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On the existence of coalition-proof Bertrand equilibrium

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  • R. R. Routledge

    (University of Liverpool)

Abstract

In Baye and Morgan (Econ Theory 19:271–282, 2002) and Hoernig (Econ Theory 31:573–585, 2007), sufficient conditions for the existence of Bertrand equilibrium with arbitrary sharing rules were provided. Here, sufficient conditions for the existence of a coalition-proof Bertrand equilibrium with an arbitrary tie-breaking rule are provided. A classical Bertrand game in which sellers have convex costs is analyzed and sufficient conditions for the existence of coalition-proof Bertrand equilibrium which admit discontinuities in tied payoffs and a general class of tie-breaking rules are stated. Finally, an example is provided where one of the conditions is violated and there is non-existence of coalition-proof Bertrand equilibrium. This work generalizes an existence result of Chowdhury and Sengupta (Econ Theory 24:307–324, 2004).

Suggested Citation

  • R. R. Routledge, 2013. "On the existence of coalition-proof Bertrand equilibrium," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 1(1), pages 21-31, May.
    • Handle: RePEc:spr:etbull:v:1:y:2013:i:1:d:10.1007_s40505-013-0011-7
    DOI: 10.1007/s40505-013-0011-7
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    References listed on IDEAS

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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.
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    6. Prabal Chowdhury & Kunal Sengupta, 2004. "Coalition-proof Bertrand equilibria," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 24(2), pages 307-324, August.
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    More about this item

    Keywords

    Equilibrium existence; Discontinuous payoffs; Coalition-proofness; Bertrand games;
    All these keywords.

    JEL classification:

    • 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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