Endogenous timing in a mixed duopoly

This paper addresses the issue of endogenizing the equilibrium solution when a private domestic or foreign \u85 rm competes in the quantities with a public, welfare maximizing \u85rm. Theoretical literature on mixed oligopolies provides results and policy implications that crucially rely on the notion of equilibrium assumed, either sequential or simultaneous. In the framework of the endogenous timing model of Hamilton and Slutsky (1990), we show that simultaneous play never emerges as the equilibrium of mixed duopoly games. We provide su ¢ cient conditions for the emergence of public and/or private leadership equilibria. These results are in sharp contrast with those obtained in private duopoly games in which simultaneous play is the general result. We show that the key di¤erence is in the fact that the objective of a welfare maxi-mizing rm is in general increasing in the rivals output, while the contrary holds for private \u85rms. From a methodological viewpoint we make large use of the basic re-sults of the theory of supermodular games in order to avoid extraneous assumptions such as concavity, existence and uniqueness of the equilibria