  The timing of strategic exit is one of the most important but difficult
business decisions, especially under competition and uncertainty. Motivated by
this problem, we examine a stochastic game of exit in which players are
uncertain about their competitor's exit value. We construct an equilibrium for
a large class of payoff flows driven by a general one-dimensional diffusion. In
the equilibrium, the players employ sophisticated exit strategies involving
both the state variable and the posterior belief process. These strategies are
specified explicitly in terms of the problem data and a solution to an
auxiliary optimal stopping problem. The equilibrium we obtain is further shown
to be unique within a wide subclass of symmetric Bayesian equilibria.
