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Stackelberg Oligopoly TU-Games: Characterization and Nonemptiness of the Core

Dongshuang Hou (), Aymeric Lardon () and T. S. H. Driessen ()
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Dongshuang Hou: Department of Applied Mathematics, Northwestern Polytechnical University, 710072, Xi’An, P. R. China
Aymeric Lardon: Université Côte d’Azur, GREDEG, CNRS, Valbonne, France
T. S. H. Driessen: Faculty of Electrical Engineering, Mathematics and Computer Science, Department of Applied Mathematics, University of Twente, P. O. Box 217, 7500 AE Enschede, The Netherlands

International Game Theory Review (IGTR), 2017, vol. 19, issue 04, 1-16

Abstract: In this paper, we consider the dynamic setting of Stackelberg oligopoly TU-games in γ-characteristic function form. Any deviating coalition produces an output at a first period as a leader and then, 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. First, we show that the core of any Stackelberg oligopoly TU-game always coincides with the set of imputations. Second, we provide a necessary and sufficient condition, depending on the heterogeneity of firms’ marginal costs, under which the core is nonempty.

Keywords: Stackelberg oligopoly; TU-game; set of imputations; core (search for similar items in EconPapers)
Date: 2017
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