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Relative profit maximization in asymmetric oligopoly

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  • Satoh, Atsuhiro
  • Tanaka, Yasuhito

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

  • Satoh, Atsuhiro & Tanaka, Yasuhito, 2014. "Relative profit maximization in asymmetric oligopoly," MPRA Paper 57598, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:57598
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    References listed on IDEAS

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    9. Yuanzhu Lu, 2011. "The Relative-Profit-Maximization Objective Of Private Firms And Endogenous Timing In A Mixed Oligopoly," The Singapore Economic Review (SER), World Scientific Publishing Co. Pte. Ltd., vol. 56(02), pages 203-213.
    10. Atsuhiro Satoh & Yasuhito Tanaka, 2014. "Relative profit maximization and equivalence of Cournot and Bertrand equilibria in asymmetric duopoly," Economics Bulletin, AccessEcon, vol. 34(2), pages 819-827.
    11. Miller, Nolan H & Pazgal, Amit I, 2001. "The Equivalence of Price and Quantity Competition with Delegation," RAND Journal of Economics, The RAND Corporation, vol. 32(2), pages 284-301, Summer.
    12. Satoh, Atsuhiro & Tanaka, Yasuhito, 2014. "Relative profit maximization and equivalence of Cournot and Bertrand equilibria in an asymmetric differentiated duopoly," MPRA Paper 55895, University Library of Munich, Germany.
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    Cited by:

    1. 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.
    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. "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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. Tanaka, Yasuhito & Satoh, Atsuhiro, 2016. "Maximin and minimax strategies in asymmetric duopoly: Cournot and Bertrand," MPRA Paper 73925, University Library of Munich, Germany.
    10. 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.
    11. 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).
    12. 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.
    13. 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.
    14. 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.
    15. Atsuhiro Satoh & Yasuhito Tanaka, 2018. "Nash equilibrium of partially asymmetric three-players zero-sum game with two strategic variables," Papers 1809.02465, arXiv.org.
    16. 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.
    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. 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.
    19. 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.
    20. Satoh, Atsuhiro & Tanaka, Yasuhito, 2016. "Maximin and minimax strategies in symmetric oligopoly: Cournot and Bertrand," MPRA Paper 75837, University Library of Munich, Germany.

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    More about this item

    Keywords

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

    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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