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Bertrand-Edgeworth equilibrium with a large number of firms

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  • Roy Chowdhury, Prabal

Abstract

We examine a model of price competition with strictly convex costs where the firms simultaneously decide on both price and quantity, are free to supply less than the quantity demanded, and there is discrete pricing. If firms are symmetric then, for a large class of residual demand functions, there is a unique equilibrium in pure strategies whenever, for a fixed grid size, the number of firms is sufficiently large. Moreover, this equilibrium price is within a grid-unit of the competitive price. The results go through to a large extent when the firms are asymmetric, or they are symmetric but play a two stage game and the tie-breaking rule is `weakly manipulable'.

Suggested Citation

  • Roy Chowdhury, Prabal, 2007. "Bertrand-Edgeworth equilibrium with a large number of firms," MPRA Paper 3353, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:3353
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    Cited by:

    1. Hirata, Daisuke, 2008. "Bertrand-Edgeworth Equilibrium in Oligopoly," MPRA Paper 7946, University Library of Munich, Germany.
    2. 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.
    3. van den Berg, Anita & Bos, Iwan, 2017. "Collusion in a price-quantity oligopoly," International Journal of Industrial Organization, Elsevier, vol. 50(C), pages 159-185.
    4. repec:ebl:ecbull:v:12:y:2008:i:29:p:1-8 is not listed on IDEAS
    5. Massimo A. De Francesco, 2008. "Existence of pure strategy equilibrium in Bertrand-Edgeworth games with imperfect divisibility of money," Economics Bulletin, AccessEcon, vol. 12(29), pages 1-8.

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    More about this item

    Keywords

    Bertrand equilibrium; Edgeworth paradox; tie-breaking rule; rationing rule; folk theorem of perfect competition;
    All these keywords.

    JEL classification:

    • D41 - Microeconomics - - Market Structure, Pricing, and Design - - - Perfect Competition
    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection
    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets

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