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On Noncooperative Oligopoly Equilibrium in the Multiple Leader-Follower Game

Author

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  • Ludovic A. Julien

    (EconomiX - EconomiX - UPN - Université Paris Nanterre - CNRS - Centre National de la Recherche Scientifique)

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-step game of perfect and complete 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. The existence (and uniqueness) problem is complexified in this framework since strategic interactions occur within each partial game but also between both partial games through sequential decisions. 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 leaders'strategy profile only. Some examples outline our procedure and discuss our assumptions.

Suggested Citation

  • Ludovic A. Julien, 2016. "On Noncooperative Oligopoly Equilibrium in the Multiple Leader-Follower Game," Working Papers hal-04141597, HAL.
    • Handle: RePEc:hal:wpaper:hal-04141597
    Note: View the original document on HAL open archive server: https://hal.science/hal-04141597
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    References listed on IDEAS

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    Cited by:

    1. Ludovic A. Julien, 2024. "Noncooperative oligopoly equilibrium in markets with hierarchical competition," International Journal of Game Theory, Springer;Game Theory Society, vol. 53(2), pages 325-371, June.
    2. Ludovic A. Julien, 2017. "Hierarchical competition and heterogeneous behavior in noncooperative oligopoly markets," Working Papers hal-04141649, HAL.
    3. Aymeric Lardon, 2020. "Convexity of Bertrand oligopoly TU-games with differentiated products," Annals of Operations Research, Springer, vol. 287(1), pages 285-302, April.
    4. 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.
    5. 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.
    6. Guennady Ougolnitsky & Alexey Korolev, 2023. "Game-Theoretic Models of Coopetition in Cournot Oligopoly," Stats, MDPI, vol. 6(2), pages 1-20, May.
    7. Maja Barac & Rafael Moner‐Colonques, 2022. "Leadership in internationalization strategies," Manchester School, University of Manchester, vol. 90(3), pages 293-318, June.

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    More about this item

    Keywords

    Best response functions; 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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