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Correlated equilibria in homogeneous good Bertrand competition

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  • Jann, Ole
  • Schottmüller, Christoph

Abstract

We show that there is a unique correlated equilibrium, identical to the unique Nash equilibrium, in the classic Bertrand oligopoly model with homogeneous goods and identical marginal costs. This provides a theoretical underpinning for the so-called “Bertrand paradox” as well as its most general formulation to date. Our proof generalizes to asymmetric marginal costs and arbitrarily many players in the following way: The market price cannot be higher than the second lowest marginal cost in any correlated equilibrium.

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  • Jann, Ole & Schottmüller, Christoph, 2015. "Correlated equilibria in homogeneous good Bertrand competition," Journal of Mathematical Economics, Elsevier, vol. 57(C), pages 31-37.
    • Handle: RePEc:eee:mateco:v:57:y:2015:i:c:p:31-37
    DOI: 10.1016/j.jmateco.2015.01.005
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    1. R. A. Edwards & R. R. Routledge, 2023. "Existence and uniqueness of Nash equilibrium in discontinuous Bertrand games: a complete characterization," International Journal of Game Theory, Springer;Game Theory Society, vol. 52(2), pages 569-586, June.
    2. de Almeida Prado, Fernando Pigeard & Blavatskyy, Pavlo, 2021. "Existence and uniqueness of price equilibrium in oligopoly model with power demand," Mathematical Social Sciences, Elsevier, vol. 111(C), pages 1-10.

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    More about this item

    Keywords

    Bertrand paradox; Correlated equilibrium; Price competition;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • 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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