Lumps and Clusters in Duopolistic Investment Games: An Early Exercise Premium Approach

This paper investigates strategic investment policies in a duopolistic continuous-time real options game. Our contribution is twofold, economic and methodological. The former is the recognition that, under fixed costs of investment and time-to-build, a firm's exercise of its capital-replacement option leads to a significant temporary reallocation of the firm's revenues to its competitor. The latter is the introduction of the early exercise premium representation as a valuable device for the characterization of optimal exercise policies in real options games. Assuming exogenous firm roles, we find that (i) as the leader installs its newly purchased capital, the follower's optimal investment policy displays a markedly convex and monotonically decreasing pattern over time, which finds its justification in the temporary transfer of the leader's consumer demand to its competitor, and (ii) once the leader has completed its investment process, the follower's trigger boundary -- i.e., the level of market demand that renders capital replacement optimal -- is time-independent. Moreover, we demonstrate that the follower's willingness to delay investment is enhanced by a longer time-to-build and a more volatile market demand, while it is weakened by a higher quality improvement upon replacement and by a higher expected growth in market demand. Finally, we study the probability that the follower mimics the leader's decision within the leader's time-to-build window. We conclude that, while a higher quality advancement upon investment and a higher growth rate in market demand make it more likely for the follower to exercise its investment option promptly, a higher market uncertainty and a longer time-to-build alter the probability of an investment cluster non-monotonically.