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Bertrand-Edgeworth Equilibrium in Oligopoly

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Hirata, Daisuke

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Abstract

This paper investigates simultaneous move capacity constrained price competition game among three firms. I find that equilibria in an asymmetric oligopoly are substantially different from those in the duopoly and symmetric oligopoly. I characterize mixed strategy equilibria and show there exist possibilities of i) the existence of a continuum of equilibria ii) the smallest firm earning the largest profit per capacity and iii) non-identical supports of equilibrium mixed strategies, all of which never arise either in the duopoly or symmetric oligopoly. In particular, the second finding sheds light on a completely new pricing incentive in Bertrand competitions.

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 7946.

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Date of creation: Mar 2008
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Handle: RePEc:pra:mprapa:7946

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Related research
Keywords: Price Competition Oligopoly Capacity Constraint Homogeneous Goods

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Find related papers by JEL classification:
L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets
C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

This paper has been announced in the following NEP Reports:

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. Chowdhury, Prabal Roy, 2003. "Bertrand-Edgeworth equilibrium large markets with non-manipulable residual demand," Economics Letters, Elsevier, vol. 79(3), pages 371-375, June. [Downloadable!] (restricted)
  2. Vives, Xavier, 1986. "Rationing rules and Bertrand-Edgeworth equilibria in large markets," Economics Letters, Elsevier, vol. 21(2), pages 113-116. [Downloadable!] (restricted)
  3. Boccard, Nicolas & Wauthy, Xavier, 2000. "Bertrand competition and Cournot outcomes: further results," Economics Letters, Elsevier, vol. 68(3), pages 279-285, September. [Downloadable!] (restricted)
  4. Brock, William A & Scheinkman, Jose A, 1985. "Price Setting Supergames with Capacity Constraints," Review of Economic Studies, Blackwell Publishing, vol. 52(3), pages 371-82, July. [Downloadable!] (restricted)
  5. Osborne, Martin J. & Pitchik, Carolyn, 1986. "Price competition in a capacity-constrained duopoly," Journal of Economic Theory, Elsevier, vol. 38(2), pages 238-260, April. [Downloadable!] (restricted)
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  6. Dixon, Huw, 1984. "The existence of mixed-strategy equilibria in a price-setting oligopoly with convex costs," Economics Letters, Elsevier, vol. 16(3-4), pages 205-212. [Downloadable!] (restricted)
  7. Massimo A. De Francesco, 2003. "On a property of mixed strategy equilibria of the pricing game," Economics Bulletin, Economics Bulletin, vol. 4(30), pages 1-8. [Downloadable!]
  8. Dixon, Huw, 1987. "Approximate Bertrand Equilibria in a Replicated Industry," Review of Economic Studies, Blackwell Publishing, vol. 54(1), pages 47-62, January. [Downloadable!] (restricted)
  9. Roy Chowdhury, Prabal, 2007. "Bertrand-Edgeworth equilibrium with a large number of firms," MPRA Paper 3353, University Library of Munich, Germany. [Downloadable!]
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  10. 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)
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  1. De Francesco, Massimo A. & Salvadori, Neri, 2008. "Bertrand-Edgeworth games under oligopoly with a complete characterization for the triopoly," MPRA Paper 8634, University Library of Munich, Germany. [Downloadable!]
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