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Pré-Publication, Document De Travail Année : 2011

Stackelberg oligopoly TU-games: characterization of the core and 1-concavity of the dual game

Résumé

In this article we consider Stackelberg oligopoly TU-games in gamma-characteristic function form (Chander and Tulkens 1997) in which any deviating coalition produces an output at a first period as a leader and 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. Generally speaking, for any TU-game we show that the 1-concavity property of its dual game is a necessary and sufficient condition under which the core of the initial game is non-empty and coincides with the set of imputations. The dual game of a Stackelberg oligopoly TU-game is of great interest since it describes the marginal contribution of followers to join the grand coalition by turning leaders. The aim is to provide a necessary and sufficient condition which ensures that the dual game of a Stackelberg oligopoly TU-game satisfies the 1-concavity property. Moreover, we prove that this condition depends on the heterogeneity of firms' marginal costs, i.e., the dual game is 1-concave if and only if firms' marginal costs are not too heterogeneous. This last result extends Marini and Currarini's core non-emptiness result (2003) for oligopoly situations.
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Dates et versions

halshs-00610840 , version 1 (25-07-2011)

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  • HAL Id : halshs-00610840 , version 1

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Theo Driessen, Dongshuang Hou, Aymeric Lardon. Stackelberg oligopoly TU-games: characterization of the core and 1-concavity of the dual game. 2011. ⟨halshs-00610840⟩
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