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Existence of pure strategy equilibria in Bertrand-Edgeworth games with imperfect divisibility of money

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  • De Francesco, Massimo A.

Abstract

This paper incorporates imperfect divisibility of money in a price game where a given number of identical firms produce a homogeneous product at constant unit cost up to capacity. We find necessary and sufficient conditions for the existence of a pure strategy equilibrium. Unlike in the continuous action space case, under discrete pricing there may be a range of symmetric pure strategy equilibria - which we fully characterize - a range which may or may not include the competitive price. Also, we determine the maximum number of such equilibria when competitive pricing is itself an equilibrium.

Suggested Citation

  • De Francesco, Massimo A., 2008. "Existence of pure strategy equilibria in Bertrand-Edgeworth games with imperfect divisibility of money," MPRA Paper 10826, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:10826
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    1. Dastidar, Krishnendu Ghosh, 1995. "On the Existence of Pure Strategy Bertrand Equilibrium," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 5(1), pages 19-32, January.
    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. Vives, Xavier, 1986. "Rationing rules and Bertrand-Edgeworth equilibria in large markets," Economics Letters, Elsevier, vol. 21(2), pages 113-116.
    4. Dixon, Huw David, 1993. "Integer Pricing and Bertrand-Edgeworth Oligopoly with Strictly Convex Costs: Is It Worth More Than a Penny?," Bulletin of Economic Research, Wiley Blackwell, vol. 45(3), pages 257-268, July.
    5. Jean Tirole, 1988. "The Theory of Industrial Organization," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262200716.
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    7. Harrington, Joseph Jr., 1989. "A re-evaluation of perfect competition as the solution to the Bertrand price game," Mathematical Social Sciences, Elsevier, vol. 17(3), pages 315-328, June.
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    More about this item

    Keywords

    Bertrand-Edgeworth competition; Price game; Oligopoly; Pure strategy equilibrium; Discrete pricing;
    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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