Abstract
We develop a notion of subgames and the related notion of subgame-perfect
equilibrium – possibly in mixed strategies – for stochastic timing games. To
capture all situations that can arise in continuous-time models, it is necessary to
consider stopping times as the starting dates of subgames. We generalize Fudenberg
and Tirole’s (1985) mixed-strategy extensions to make them applicable to
stochastic timing games and thereby provide a sound basis for subgame-perfect
equilibria of preemption games. Sufficient conditions for equilibrium existence
are presented, and examples illustrate their application as well as the fact that
intuitive arguments can break down in the presence of stochastic processes with
jumps.