This paper analyzes the impact of investment cost asymmetry on the optimal real option exercise strategies and the value of firms in duopoly. Both firms have an opportunity to invest in a project enhancing (ceteris paribus) the profit flow. We show that three types of equilibrium strategies exist. Furthermore, we express the critical levels of cost asymmetry delineating the equilibrium regions as functions of basic economic variables. The presence of strategic interactions among the firms leads to counterintuitive results. First, for a certain range of the asymmetry level, a marginal increase in the investment cost of the firm with the cost disadvantage can enhance this firm's own value. Moreover, such a cost increase can reduce the value of the competitor. Finally, we discuss the welfare implications of the optimal exercise strategies and show that the presence of identical firms can result in a socially less desirable outcome than if one of the competitors has a significant cost (dis)advantage.