  We introduce a notion of subgames for stochastic timing games and the related
notion of subgame-perfect equilibrium in possibly mixed strategies. While a
good notion of subgame-perfect equilibrium for continuous-time games is not
available in general, we argue that our model is the appropriate version for
timing games. We show that the notion coincides with the usual one for
discrete-time games. Many timing games in continuous time have only equilibria
in mixed strategies -- in particular preemption games, which often occur in the
strategic real option literature. We provide a sound foundation for some
workhorse equilibria of that literature, which has been lacking as we show. We
obtain a general constructive existence result for subgame-perfect equilibria
in preemption games and illustrate our findings by several explicit
applications.
