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

Abstract

In this paper, we consider the dynamic setting of Stackelberg oligopoly TU-games in [Formula: see text]-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.