Exit in Duopoly Under Uncertainty

I examine a declining duopoly in which the firms must choose when to exit from the market. The uncertainty is modelled by letting the revenue stream follow a geometric Brownian motion. I consider the Markov-perfect equilibrium in firms' exit strategies. With a low degree of uncertainty there is a unique equilibrium, where one of the firms always exits before the other. When uncertainty is increased, however, another equilibrium with the reversed order of exit may appear, ruining the uniqueness. Whether this happens or not depends on the degree of asymmetry in the firm-specific parameters.