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. 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.