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Bertrand-Edgeworth Equilibrium in Oligopoly

Author

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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.

Suggested Citation

  • Hirata, Daisuke, 2008. "Bertrand-Edgeworth Equilibrium in Oligopoly," MPRA Paper 7946, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:7946
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    References listed on IDEAS

    as
    1. Roy Chowdhury, Prabal, 2008. "Bertrand-Edgeworth equilibrium with a large number of firms," International Journal of Industrial Organization, Elsevier, vol. 26(3), pages 746-761, May.
    2. Boccard, Nicolas & Wauthy, Xavier, 2000. "Bertrand competition and Cournot outcomes: further results," Economics Letters, Elsevier, vol. 68(3), pages 279-285, September.
    3. Vives, Xavier, 1986. "Rationing rules and Bertrand-Edgeworth equilibria in large markets," Economics Letters, Elsevier, vol. 21(2), pages 113-116.
    4. Huw Dixon, 1987. "Approximate Bertrand Equilibria in a Replicated Industry," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 54(1), pages 47-62.
    5. Chowdhury, Prabal Roy, 2003. "Bertrand-Edgeworth equilibrium large markets with non-manipulable residual demand," Economics Letters, Elsevier, vol. 79(3), pages 371-375, June.
    6. 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.
    7. Unknown, 1986. "Letters," Choices: The Magazine of Food, Farm, and Resource Issues, Agricultural and Applied Economics Association, vol. 1(4), pages 1-9.
    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. Beth Allen & Martin Hellwig, 1986. "Bertrand-Edgeworth Oligopoly in Large Markets," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(2), pages 175-204.
    10. 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.
    11. repec:ebl:ecbull:v:4:y:2003:i:30:p:1-8 is not listed on IDEAS
    12. William A. Brock & José A. Scheinkman, 1985. "Price Setting Supergames with Capacity Constraints," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 52(3), pages 371-382.
    13. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Hirata Daisuke, 2009. "Asymmetric Bertrand-Edgeworth Oligopoly and Mergers," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 9(1), pages 1-25, July.
    2. De Francesco, Massimo A. & Salvadori, Neri, 2015. "Bertrand-Edgeworth games under triopoly: the payoffs," MPRA Paper 64638, University Library of Munich, Germany.
    3. De Francesco, Massimo A. & Salvadori, Neri, 2008. "Bertrand-Edgeworth games under oligopoly with a complete characterization for the triopoly," MPRA Paper 10767, University Library of Munich, Germany, revised 26 Sep 2008.
    4. Kalyan Talluri & Victor Martínez-de-Albéniz, 2010. "Dynamic Price Competition with Fixed Capacities," Working Papers 425, Barcelona School of Economics.
    5. De Francesco, Massimo A. & Salvadori, Neri, 2016. "Bertrand-Edgeworth games under triopoly: the equilibrium strategies when the payoffs of the two smallest firms are proportional to their capacities," MPRA Paper 69999, University Library of Munich, Germany.
    6. 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.

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    More about this item

    Keywords

    Price Competition; Oligopoly; Capacity Constraint; Homogeneous Goods;
    All these keywords.

    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

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