Abstract: Assuming that production price(stochastic demand) follows geometric Brown motion with jumps,uncertainty features coming from sudden events and future market in the research and development projects can be simulated.Previous duopoly option game models in which the stochastic demand follows geometric Brown motion to simulate market uncertainties are extended.In the same time,real option approach under geometric Brown motion with jumps merges with the competition strategic interaction.And sensitivity analyses show that different uncertainties effect on research and development projects option value and the participants' entry threshold.The more is uncertainty,the more is participants' threshold.Sudden events occurring can reduce the project option value.If market uncertainty is lager,the follower's option value will increase,but the leader's value does not always increase.

Key words: option game, jump diffusion, uncertainty, sudden events