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

Author

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  • Massimo A. De Francesco

    () (Department of Economics, University of Siena)

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, with 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

  • 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.
  • Handle: RePEc:ebl:ecbull:eb-08l10034
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    References listed on IDEAS

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    1. Jean Tirole, 1988. "The Theory of Industrial Organization," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262200716, January.
    2. 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.
    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. 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.
    6. 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.
    7. Prabal Roy Chowdhury, 2002. "Limit-pricing as Bertrand equilibrium," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 19(4), pages 811-822.
    8. Chaudhuri, Prabal Ray, 1996. "The contestable outcome as a Bertrand equilibrium," Economics Letters, Elsevier, vol. 50(2), pages 237-242, February.
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    More about this item

    Keywords

    Bertrand-Edgeworth competition;

    JEL classification:

    • L1 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory

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