This paper investigates a duopoly with two alternative investment projects. We examine a situation in which a firm cannot invest in any project that has been taken by the rival firm. The first mover's advantage in project choice leads to an equilibrium quite different from that in previous studies. Specifically, we show that in equilibrium, the investment time and the option value are between those in a duopoly with one project and a monopoly with one project. Moreover, we show that a high correlation between project values, unlike in a monopoly with two projects, plays a positive role in mitigating preemptive competition. The results complement the literature of real options games and of max-options and entail new empirical implications.