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

Author

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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, EconSciences Journals, vol. 3(3), pages 513-523, September.
    • Handle: RePEc:cvv:journ1:v:3:y:2016:i:3:p:513-523
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    1. 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.
    2. 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.
    3. Yasuhito Tanaka, 2013. "Equivalance of Cournot and Bertrand equilibria in differentiated duopoly under relative profit maximization with linear demand," Economics Bulletin, AccessEcon, vol. 33(2), pages 1479-1486.
    4. 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.
    5. Fernando Vega-Redondo, 1997. "The Evolution of Walrasian Behavior," Econometrica, Econometric Society, vol. 65(2), pages 375-384, March.
    6. Armen A. Alchian, 1950. "Uncertainty, Evolution, and Economic Theory," Journal of Political Economy, University of Chicago Press, vol. 58(3), pages 211-211.
    7. Masahiko Hattori & Yasuhito Tanaka, 2014. "Incentive for adoption of new technology in duopoly under absolute and relative profit maximization," Economics Bulletin, AccessEcon, vol. 34(3), pages 2051-2059.
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    2. Peng, Yu & Xiao, Yue & Lu, Qian & Wu, Xue & Zhao, Yueru, 2020. "Chaotic dynamics in Cournot duopoly model with bounded rationality based on relative profit delegation maximization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 560(C).
    3. Atsuhiro Satoh & Yasuhito Tanaka, 2014. "Free Entry Oligopoly, Cournot, Bertrand and Relative Profit Maximization," International Journal of Business and Economics, School of Management Development, Feng Chia University, Taichung, Taiwan, vol. 13(2), pages 143-155, December.

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    Keywords

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    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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