Avoiding the Curse of Dimensionality in Dynamic Stochastic Games∗

Discrete-time stochastic games with a finite number of states have been widely applied to study the strategic interactions among forward-looking players in dynamic environments. However, these games suffer from a “curse of dimensionality” since the cost of computing players’ expectations over all possible future states increases exponentially in the number of state variables. We explore the alternative of continuous-time stochastic games with a finite number of states and show that continuous time has substantial advantages. Most important, continuous time avoids the curse of dimensionality, thereby speeding up the computations by orders of magnitude in games with more than a few state variables. This much smaller computational burden greatly extends the range and richness of applications of stochastic games. ∗We thank Victor Aguirregabiria, Ken Arrow, Lanier Benkard, Michaela Draganska, Gautam Gowrisankaran, Rustam Ibragimov, Sarit Markovich, Ariel Pakes, Katja Seim, Gabriel Weintraub, and the participants of SITE 2004, the CRES IO Conference in 2005, and the Informs Annual Meeting in 2006 for their comments. Doraszelski gratefully acknowledges the hospitality of the Hoover Institution during the academic year 2006/07. An Online Appendix with supplemental material is available on the authors’ websites. †Cambridge, MA 02138, U.S.A., [email protected]. ‡Stanford, CA 94305-6010, U.S.A., [email protected].