First and Second Mover Advantage in Asymmetric Price Duopoly

Abstract

We consider the issue of first versus second mover advantage in differentiated-product Bertrand duopoly with asymmetric linear costs. We provide a generalization of some well-known results in the cases where prices are strategic substitutes or complements, dispensing with extraneous assumptions of single-valued optimal reactions, uniqueness of Bertrand equilibrium, ... We also consider a new mixed case. Our approach is based on the theory of supermodular optimization/games. Furthermore, we show that even when prices are strategic complemnts, one firm may have a first mover advantage under a linear demand.