||In this thesis, we analyze a two-stage investment game between two asymmetric firms by using the real option game approach. In the first stage two firms compete to acquire the patent of a patent-protected product. A firm which has acquired the patent holds the option to commercialize the product in the second stage for monopolistic profit flow with uncertain demand. We investigate the investment game option models under both complete information and asymmetric information cases. In the complete information model, we give a comprehensive study on the investment behaviour of both firms as well as the sleeping patent phenomena. Besides, we also give a full characterization of them with respect to the investment costs and revenue flow rates. In the asymmetric information model, we first derive the optimal investment strategies of both firms. Next, we investigate how the asymmetric information affects the investment behaviour of both firms and the sleeping patent phenomena by comparing the results in complete information model. Under the asymmetric information, both firms will act earlier in order to preempt the opponent. On the other hand, the duration of sleeping patent may be lengthened or shortened depending on whether there is any interchange of winner role between the complete information case and the asymmetric information case.