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The gamma-core in Cournot oligopoly TU-games with capacity constraints

Author

Listed:
  • Aymeric Lardon

    (GATE Lyon Saint-Étienne - Groupe d'Analyse et de Théorie Economique Lyon - Saint-Etienne - ENS de Lyon - École normale supérieure de Lyon - UL2 - Université Lumière - Lyon 2 - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon - UJM - Université Jean Monnet - Saint-Étienne - CNRS - Centre National de la Recherche Scientifique)

Abstract

In cooperative Cournot oligopoly games, it is known that the alpha-core is equal to the beta-core, and both are non-empty if every individual profit function is continuous and concave (Zhao 1999b). Following Chander and Tulkens (1997), we assume that firms react to a deviating coalition by choosing individual best reply strategies. We deal with the problem of the non-emptiness of the induced core, the gamma-core, by two different approaches. The first establishes that the associated Cournot oligopoly TU(Transferable Utility)-games are balanced if the inverse demand function is differentiable and every individual profit function is continuous and concave on the set of strategy profiles, which is a step forward beyond Zhao's core existence result for this class of games. The second approach, restricted to the class of Cournot oligopoly TU-games with linear cost functions, provides a single-valued allocation rule in the gamma-core called NP(Nash Pro rata)-value. This result generalizes Funaki and Yamato's core existence result (1999) from no capacity constraint to asymmetric capacity constraints. Moreover, we provide an axiomatic characterization of this solution by means of four properties: efficiency, null firm, monotonicity and non-cooperative fairness.

Suggested Citation

  • Aymeric Lardon, 2009. "The gamma-core in Cournot oligopoly TU-games with capacity constraints," Post-Print halshs-00544042, HAL.
    • Handle: RePEc:hal:journl:halshs-00544042
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00544042
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    Cited by:

    1. 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.
    2. Stamatopoulos, Giorgos, 2018. "On the gamma-core of asymmetric aggregative games," MPRA Paper 88722, University Library of Munich, Germany.
    3. Meinhardt, Holger Ingmar, 2015. "The Incorrect Usage of Propositional Logic in Game Theory: The Case of Disproving Oneself," MPRA Paper 66637, University Library of Munich, Germany.

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