Optimal Pricing Strategies for New Products in Dynamic Oligopolies

This paper deals with the determination of optimal pricing policies for firms in oligopolistic markets. The problem is studied as a differential game and optimal pricing policies are established as Nash open-loop controls. Cost learning effects are assumed such that unit costs are decreasing with cumulative output. Discounting of future profits is also taken into consideration. Initially, the problem is addressed in a general framework, and we proceed to study some specific cases that are related to models presented in recent literature. Three basic classes of sales dynamics are analyzed: competition with price effects only, competition with price as well as adoption effects, and competition with adoption effects only. In some cases it turns out that results which hold for the monopoly case, carry over to the multi-firm case, in the sense that the qualitative structure of optimal pricing strategies is the same in the monopoly and the oligopoly cases. However, due to competitive interdependencies, differences certainly exist in the levels as well as the rates of change of optimal prices.