Cournot-Nash equilibrium is introduced into the traditional options game model, and the manifestation of this model under the condition is studied. Besides, a numerical method is used for solving investment values and thresholds of the leader enterprise and the follower enterprise. The results showed that both enterprises still have determined investment thresholds under Cournot-Nash equilibrium. In contrast, the follower enterprise investment threshold has a higher sensitivity to its own factors, but its present investment value is less subject to its own threshold and market demand; the leader enterprise performs contrary to the follower. Comparative advantages of marginal operating costs and investment sunk costs determine enterprise roles.