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Bertrand-Edgeworth competition in an almost symmetric oligopoly

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  • De Francesco, Massimo A.
  • Salvadori, Neri

Abstract

We analyze a Bertrand-Edgeworth game in homogeneous product industry, under effcient rationing, constant marginal cost until full capacity utilization, and identical technology across firms. We solve for the equilibrium and establish its uniqueness for capacity configurations in the mixed strategy region of the capacity space such that the capacities of the largest and smallest firm are sufficiently close.

Suggested Citation

  • De Francesco, Massimo A. & Salvadori, Neri, 2010. "Bertrand-Edgeworth competition in an almost symmetric oligopoly," MPRA Paper 24228, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:24228
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    References listed on IDEAS

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    1. 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.
    2. Davidson, Carl & Deneckere, Raymond, 1984. "Horizontal mergers and collusive behavior," International Journal of Industrial Organization, Elsevier, vol. 2(2), pages 117-132, June.
    3. 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.
    4. Vives, Xavier, 1986. "Rationing rules and Bertrand-Edgeworth equilibria in large markets," Economics Letters, Elsevier, vol. 21(2), pages 113-116.
    5. Partha Dasgupta & Eric Maskin, 1986. "The Existence of Equilibrium in Discontinuous Economic Games, I: Theory," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(1), pages 1-26.
    6. Partha Dasgupta & Eric Maskin, 1986. "The Existence of Equilibrium in Discontinuous Economic Games, II: Applications," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(1), pages 27-41.
    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. 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.
    9. 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.
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    Citations

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    Cited by:

    1. 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.
    2. Elliott, M. & Galeotti., A. & Koh., A. & Li, W., 2021. "Market Segmentation Through Information," Cambridge Working Papers in Economics 2105, Faculty of Economics, University of Cambridge.
    3. 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.
    4. Massimo A. De Francesco & Neri Salvadori, 2022. "Bertrand–Edgeworth oligopoly: Characterization of mixed strategy equilibria when some firms are large and the others are small," Metroeconomica, Wiley Blackwell, vol. 73(3), pages 803-824, July.
    5. Mark Armstrong & John Vickers, 2018. "Patterns of Competition with Captive Customers," Economics Series Working Papers 864, University of Oxford, Department of Economics.
    6. 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.
    7. Charlson, G., 2020. "Searching for Results: Optimal Platform Design in a Network Setting," Cambridge Working Papers in Economics 20118, Faculty of Economics, University of Cambridge.
    8. Charlson, G., 2021. "Rating the Competition: Seller Ratings and Intra-Platform Competition," Cambridge Working Papers in Economics 2106, Faculty of Economics, University of Cambridge.
    9. Zhiqi Chen & Gang Li, 2018. "Horizontal Mergers In The Presence Of Capacity Constraints," Economic Inquiry, Western Economic Association International, vol. 56(2), pages 1346-1356, April.
    10. De Francesco, Massimo A. & Salvadori, Neri, 2015. "Bertrand-Edgeworth games under triopoly: the payoffs," MPRA Paper 64638, University Library of Munich, Germany.

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    More about this item

    Keywords

    Bertrand-Edgeworth competition; mixed strategy equilibrium; almost symmetric oligopoly; Mixed strategy equilibrium;
    All these keywords.

    JEL classification:

    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets
    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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