A Differential Duopoly Game with Sticky Prices, Advertising and Differentiated Goods Based on Goodwill: A Memoryless Closed-Loop Nash Equilibrium

This paper develops a differential duopolistic game where goods are differentiated and prices are sticky, and the competitive and informative contents of advertising are explicitly considered, allowing advertising to have market size and business-stealing effects. Compared to previous literature, the novelty of this paper rests on the fact that this paper proposes 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 efforts, and we investigate how good differentiation, advertising and price stickiness interact in shaping the memoryless closed-loop Nash equilibrium allocation, and obtain the following three conclusions. First, the memoryless closed-loop Nash equilibrium output is increasing in product differentiation, price stickiness, and promotional efficiency. Second, the memoryless closed-loop Nash equilibrium advertising efforts are also increasing in both product differentiation and the speed of price adjustment, while the memoryless closed-loop Nash equilibrium advertising efforts is decreasing in promotional efficiency. Third, the steady state level of output is larger in the memoryless closed-loop Nash equilibrium as compared to the Cournot static equilibrium, while the steady state level of prices and advertising efforts is smaller in the memoryless closed-loop Nash equilibrium as compared to the Cournot static equilibrium.