The Core in Bertrand Oligopoly TU-Games with Transferable Technologies

Abstract

Abstract In this article we study Bertrand oligopoly TU-games with transferable technologies under the α and β-approaches. We first prove that the core of any game can be partially characterized by associating a Bertrand oligopoly TU-game derived from the most efficient technology. Such a game turns to be an efficient convex cover of the original one. This result implies that the core is non-empty and contains a subset of payoff vectors with a symmetric geometric structure easy to compute. We also deduce from this result that the equal division solution is a core selector satisfying the coalitional monotonicity property on this set of games. Moreover, although the convexity property does not always hold even for standard Bertrand oligopolies, we show that it is satisfied when the difference between the marginal cost of the most efficient firm and the one of the least efficient firm is not too large.