Cooperative and Non-Cooperative Differential Game Solutions to an Investment and Pricing Problem

A monopoly possesses a finite stock of a resource and wishes to determine an optimal pricing policy. The competitive fringe invests in production capacity and wishes to select an optimal investment rate. Demand towards the monopoly depends on price as well as on the sales rate of the competition. Modelling the situation as a differential game, non-cooperative (Nash and Stackelberg) and cooperative (Pareto) equilibria are determined. Owing to the special structure of the game, these solutions can be found in closed form.