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Bertrand-Edgeworth Equilibrium in Oligopoly

  • Hirata, Daisuke

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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  1. Prabal Roy Chowdhury, 2004. "Bertrand-Edgeworth equilibrium with a large number of firms," Indian Statistical Institute, Planning Unit, New Delhi Discussion Papers 04-12, Indian Statistical Institute, New Delhi, India.
  2. Vives, Xavier, 1986. "Rationing rules and Bertrand-Edgeworth equilibria in large markets," Economics Letters, Elsevier, vol. 21(2), pages 113-116.
  3. Dixon, Huw, 1987. "Approximate Bertrand Equilibria in a Replicated Industry," Review of Economic Studies, Wiley Blackwell, vol. 54(1), pages 47-62, January.
  4. 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).
  5. Osborne, Martin J. & Pitchik, Carolyn, 1983. "Price Competition in a Capacity-Constrained Duopoly," Working Papers 83-08, C.V. Starr Center for Applied Economics, New York University.
  6. Allen, Beth & Hellwig, Martin, 1986. "Bertrand-Edgeworth Oligopoly in Large Markets," Review of Economic Studies, Wiley Blackwell, vol. 53(2), pages 175-204, April.
  7. 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.
  8. 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.
  9. Chowdhury, Prabal Roy, 2003. "Bertrand-Edgeworth equilibrium large markets with non-manipulable residual demand," Economics Letters, Elsevier, vol. 79(3), pages 371-375, June.
  10. 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.
  11. 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.
  12. repec:ebl:ecbull:v:4:y:2003:i:30:p:1-8 is not listed on IDEAS
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