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Equivalence of Cournot and Bertrand equilibria in duopoly under relative profit maximization: A general analysis

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  • Atsuhiro SATOH

    () (Faculty of Economics, Doshisha University, Japan.)

  • Yasuhito TANAKA

    () (Faculty of Economics, Doshisha University, Kyoto, Japan.)

Abstract

We study the relationship between Cournot equilibrium and Bertrand equilibrium in duopoly with differentiated goods in which each firm maximizes its relative profit. We show that Cournot equilibrium and Bertrand equilibrium coincide under relative profit maximization even with general demand and cost functions. This result is due to the fact that a game of relative profit maximization in duopoly is a two-person zero-sum game.

Suggested Citation

  • Atsuhiro SATOH & Yasuhito TANAKA, 2016. "Equivalence of Cournot and Bertrand equilibria in duopoly under relative profit maximization: A general analysis," Journal of Economics and Political Economy, KSP Journals, vol. 3(3), pages 513-523, September.
  • Handle: RePEc:ksp:journ1:v:3:y:2016:i:3:p:513-523
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    References listed on IDEAS

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    1. Armen A. Alchian, 1950. "Uncertainty, Evolution, and Economic Theory," Journal of Political Economy, University of Chicago Press, vol. 58, pages 211-211.
    2. Kandori, Michihiro & Mailath, George J & Rob, Rafael, 1993. "Learning, Mutation, and Long Run Equilibria in Games," Econometrica, Econometric Society, vol. 61(1), pages 29-56, January.
    3. Fernando Vega-Redondo, 1997. "The Evolution of Walrasian Behavior," Econometrica, Econometric Society, vol. 65(2), pages 375-384, March.
    4. Atsuhiro Satoh & Yasuhito Tanaka, 2013. "Relative profit maximization and Bertrand equilibrium with quadratic cost functions," Economics and Business Letters, Oviedo University Press, vol. 2(3), pages 134-139.
    5. Robert Gibbons & Kevin J. Murphy, 1990. "Relative Performance Evaluation for Chief Executive Officers," ILR Review, Cornell University, ILR School, vol. 43(3), pages 30, April.
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    Cited by:

    1. Atsuhiro Satoh & Yasuhito Tanaka, 2014. "Free Entry Oligopoly, Cournot, Bertrand and Relative Profit Maximization," International Journal of Business and Economics, College of Business and College of Finance, Feng Chia University, Taichung, Taiwan, vol. 13(2), pages 143-155, December.

    More about this item

    Keywords

    Relative profit maximization; Duopoly; Cournot equilibrium; Bertrand equilibrium.;

    JEL classification:

    • 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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