Fear of the Market or Fear of the Competitor? Ambiguity in a Real Options Game

In this paper we study an investment game between two firms with a first--mover advantage, where payoffs are driven by a geometric Brownian motion. At least one of the firms is assumed to be ambiguous over the drift, with maxmin preferences over a strongly rectangular set of priors. We develop a strategy and equilibrium concept allowing for ambiguity and show that equilibria can be preemptive (a firm invests at a point where investment is Pareto dominated by waiting) or sequential (one firm invests as if it were the exogenously appointed leader). Following the standard literature, the worst--case prior for an ambiguous firm in the follower role is obtained by setting the lowest possible trend in the set of priors. However, if an ambiguous firm is the first mover, then the worst--case drift can fluctuate between the lowest and the highest trends. This novel result shows that ``worst--case prior'' in a setting with drift ambiguity does not always equate to ``lowest trend''. As a consequence, preemptive pressure reduces. We show that this results in the possibility of firm value being increasing in the level of ambiguity. If only one firm is ambiguous, then the value of the non--ambiguous firm can be increasing in the level of ambiguity of the ambiguous firm.