a Differential R & D Duopoly Game

At each date, the two players play an R & D investment game "followed" by a Cournot quantity setting game. Each player's R & D augments the common stock of technical knowledge and lowers goods production costs for each player. Profit gross of R & D investment expenditures are quadratic in the state (knowledge here) for each player. R & D investment costs are assumed quadratic in each player's investment. The Nash feedback and Nash open-loop solutions differ in general with the feedback solution being "more competitive", i.e., yielding lower production costs in the steady state.