In prior research, the firm's strategies to enter or to leave a market with irreversible costs have been determined assuming no competition. However, in practice business managers do take into account what their competitors will do in their decision making. In most industries where there are only a handful of major competitors, the effects of competitors' responses to a firm's entry, operating and exit decisions are extremely important. In this paper, the optimal strategies (capacity choices and demand levels at which the firm enters and leaves the market) in the continuous-time case of two firms with different production costs are determined in a duopoly setting. I find that under Cournot competition, the firm with low production cost will enter sooner with a lower capacity and exit later relative to the case where the firm is a monopolist. The firm with high production cost will enter later with a higher capacity and exit earlier relative to the case where the firm is a monopolist. The capacity choice turns out to be an important strategic variable. In the case of Stackelberg competition where the low cost firm is the "leader" and the high cost firm is the "follower", the results are similar. The results are also similar for settings with linear and isoelastic demand functions. The value of the firm with high production cost drops significantly under competition. This points to the importance of having a cost advantage in a competitive market and thereby choosing operating strategies to minimize the effects of competitors' actions.
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