Cournotian duopolistic firms may be Walrasian: a case in the Gabszewicz and Vial model

Abstract

In this paper, we present a refreshed version of the original model proposed by Gabszewicz and Vial (J Econ Theory 4:381–400, 1972) and we use their main example to review the main theoretical issues related to the notion of Cournot-Walras equilibrium. We compute, in the Gabszewicz and Vial main example, two different Cournot-Walras equilibria associated with different normalization rules. Moreover, in the same example, we compute a Utility-Cournot-Walras equilibrium as defined by Grodal (in: Allen (ed) Economics in a changing world, Macmillan, London, 1996) and we show that it coincides with the unique Walras equilibrium. Furthermore, using a proposition proved by Grodal (1996), we build a normalization rule with respect to which there is a Cournot-Walras equilibrium that coincides with the Utility-Cournot-Walras equilibrium and hence with the unique Walras equilibrium. To the best of our knowledge, this example provides the first case of Cournotian duopolistic firms being Walrasian in a production economy.