Quantitative Economics: Mar, 2012, Volume 3, Issue 1

Avoiding the curse of dimensionality in dynamic stochastic games

Ulrich Doraszelski, Kenneth L. Judd

Discrete-time stochastic games with a finite number of states have been widely
applied to study the strategic interactions among forward-looking players in dy-
namic environments. These games suffer from a “curse of dimensionality” when
the cost of computing players’ expectations over all possible future states in-
creases exponentially in the number of state variables. We explore the alterna-
tive of continuous-time stochastic games with a finite number of states and ar-
gue that continuous time may have substantial advantages. In particular, under
widely used laws of motion, continuous time avoids the curse of dimensional-
ity 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.
Keywords. Dynamic stochastic games, continuous time, Markov perfect equilib-
rium, numerical methods.
JEL classification. C63, C73, L13.

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