Avoiding the curse of dimensionality in dynamic stochastic games

Abstract

Discrete-time stochastic games with a flnite number of states have been widely applied to study the strategic interactions among forward-looking players in dynamic environments. However, these games sufier 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 flnite number of states, and show that continuous time has substantial computational and conceptual 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. Overall, the continuous-time approach opens the way to analyze more complex and realistic stochastic games than currently feasible.