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Irrelevance of the choice of strategic variables in duopoly under relative profit maximization

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  • Yasuhito Tanaka

Abstract

We study the choice of strategic variables by firms in a duopoly in which two firms produce differentiated substitutable goods and each firm maximizes its relative profit that is the difference between its profit and the profit of the rival firm. We consider a two stage game such that in the first stage the firms choose their strategic variables and in the second stage they determine the values of their strategic variables. We show that when the firms maximize their relative profits, the choice of strategic variables is irrelevant to the outcome of the game in the sense that the equilibrium outputs, prices and profits of the firms are the same in all situations, and so any combination of strategy choice by the firms constitutes a sub-game perfect equilibrium in the two stage game. We assume that demand functions for the goods are symmetric and linear, the marginal costs of the firms are common and constant, and the fixed costs are zero.

Suggested Citation

  • Yasuhito Tanaka, 2013. "Irrelevance of the choice of strategic variables in duopoly under relative profit maximization," Economics and Business Letters, Oviedo University Press, vol. 2(2), pages 75-83.
  • Handle: RePEc:ove:journl:aid:9904
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    References listed on IDEAS

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    1. Kockesen, Levent & Ok, Efe A. & Sethi, Rajiv, 2000. "The Strategic Advantage of Negatively Interdependent Preferences," Journal of Economic Theory, Elsevier, vol. 92(2), pages 274-299, June.
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    4. 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.
    5. Schaffer, Mark E., 1989. "Are profit-maximisers the best survivors? : A Darwinian model of economic natural selection," Journal of Economic Behavior & Organization, Elsevier, vol. 12(1), pages 29-45, August.
    6. Fernando Vega-Redondo, 1997. "The Evolution of Walrasian Behavior," Econometrica, Econometric Society, vol. 65(2), pages 375-384, March.
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    Cited by:

    1. Satoh, Atsuhiro & Tanaka, Yasuhito, 2015. "Relative profit maximization and the choice of strategic variables in duopoly," MPRA Paper 63000, University Library of Munich, Germany.
    2. 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.
    3. Tanaka, Yasuhito & Satoh, Atsuhiro, 2016. "Maximin and minimax strategies in asymmetric duopoly: Cournot and Bertrand," MPRA Paper 73925, University Library of Munich, Germany.
    4. 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.
    5. Atsuhiro Satoh & Yasuhito Tanaka, 2014. "Choice of strategic variables under relative profit maximization in asymmetric oligopoly: non-equivalence of price strategy and quantity strategy," Economics and Business Letters, Oviedo University Press, vol. 3(2), pages 115-126.
    6. 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.
    7. Atsuhiro Satoh & Yasuhito Tanaka, 2014. "Relative Profit Maximization in Duopoly: Difference or Ratio," International Journal of Business and Economics, College of Business and College of Finance, Feng Chia University, Taichung, Taiwan, vol. 13(2), pages 127-141, December.
    8. Satoh, Atsuhiro & Tanaka, Yasuhito, 2014. "Choice of strategic variables under relative profit maximization in asymmetric oligopoly," MPRA Paper 55886, University Library of Munich, Germany.
    9. Tanaka, Yasuhito, 2014. "Relative profit maximization and irrelevance of leadership in Stackelberg model," MPRA Paper 55887, University Library of Munich, Germany.
    10. Satoh, Atsuhiro & Tanaka, Yasuhito, 2018. "Sion's minimax theorem and Nash equilibrium of symmetric three-players zero-sum game," MPRA Paper 85452, University Library of Munich, Germany.
    11. Satoh, Atsuhiro & Tanaka, Yasuhito, 2016. "Two person zero-sum game with two sets of strategic variables," MPRA Paper 73272, University Library of Munich, Germany.
    12. 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.
    13. Masahiko HATTORI & Yasuhito TANAKA, 2016. "Subsidy for New Technology Adoption in Duopoly with Differentiated Goods under Absolute and Relative Profit Maximization," Journal of Economics Library, KSP Journals, vol. 3(3), pages 411-428, September.
    14. 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.
    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. 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

    JEL classification:

    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection

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