Dynamic analysis of R&D in an oligopoly under general demand and cost functions

This paper presents an analysis of cost reducing R&D investment in a dynamic oligopoly under general demand and cost functions by differential game approach. The steady state value of the R&D investment by each firm is decreasing in the number of firms. If the direct effect of R&D investment is larger (smaller) than the spillover effect, the steady state value of the industry R&D investment is increasing (decreasing) in the number of firms. If the outputs of the firms are strategic substitutes, the R&D investment by each firm given the cost level is decreasing in the number of firms. If there is no spillover effect of R&D investment, and the outputs of the firms are strategic substitutes (or strategic complements), the R&D investment of each firm given the cost level in a memoryless closed-loop solution is larger (smaller) than that in an open-loop solution. Also we show that if there is no spillover effect of R&D investment, a memoryless closed-loop solution and a feedback solution (by the Hamilton-Jacobi-Bellman equation) are equivalent.