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Relative profit maximization in asymmetric oligopoly

Author

Listed:
  • Atsuhiro Satoh

    (Faculty of Economics, Doshisha University)

  • Yasuhito Tanaka

    (Faculty of Economics, Doshisha University)

Abstract

We analyze Bertrand and Cournot equilibria in an asymmetric oligopoly in which the firms produce differentiated substitutable goods and seek to maximize their relative profits instead of their absolute profits. Assuming linear demand functions and constant marginal costs we show the following results. If the marginal cost of a firm is lower (higher) than the average marginal cost over the industry, its output at the Bertrand equilibrium is larger (smaller) than that at the Cournot equilibrium, and the price of its good at the Bertrand equilibrium is lower (higher) than that at the Cournot equilibrium.

Suggested Citation

  • Atsuhiro Satoh & Yasuhito Tanaka, 2014. "Relative profit maximization in asymmetric oligopoly," Economics Bulletin, AccessEcon, vol. 34(3), pages 1653-1664.
    • Handle: RePEc:ebl:ecbull:eb-13-00828
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    References listed on IDEAS

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    10. Satoh, Atsuhiro & Tanaka, Yasuhito, 2014. "Relative profit maximization in asymmetric oligopoly: Cournot and Bertrand equilibria," MPRA Paper 55883, University Library of Munich, Germany.
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    Cited by:

    1. Satoh, Atsuhiro & Tanaka, Yasuhito, 2018. "Sion's mini-max theorem and Nash equilibrium in a multi-players game with two groups which is zero-sum and symmetric in each group," MPRA Paper 88977, University Library of Munich, Germany.
    2. Atsuhiro Satoh & Yasuhito Tanaka, 2020. "Sion's minimax theorem and Nash equilibrium of symmetric three-players zero-sum game," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 16(2), pages 279-289.
    3. Atsuhiro Satoh & Yasuhito Tanaka, 2018. "Nash equilibrium of partially asymmetric three-players zero-sum game with two strategic variables," Papers 1809.02465, arXiv.org.
    4. Tanaka, Yasuhito, 2019. "Stackelberg type dynamic symmetric three-players zero-sum game with a leader and two followers," MPRA Paper 91934, University Library of Munich, Germany.
    5. Atsuhiro Satoh & Yasuhito Tanaka, 2019. "Two Person Zero-Sum Game with Two Sets of Strategic Variables," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 21(03), pages 1-15, September.
    6. Satoh, Atsuhiro & Tanaka, Yasuhito, 2016. "Symmetric multi-person zero-sum game with two sets of strategic variables," MPRA Paper 75838, University Library of Munich, Germany.
    7. Satoh, Atsuhiro & Tanaka, Yasuhito, 2017. "Sion's minimax theorem and Nash equilibrium of symmetric multi-person zero-sum game," MPRA Paper 82148, University Library of Munich, Germany.
    8. Tanaka, Yasuhito & Satoh, Atsuhiro, 2016. "Maximin and minimax strategies in asymmetric duopoly: Cournot and Bertrand," MPRA Paper 73925, University Library of Munich, Germany.
    9. Satoh, Atsuhiro & Tanaka, Yasuhito, 2018. "Nash equilibrium in asymmetric multi-players zero-sum game with two strategic variables and only one alien," MPRA Paper 88978, University Library of Munich, Germany.
    10. Tanaka, Yasuhito, 2019. "On the equivalence of Stackelberg equilibrium and static equilibrium of symmetric multi-players zero-sum game," MPRA Paper 91897, University Library of Munich, Germany.
    11. Atsuhiro Satoh & Yasuhito Tanaka, 2018. "On the relation between Sion's minimax theorem and existence of Nash equilibrium in asymmetric multi-players zero-sum game with only one alien," Papers 1806.07253, arXiv.org.
    12. Tanaka, Yasuhito, 2019. "Stackelberg equilibrium of dynamic symmetric multi-players zero-sum game with a leader and followers without differentiability of payoff functions," MPRA Paper 91898, University Library of Munich, Germany.
    13. Li, Hui & Zhou, Wei & Elsadany, A. A & Chu, Tong, 2021. "Stability, multi-stability and instability in Cournot duopoly game with knowledge spillover effects and relative profit maximization," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    14. Masahiko Hattori & Atsuhiro Satoh & Yasuhito Tanaka, 2018. "Minimax theorem and Nash equilibrium of symmetric multi-players zero-sum game with two strategic variables," Papers 1806.07203, arXiv.org.
    15. Satoh, Atsuhiro & Tanaka, Yasuhito, 2016. "Maximin and minimax strategies in symmetric oligopoly: Cournot and Bertrand," MPRA Paper 75837, University Library of Munich, Germany.
    16. Hattori, Masahiko & Satoh, Atsuhiro & Tanaka, Yasuhito, 2018. "Minimax theorem and Nash equilibrium of symmetric three-players zero-sum game with two strategic variables," MPRA Paper 85503, University Library of Munich, Germany.
    17. Satoh, Atsuhiro & Tanaka, Yasuhito, 2018. "The equivalence of mini-max theorem and existence of Nash equilibrium in asymmetric three-players zero-sum game with two groups," MPRA Paper 87249, University Library of Munich, Germany.
    18. Atsuhiro Satoh & Yasuhito Tanaka, 2018. "Maximin and Minimax Strategies in Two-Players Game with Two Strategic Variables," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 20(01), pages 1-13, March.
    19. Tanaka, Yasuhito, 2019. "Analysis of dynamic symmetric three-players zero-sum game with a leader and two followers without differentiability of payoff functions," MPRA Paper 91919, University Library of Munich, Germany.
    20. Atsuhiro Satoh & Yasuhito Tanaka, 2018. "Sion's mini-max theorem and Nash equilibrium in a five-players game with two groups which is zero-sum and symmetric in each group," Papers 1809.02466, arXiv.org.

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    More about this item

    Keywords

    relative profit maximization; asymmetric oligopoly; Cournot and Bertrand equilibria;
    All these keywords.

    JEL classification:

    • D4 - Microeconomics - - Market Structure, Pricing, and Design
    • L1 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance

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