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Endogenous interval games in oligopolies and the cores

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  • Aymeric Lardon

    (GREDEG - Groupe de Recherche en Droit, Economie et Gestion - UNS - Université Nice Sophia Antipolis (1965 - 2019) - CNRS - Centre National de la Recherche Scientifique - UniCA - Université Côte d'Azur)

Abstract

In this article we study interval games in oligopolies following the γ-approach. First, we analyze their non-cooperative foundation and show that each coalition is associated with an endogenous real interval. Second, the Hurwicz criterion turns out to be a key concept to provide a necessary and sufficient condition for the non-emptiness of each of the induced core solution concepts: the interval and the standard γ-cores. The first condition permits to ascertain that even for linear and symmetric industries the interval γ-core is empty. Moreover, by means of the approximation technique of quadratic Bézier curves we prove that the second condition always holds, hence the standard γ-core is non-empty, under natural properties of profit and cost functions.

Suggested Citation

  • Aymeric Lardon, 2016. "Endogenous interval games in oligopolies and the cores," Post-Print halshs-00544044, HAL.
    • Handle: RePEc:hal:journl:halshs-00544044
    DOI: 10.1007/s10479-016-2211-7
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00544044
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    14. Paraskevas Lekeas & Giorgos Stamatopoulos, 2014. "Cooperative oligopoly games with boundedly rational firms," Annals of Operations Research, Springer, vol. 223(1), pages 255-272, December.
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    Cited by:

    1. Lina Mallozzi & Juan Vidal-Puga, 2021. "Uncertainty in cooperative interval games: how Hurwicz criterion compatibility leads to egalitarianism," Annals of Operations Research, Springer, vol. 301(1), pages 143-159, June.
    2. Theo Driessen & Dongshuang Hou & Aymeric Lardon, 2011. "Stackelberg oligopoly TU-games: characterization of the core and 1-concavity of the dual game," Working Papers halshs-00610840, HAL.
    3. Stamatopoulos, Giorgos, 2018. "On the gamma-core of asymmetric aggregative games," MPRA Paper 88722, University Library of Munich, Germany.
    4. Martin Černý & Jan Bok & David Hartman & Milan Hladík, 2024. "Positivity and convexity in incomplete cooperative games," Annals of Operations Research, Springer, vol. 340(2), pages 785-809, September.
    5. Aymeric Lardon, 2020. "Convexity of Bertrand oligopoly TU-games with differentiated products," Annals of Operations Research, Springer, vol. 287(1), pages 285-302, April.
    6. Giorgos Stamatopoulos, 2020. "On the $$\gamma $$γ-core of asymmetric aggregative games," Theory and Decision, Springer, vol. 88(4), pages 493-504, May.

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    More about this item

    Keywords

    Interval game; Oligopoly; γ-Cores; Hurwicz criterion; Quadratic Bézier curve;
    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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