Price and quality competition in a mixed duopoly : Differential game approach

This paper investigates price and quality competition in a mixed duopoly market, where a state-owned welfare-maximizing public firm competes against a profit-maximizing private firm. We use a differential game approach with a Hotelling spatial competition framework. We extend Cellini et al.(2018) by incorporating a state-owned public firm and derive open- and closed-loop solutions. The steady-state quality levels are optimal in the open-loop solution. Numerical results show that the steady-state quality level of the public firm in the closed-loop solution does not necessarily lower than that in the open-loop solution. As a private firm's investment is large, the public firm’s incentive for quality improvement increases since there exists intertemporal strategic substitutability between investment and quality. Competition and privatization policies are neutral under the open-loop solution but not under the closed-loop solution. Competition policy improves social welfare with an increase in quality and privatization policy improves it with an decrease in quality in the closed-loop solution.