Fear of the market or fear of the competitor? Ambiguity in a real options game

In this paper we study a two–player investment game with a first mover advantage in continuous time with stochastic payoffs, driven by a geometric Brownian motion. One of the players is assumed to be ambiguous with max–min 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 player invests at a point where investment is Pareto dominated by waiting) or sequential (one player invests as if she were the exogenously appointed leader). Following the standard literature, the worst–case prior for the ambiguous player if she is the second mover is obtained by setting the lowest possible trend in the set of priors. However, if the ambiguous player is the first mover, then the worst–case prior can be given by either the lowest or the highest trend in the set of priors. This novel result shows that “worst–case prior” in a setting with geometric Brownian motion and –ambiguity over the drift does not always equate to “lowest trend”.