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On noncooperative oligopoly equilibrium in the multiple leader–follower game

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  • Julien, Ludovic A.

Abstract

In this paper, we provide new proofs of existence and uniqueness of a Stackelberg market equilibrium for a multiple leader–follower noncooperative oligopoly model in which heterogeneous firms compete on quantities. To this end, we consider a two-stage game of complete and perfect information in which many leaders interact strategically with many followers. The Stackelberg market equilibrium constitutes a pure strategy subgame perfect Nash equilibrium of this game. Existence and uniqueness are more difficult to handle in this framework, insofar as the presence of several leaders and followers displays a richer set of strategic interactions. Then, to prove existence, we notably provide a new procedure to determine (the conditions under which) the optimal behavior of the followers (may be written) as functions of the sole strategy profile of the leaders. Some examples outline our procedure and discuss our assumptions.

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  • Julien, Ludovic A., 2017. "On noncooperative oligopoly equilibrium in the multiple leader–follower game," European Journal of Operational Research, Elsevier, vol. 256(2), pages 650-662.
    • Handle: RePEc:eee:ejores:v:256:y:2017:i:2:p:650-662
    DOI: 10.1016/j.ejor.2016.06.070
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    Cited by:

    1. Maja Barac & Rafael Moner‐Colonques, 2022. "Leadership in internationalization strategies," Manchester School, University of Manchester, vol. 90(3), pages 293-318, June.
    2. You-hua Chen & Pu-yan Nie & Chan Wang, 2021. "Effects of carbon tax on environment under duopoly," Environment, Development and Sustainability: A Multidisciplinary Approach to the Theory and Practice of Sustainable Development, Springer, vol. 23(9), pages 13490-13507, September.
    3. Ludovic A. Julien, 2017. "Hierarchical Competition and Heterogeneous Behavior in Noncooperative Oligopoly Markets," Post-Print hal-01637298, HAL.
    4. Guennady Ougolnitsky & Anatoly Usov, 2023. "Differential Game-Theoretic Models of Cournot Oligopoly with Consideration of the Green Effect," Games, MDPI, vol. 14(1), pages 1-18, January.
    5. Ludovic A. Julien, 2021. "Noncooperative oligopoly equilibrium in markets with hierarchical competition," Working Papers hal-04159741, HAL.
    6. Guennady Ougolnitsky & Alexey Korolev, 2023. "Game-Theoretic Models of Coopetition in Cournot Oligopoly," Stats, MDPI, vol. 6(2), pages 1-20, May.
    7. Aymeric Lardon, 2020. "Convexity of Bertrand oligopoly TU-games with differentiated products," Annals of Operations Research, Springer, vol. 287(1), pages 285-302, April.

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    More about this item

    Keywords

    Multi-agents systems; Best response; Existence; Uniqueness;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection

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