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Stackelberg Oligopoly TU-Games: Characterization and Nonemptiness of the Core

Author

Listed:
  • Dongshuang Hou

    (Department of Applied Mathematics, Northwestern Polytechnical University, 710072, Xi’An, P. R. China)

  • Aymeric Lardon

    (Université Côte d’Azur, GREDEG, CNRS, Valbonne, France)

  • T. S. H. Driessen

    (Faculty of Electrical Engineering, Mathematics and Computer Science, Department of Applied Mathematics, University of Twente, P. O. Box 217, 7500 AE Enschede, The Netherlands)

Abstract

In this paper, we consider the dynamic setting of Stackelberg oligopoly TU-games in γ-characteristic function form. Any deviating coalition produces an output at a first period as a leader and then, outsiders simultaneously and independently play a quantity at a second period as followers. We assume that the inverse demand function is linear and that firms operate at constant but possibly distinct marginal costs. First, we show that the core of any Stackelberg oligopoly TU-game always coincides with the set of imputations. Second, we provide a necessary and sufficient condition, depending on the heterogeneity of firms’ marginal costs, under which the core is nonempty.

Suggested Citation

  • Dongshuang Hou & Aymeric Lardon & T. S. H. Driessen, 2017. "Stackelberg Oligopoly TU-Games: Characterization and Nonemptiness of the Core," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 19(04), pages 1-16, December.
    • Handle: RePEc:wsi:igtrxx:v:19:y:2017:i:04:n:s0219198917500207
    DOI: 10.1142/S0219198917500207
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    References listed on IDEAS

    as
    1. Bloch, Francis & van den Nouweland, Anne, 2014. "Expectation formation rules and the core of partition function games," Games and Economic Behavior, Elsevier, vol. 88(C), pages 339-353.
    2. Marini, Marco A. & Currarini, Sergio, 2003. "A sequential approach to the characteristic function and the core in games with externalities," MPRA Paper 1689, University Library of Munich, Germany, revised 2003.
    3. Parkash Chander & Henry Tulkens, 2006. "The Core of an Economy with Multilateral Environmental Externalities," Springer Books, in: Parkash Chander & Jacques Drèze & C. Knox Lovell & Jack Mintz (ed.), Public goods, environmental externalities and fiscal competition, chapter 0, pages 153-175, Springer.
    4. Hanif D. Sherali & Allen L. Soyster & Frederic H. Murphy, 1983. "Stackelberg-Nash-Cournot Equilibria: Characterizations and Computations," Operations Research, INFORMS, vol. 31(2), pages 253-276, April.
    5. Norde, Henk & Pham Do, Kim Hang & Tijs, Stef, 2002. "Oligopoly games with and without transferable technologies," Mathematical Social Sciences, Elsevier, vol. 43(2), pages 187-207, March.
    6. Paraskevas Lekeas & Giorgos Stamatopoulos, 2014. "Cooperative oligopoly games with boundedly rational firms," Annals of Operations Research, Springer, vol. 223(1), pages 255-272, December.
    7. Driessen, Theo S.H. & Meinhardt, Holger I., 2005. "Convexity of oligopoly games without transferable technologies," Mathematical Social Sciences, Elsevier, vol. 50(1), pages 102-126, July.
    8. repec:dpr:wpaper:0418 is not listed on IDEAS
    9. Aymeric Lardon, 2012. "The γ-core in Cournot oligopoly TU-games with capacity constraints," Theory and Decision, Springer, vol. 72(3), pages 387-411, March.
    10. Ehud Lehrer & Marco Scarsini, 2013. "On the Core of Dynamic Cooperative Games," Dynamic Games and Applications, Springer, vol. 3(3), pages 359-373, September.
    11. Zhao, Jingang, 1999. "A necessary and sufficient condition for the convexity in oligopoly games," Mathematical Social Sciences, Elsevier, vol. 37(2), pages 189-204, March.
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    Cited by:

    1. Kong, Qianqian & Sun, Hao & Xu, Genjiu & Sun, Panfei, 2019. "A limit theorem for the core of Betrand oligopoly games with externalities," Economics Letters, Elsevier, vol. 185(C).
    2. 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

    Stackelberg oligopoly; TU-game; set of imputations; core;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection

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