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Relative profit maximization in asymmetric oligopoly: Cournot and Bertrand equilibria

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  • Satoh, Atsuhiro
  • Tanaka, Yasuhito

Abstract

We analyze Bertrand and Cournot equilibria in an asymmetric oligopoly with more than two firms 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: Cournot and Bertrand equilibria," MPRA Paper 55883, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:55883
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    References listed on IDEAS

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    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. 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.
    5. 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.
    6. 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.
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    8. 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. 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.
    2. 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.
    3. 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.
    4. 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.
    5. Atsuhiro Satoh & Yasuhito Tanaka, 2014. "Relative Profit Maximization in Duopoly: Difference or Ratio," International Journal of Business and Economics, School of Management Development, Feng Chia University, Taichung, Taiwan, vol. 13(2), pages 127-141, December.
    6. 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.
    7. 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.
    8. Philipowski Robert, 2019. "Irrelevance of the Strategic Variable in the Case of Relative Performance Maximization," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 19(1), pages 1-7, January.
    9. 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.
    10. 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.
    11. Tanaka, Yasuhito & Satoh, Atsuhiro, 2016. "Maximin and minimax strategies in asymmetric duopoly: Cournot and Bertrand," MPRA Paper 73925, University Library of Munich, Germany.
    12. Satoh, Atsuhiro & Tanaka, Yasuhito, 2016. "Choice of Strategic Variables by Relative Profit Maximizing Firms in Oligopoly," Economic Review, Hitotsubashi University, vol. 67(1), pages 17-25, January.
    13. 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.
    14. Atsuhiro Satoh & Yasuhito Tanaka, 2014. "Relative profit maximization in asymmetric oligopoly," Economics Bulletin, AccessEcon, vol. 34(3), pages 1653-1664.
    15. 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).
    16. 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.
    17. 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.
    18. PAPADOPOULOS Kosmas & SARAFOPOULOS Georges, 2019. "Dynamics of a Cournot Game with Differentiated Goods and Asymmetric Cost Functions based on Relative Profit Maximization," European Journal of Interdisciplinary Studies, Bucharest Economic Academy, issue 02, June.
    19. 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.
    20. 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.
    21. 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.
    22. 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).
    23. 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

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