• Open Access

Avoiding the curse of dimensionality in dynamic stochastic games

Authors

  • Ulrich Doraszelski,

    1. University of Pennsylvania and CEPR; doraszelski@wharton.upenn.edu
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  • Kenneth L. Judd

    1. Hoover Institution and NBER; judd@hoover.stanford.edu
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    • We thank Victor Aguirregabiria, Ken Arrow, Lanier Benkard, Michaela Draganska, Gautam Gowrisankaran, Rustam Ibragimov, Sarit Markovich, Ariel Pakes, Katja Seim, Gabriel Weintraub, a co-editor, two anonymous referees, 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 2006–2007.


Abstract

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. These games suffer from a “curse of dimensionality” when 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 argue that continuous time may have substantial advantages. In particular, under widely used laws of motion, continuous time avoids the curse of dimensionality in computing expectations, 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.

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