Mixed Duopoly: Differential Game Approach

Previous studies in differential games reveal that intertemporal strategic behaviors have an important role for various economic problems. However, most of their analyses are limited to cases where objective functions are identical among agents. In this paper, we characterize the open-loop Nash equilibrium and the Markov perfect Nash equilibrium of a mixed duopoly game where a fully or partially state-owned firm and a fully private rm compete in the quantities of homogeneous goods with sticky prices. We show that in the Markov perfect Nash equilibrium, an increase in the governments' share-holdings of the state-owned firm has a non-monotonic effect on the price, and in a wide range of parameter spaces, it increases the price. These results are derived from the interaction of an asymmetric structure of agents' objectives and inter-temporal strategic behaviors, which are in sharp contrast with those in the open-loop Nash equilibrium. We provide new implications for privatization policies in the presence of dynamic interactions, against the static analyses.