Abstract:Considering the uncertainty of demand and R&D level, and R & D competition, we construct a geometric Brownian motion with random jump. On this basis, we use real options and Stackelberg game to establish a leader and follower R & D investment decision model. The research on the model shows that the R&D success rate affects the game equilibrium. When the average R&D success rate of the leader is higher than the corresponding success rate of the tangent of the two option values, or the average R&D success rate of the followers is lower than the corresponding success rate of the tangent of the two option values, there is a preemptive equilibrium, otherwise, there is a sequential equilibrium. Leader and follower will postpone R&D investment as the demand fluctuation increases, the competitor’s R&D level increases or the degree of declining in demand increases for R & D success of competitor, advance R&D investment as self R&D level increases. Finally, the validity of the model is verified empirically.