Open-Loop and Closed-Loop Differential Duopolistic Models of Optimal Sticky Prices and Advertising in Product Differentiation Market

This paper develops a differential duopolistic game model of optimal sticky prices and advertising in product differentiation market, and investigates the properties of open-loop, and closed-loop memoryless Nash equilibrium. Specifically, we have made two contributions with respect to the available literature. First, we have proposed the new assumption of the price adjustment speed is decided by the goodwill levels that are composed of consumer preference structure, the levels of the product differentiation and advertising expenditures, which extend the assumptions in existing literature. Second, we have analyzed the case of the closed-loop (memoryless) solution concept, in addition to the open-loop solution. We show that the latter equilibrium entails a larger level of steady state production as compared to the former; both equilibriums entail a larger level of production in steady state than the static Cournot game.