is proven to exist. It is also shown that, in environments with fixed costs and constant marginal costs, all (symmetric and asymmetric) equilibria exhibit price dispersion across stores. Furthermore, the paper identifies scenarios in which prices will necessarily be random. In these markets, stores keep each other guessing because, given the fixed costs, they would incur a loss if their price strategies were anticipated and beaten by competitors. This is interpreted as an important economic feature that is possibly behind random price promotions such as weekly specials.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Mathematical Economics.

Volume (Year): 45 (2009)
Issue (Month): 9-10 (September)
Pages: 526-534

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Handle: RePEc:eee:mateco:v:45:y:2009:i:9-10:p:526-534

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Web page: http://www.elsevier.com/locate/jmateco

Related research

Keywords: Bertrand competition Discontinuous games Mixed strategy Weekly specials Price dispersion;

References

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  1. Luis Braido, 2005. "General equilibrium with endogenous securities and moral hazard," Economic Theory, Springer, vol. 26(1), pages 85-101, 07.
  2. Burdett, Kenneth & Judd, Kenneth L, 1983. "Equilibrium Price Dispersion," Econometrica, Econometric Society, vol. 51(4), pages 955-69, July.
  3. McAfee R. Preston, 1995. "Multiproduct Equilibrium Price Dispersion," Journal of Economic Theory, Elsevier, vol. 67(1), pages 83-105, October.
  4. Marquez, Robert, 1997. "A note on Bertrand competition with asymmetric fixed costs," Economics Letters, Elsevier, vol. 57(1), pages 87-96, November.
  5. Butters, Gerard R, 1977. "Equilibrium Distributions of Sales and Advertising Prices," Review of Economic Studies, Wiley Blackwell, vol. 44(3), pages 465-91, October.
  6. Michael R. Baye & John Morgan, 2004. "Price Dispersion in the Lab and on the Internet: Theory and Evidence," Working Papers 2004-02, Indiana University, Kelley School of Business, Department of Business Economics and Public Policy.
  7. Dastidar, Krishnendu Ghosh, 1995. "On the Existence of Pure Strategy Bertrand Equilibrium," Economic Theory, Springer, vol. 5(1), pages 19-32, January.
  8. Salop, Steven & Stiglitz, Joseph E, 1977. "Bargains and Ripoffs: A Model of Monopolistically Competitive Price Dispersion," Review of Economic Studies, Wiley Blackwell, vol. 44(3), pages 493-510, October.
  9. Simon, Leo K. & Zame, William R., 1987. "Discontinous Games and Endogenous Sharing Rules," Department of Economics, Working Paper Series qt8n46v2wv, Department of Economics, Institute for Business and Economic Research, UC Berkeley.
  10. Sharkey, William W. & Sibley, David S., 1993. "A Bertrand model of pricing and entry," Economics Letters, Elsevier, vol. 41(2), pages 199-206.
  11. Frank H. Page, Jr. & Paulo K. Monteiro, 2007. "Endogenous Mechanisms and Nash Equilibrium in Competitive Contracting," Caepr Working Papers 2007-025, Center for Applied Economics and Policy Research, Economics Department, Indiana University Bloomington.
  12. Anderson, Simon P & de Palma, André, 2004. "Price Dispersion and Consumer Reservation Prices," CEPR Discussion Papers 4618, C.E.P.R. Discussion Papers.
  13. Shilony, Yuval, 1977. "Mixed pricing in oligopoly," Journal of Economic Theory, Elsevier, vol. 14(2), pages 373-388, April.
  14. Bliss, Christopher, 1988. "A Theory of Retail Pricing," Journal of Industrial Economics, Wiley Blackwell, vol. 36(4), pages 375-91, June.
  15. Jennifer F. Reinganum, 1978. "A Simple Model of Equilibrium Price Dispersion," Discussion Papers 335, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  16. Rob, Rafael, 1985. "Equilibrium Price Distributions," Review of Economic Studies, Wiley Blackwell, vol. 52(3), pages 487-504, July.
  17. Dastidar, Krishnendu Ghosh, 1997. "Comparing Cournot and Bertrand in a Homogeneous Product Market," Journal of Economic Theory, Elsevier, vol. 75(1), pages 205-212, July.
  18. Michael R. Baye & John Morgan, 2001. "Information Gatekeepers on the Internet and the Competitiveness of Homogeneous Product Markets," American Economic Review, American Economic Association, vol. 91(3), pages 454-474, June.
  19. Varian, Hal R, 1980. "A Model of Sales," American Economic Review, American Economic Association, vol. 70(4), pages 651-59, September.
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Citations

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Cited by:
  1. Bruno Aurichio & Luis H. B. Braido, 2009. "Dynamic Price Competition in Auto-Insurance Brokerage," Fucape Working Papers 17, Fucape Business School.
  2. Monteiro, Paulo K. & Page Jr., Frank H., 2009. "Endogenous mechanisms and Nash equilibrium in competitive contracting games," Journal of Mathematical Economics, Elsevier, vol. 45(9-10), pages 664-678, September.

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