Endogenous timing in a mixed duopoly

Abstract

This paper applies the framework of endogenous timing in games to mixed quantity duopoly, wherein a private—domestic or foreign—firm competes with a public, welfare-maximizing firm. A central goal of the paper is to present a unified and general treatment of the basic question of what constitutes the appropriate solution concept—Cournot or Stackelberg—in such duopolies. We show that simultaneous play never emerges as a subgame-perfect equilibrium of the extended game, in sharp contrast to private duopoly games. We demonstrate that this result is due to the objective function of the public firm being increasing in the rival’s output (instead of decreasing for a private firm). We provide sufficient conditions for the emergence of public and/or private leadership equilibrium. In all cases, private profits and social welfare are higher than under the corresponding Cournot equilibrium. We make extensive use of the basic results from the theory of supermodular games in order to avoid common extraneous assumptions such as concavity, existence and uniqueness of the different equilibria, whenever possible. Some policy implications are drawn, in particular those relating to the merits of privatization.