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Convexity of Bertrand oligopoly TU-games with differentiated products

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  • Aymeric Lardon

    ()
    (GATE Lyon Saint-Etienne - Groupe d'analyse et de théorie économique - CNRS : UMR5824 - Université Lumière - Lyon II - Ecole Normale Supérieure Lettres et Sciences Humaines)

Abstract

In this article we consider Bertrand oligopoly TU-games with differentiated products. We assume that the demand system is Shubik's (1980) and that firms operate at a constant and identical marginal and average cost. First, we show that the alpha and beta- characteristic functions (Aumann 1959) lead to the same class of Bertrand oligopoly TU-games and we prove that the convexity property holds for this class of games. Then, following Chander and Tulkens (1997) we consider the gamma-characteristic function where firms react to a deviating coalition by choosing individual best reply strategies. For this class of games, we show that the Equal Division Solution belongs to the core and we provide a sufficient condition under which such games are convex.

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Bibliographic Info

Paper provided by HAL in its series Post-Print with number halshs-00544056.

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Date of creation: 2010
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Handle: RePEc:hal:journl:halshs-00544056

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Related research

Keywords: Bertrand oligopoly TU-games; Core; Convexity; Equal Division Solution;

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Cited by:
  1. Dongshuang Hou & Theo Driessen & Aymeric Lardon, 2011. "Convexity and the Shapley value in Bertrand oligopoly TU-games with Shubik's demand functions," Working Papers halshs-00610838, HAL.

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