Repeated games with uncertain repeat times are more consistent with natural practice than repeated game with unlimited times. First, this paper proposes both the Cournot model with uncertain repeat times and different game strategies. Second, the paper simulates the course of Cournot model game with uncertain repeat times according to the designed simulation plans. The players' gains for different discount rates are obtained under the condition of each simulation plan. Finally, the paper analyzes the results of every simulation plan and works out the critical discount rate and equilibrium strategy in the statistical sense. In addition, this paper explains the concept of input elasticity of simulation results and analyses the reason why there are differences in the results of different simulation strategies using the concept.