||This thesis analyzes the entry decisions of competing firms in a two-person real option game on an irreversible investment project with uncertainties in revenue returns. Three types of strategic interactions are considered. In the first type, the roles of being the leader and the follower are pre-assigned. The second type is pre-emption where there is some advantage to being the first to take up the investment project. The last type is co-operation between the players. The two players are endowed with different investment costs. When the roles are pre-assigned, higher revenue uncertainties always delay the investment trigger point. Also, higher investment costs lead to delay in investment. For the case of pre-emption, the lower-cost investor always invests earlier. Interestingly, when the level of revenue uncertainty is low and / or positive externalities are sufficiently large, it may occur that greater uncertainties hasten investment. Under the scenario of competitive game, the low-cost leader invests at the same trigger point as that under the case of pre-assigned role. However, the high-cost follower under cooperative game invests earlier when there are positive externalities. The thesis also extends uncertainties to the form that the technological success of the investment is probabilistic, where the actual delivery of the project after investment cost has been sunk is modeled as a Poisson arrival process. The effects of the Poisson arrival rate on entry decisions of the two players under different scenarios are investigated. This research work represents a nice application of real options theory and game theory on the analysis of strategic interactions among competing firms on irreversible investment decisions under various forms of uncertainties.