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Bertrand-Edgeworth Duopoly with Proportional Residual Demand

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  • Allen, Beth
  • Hellwig, Martin

Abstract

A complete characterization is given for the prices charged by Bertrand-Edgeworth duopolists with capacity constraints. In general, for the game in which firms' strategy spaces consist of price offers, Nash equilibrium involves nondegenerate mixed strategi es. Equilibria never extend below the highest competitive price. With tw o firms, the Bertrand-Edgeworth model displays a bias for the highest of several market clearing prices. Moreover, these strategies never stop short of the lowest monopoly price. If firms are of unequal siz e, the larger firm assigns positive probability to a monopoly price, possibly even to several monopoly prices. Copyright 1993 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.

Suggested Citation

  • 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.
  • Handle: RePEc:ier:iecrev:v:34:y:1993:i:1:p:39-60
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    Cited by:

    1. van den Berg, Anita & Bos, Iwan, 2017. "Collusion in a price-quantity oligopoly," International Journal of Industrial Organization, Elsevier, pages 159-185.
    2. 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.
    3. Jacobs, Martin & Requate, Till, 2016. "Demand rationing in Bertrand-Edgeworth markets with fixed capacities: An experiment," Economics Working Papers 2016-03, Christian-Albrechts-University of Kiel, Department of Economics.
    4. Tasnadi, Attila, 2004. "Production in advance versus production to order," Journal of Economic Behavior & Organization, Elsevier, vol. 54(2), pages 191-204, June.
    5. Sinitsyn, Maxim, 2008. "Characterization of the support of the mixed strategy price equilibria in oligopolies with heterogeneous consumers," Economics Letters, Elsevier, vol. 99(2), pages 242-245, May.
    6. Jan Zouhar, 2016. "PQ oligopoly, proportional rationing, and randomly ordered consumers," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 24(2), pages 455-471, June.
    7. Attila Tasnádi, 2016. "Endogenous timing of moves in Bertrand–Edgeworth triopolies," International Journal of Economic Theory, The International Society for Economic Theory, vol. 12(4), pages 317-334, December.
    8. Hirata, Daisuke, 2008. "Bertrand-Edgeworth Equilibrium in Oligopoly," MPRA Paper 7946, University Library of Munich, Germany.
    9. Tasnádi, Attila, 2001. "A Bertrand-Edgeworth-oligopóliumok. Irodalmi áttekintés
      [Bertrand-Edgeworth oligopolies - a survey of the literature]
      ," Közgazdasági Szemle (Economic Review - monthly of the Hungarian Academy of Sciences), Közgazdasági Szemle Alapítvány (Economic Review Foundation), vol. 0(12), pages 1081-1092.
    10. Szech, Nora & Weinschenk, Philipp, 2013. "Rebates in a Bertrand game," Journal of Mathematical Economics, Elsevier, vol. 49(2), pages 124-133.
    11. Germano, Fabrizio, 2003. "Bertrand-edgeworth equilibria in finite exchange economies," Journal of Mathematical Economics, Elsevier, vol. 39(5-6), pages 677-692, July.
    12. Sinitsyn, Maxim, 2009. "Price dispersion in duopolies with heterogeneous consumers," International Journal of Industrial Organization, Elsevier, vol. 27(2), pages 197-205, March.
    13. Evan L. Porteus & Hyoduk Shin & Tunay I. Tunca, 2010. "Feasting on Leftovers: Strategic Use of Shortages in Price Competition Among Differentiated Products," Manufacturing & Service Operations Management, INFORMS, vol. 12(1), pages 140-161, November.
    14. Lepore Jason J, 2009. "Consumer Rationing and the Cournot Outcome," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 9(1), pages 1-46, September.
    15. Jacobs, Martin & Requate, Till, 2016. "Bertrand-Edgeworth markets with increasing marginal costs and voluntary trading: Experimental evidence," Economics Working Papers 2016-01, Christian-Albrechts-University of Kiel, Department of Economics.
    16. Chiesa, Gabriella, 2001. "Incentive-Based Lending Capacity, Competition and Regulation in Banking," Journal of Financial Intermediation, Elsevier, vol. 10(1), pages 28-53, January.
    17. Allison, Blake A. & Lepore, Jason J., 2014. "Verifying payoff security in the mixed extension of discontinuous games," Journal of Economic Theory, Elsevier, vol. 152(C), pages 291-303.
    18. Lorz, Oliver, 1997. "A Bertrand model of wage competition with capital mobility," Economics Letters, Elsevier, vol. 56(3), pages 339-343, November.

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