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Relative profit maximization and irrelevance of leadership in Stackelberg model

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  • Tanaka, Yasuhito

Abstract

We study the Stackelberg equilibrium in a symmetric duopoly with differentiated goods in which each firm maximizes its relative profit that is the difference between its profit and the profit of the rival firm. We show that the equilibrium output and price of the good of the leader and those of the follower are equal, that is, the role of leader or follower is irrelevant to the equilibrium, and the equilibrium outputs and prices do not change between the case where the firms are quantity setting firms and the case where the firms are price setting firms. We assume that demand functions are linear and symmetric, the marginal costs of the firms are common and constant, and the fixed costs are zero.

Suggested Citation

  • Tanaka, Yasuhito, 2014. "Relative profit maximization and irrelevance of leadership in Stackelberg model," MPRA Paper 55887, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:55887
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    References listed on IDEAS

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    1. 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.
    2. Efe A. Ok & Levent KoÚkesen, 2000. "Negatively interdependent preferences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 17(3), pages 533-558.
    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. Fernando Vega-Redondo, 1997. "The Evolution of Walrasian Behavior," Econometrica, Econometric Society, vol. 65(2), pages 375-384, March.
    5. 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.
    6. 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.
    7. 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.
    8. Toshihiro Matsumura & Noriaki Matsushima & Susumu Cato, 2009. "Relative Performance and R&D Competition," ISER Discussion Paper 0752, Institute of Social and Economic Research, Osaka University.
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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. Tanaka, Yasuhito, 2018. "Stackelberg type dynamic zero-sum game with leader and follower," MPRA Paper 89612, University Library of Munich, Germany.
    3. 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.
    4. Jumpei Hamamura & Vinay Ramani, 2023. "Social performance versus relative performance evaluation, asymmetric costs, and quantity competition under managerial delegation," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 44(3), pages 1706-1719, April.
    5. 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.
    6. Jumpei Hamamura, 2021. "What level do disadvantaged firms weight rivals' profits in relative performance evaluations under quantity competition?," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 42(2), pages 493-501, March.
    7. 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.
    8. 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.

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    More about this item

    Keywords

    differentiated duopoly; relative profit maximization; Stackelberg model; irrelevance of leadership;
    All these keywords.

    JEL classification:

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

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