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Bertrand-Edgeworth Equilibrium in Oligopoly

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  • Hirata, Daisuke

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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Bibliographic Info

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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References

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  1. BOCCARD , Nicolas & WAUTHY, Xavier, . "Bertrand competition and Cournot outcomes: futher results," CORE Discussion Papers RP -1474, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  2. Dixon, Huw, 1987. "Approximate Bertrand Equilibria in a Replicated Industry," Review of Economic Studies, Wiley Blackwell, vol. 54(1), pages 47-62, January.
  3. Vives, Xavier, 1986. "Rationing rules and Bertrand-Edgeworth equilibria in large markets," Economics Letters, Elsevier, vol. 21(2), pages 113-116.
  4. repec:ebl:ecbull:v:4:y:2003:i:30:p:1-8 is not listed on IDEAS
  5. Roy Chowdhury, Prabal, 2007. "Bertrand-Edgeworth equilibrium with a large number of firms," MPRA Paper 3353, University Library of Munich, Germany.
  6. Brock, William A & Scheinkman, Jose A, 1985. "Price Setting Supergames with Capacity Constraints," Review of Economic Studies, Wiley Blackwell, vol. 52(3), pages 371-82, July.
  7. Allen, Beth & Hellwig, Martin, 1993. "Bertrand-Edgeworth Duopoly with Proportional Residual Demand," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 34(1), pages 39-60, February.
  8. 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.
  9. Massimo A. De Francesco, 2003. "On a property of mixed strategy equilibria of the pricing game," Economics Bulletin, AccessEcon, vol. 4(30), pages 1-8.
  10. Chowdhury, Prabal Roy, 2003. "Bertrand-Edgeworth equilibrium large markets with non-manipulable residual demand," Economics Letters, Elsevier, vol. 79(3), pages 371-375, June.
  11. 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.
  12. Allen, Beth & Hellwig, Martin, 1986. "Bertrand-Edgeworth Oligopoly in Large Markets," Review of Economic Studies, Wiley Blackwell, vol. 53(2), pages 175-204, April.
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Cited by:
  1. Kalyan Talluri & Víctor Martínez de Albéniz, 2010. "Dynamic price competition with fixed capacities," Economics Working Papers 1205, Department of Economics and Business, Universitat Pompeu Fabra.
  2. 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.
  3. Kalyan Talluri & Víctor Martínez de Albéniz, 2010. "Dynamic Price Competition with Fixed Capacities," Working Papers 425, Barcelona Graduate School of Economics.

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