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A Partial Characterization of the Core in Bertrand Oligopoly TU-games with Transferable Technologies

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  • Aymeric Lardon

    (University of Nice Sophia Antipolis, France
    GREDEG CNRS)

Abstract

In this article we study Bertrand oligopoly TU-games with transferable technologies under the Alpha and Beta-approaches (Aumann 1959). Although the convexity property does not always hold, we show that it is satisfied when firms' marginal costs are not too heterogeneous. Furthermore, we prove that the core of any game can be partially characterized by associating a Bertrand oligopoly TU-game derived from the most efficient technology. Such a game turns to be an efficient convex cover (Rulnick and Shapley 1997) of the original one. This result implies that the core is non-empty and contains a subset of payoff vectors with a symmetric geometric structure easy to compute.

Suggested Citation

  • Aymeric Lardon, 2014. "A Partial Characterization of the Core in Bertrand Oligopoly TU-games with Transferable Technologies," GREDEG Working Papers 2014-33, Groupe de REcherche en Droit, Economie, Gestion (GREDEG CNRS), University of Nice Sophia Antipolis.
  • Handle: RePEc:gre:wpaper:2014-33
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    File URL: http://www.gredeg.cnrs.fr/working-papers/GREDEG-WP-2014-33.pdf
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    References listed on IDEAS

    as
    1. Henry Tulkens & Parkash Chander, 1997. "The Core of an Economy with Multilateral Environmental Externalities," International Journal of Game Theory, Springer;Game Theory Society, vol. 26(3), pages 379-401.
    2. 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.
    3. Zhao, J, 1996. "A B-Core Existence Result and its Application to Oligopoly Markets," ISER Discussion Paper 0418, Institute of Social and Economic Research, Osaka University.
    4. Aymeric Lardon, 2018. "Convexity of Bertrand oligopoly TU-games with differentiated products," Post-Print halshs-00544056, HAL.
    5. 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.
    6. 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.
    7. 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.
    8. Ichiishi, Tatsuro, 1981. "Super-modularity: Applications to convex games and to the greedy algorithm for LP," Journal of Economic Theory, Elsevier, vol. 25(2), pages 283-286, October.
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    More about this item

    Keywords

    Bertrand oligopoly TU-games; Transferable technologies; Core; Convexity property;

    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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