Avoiding the curse of dimensionality in dynamic stochastic games

• 成果类型: Article
• 署名作者: Doraszelski, Ulrich; Judd, Kenneth L.
• 署名单位: University of Pennsylvania; National Bureau of Economic Research
• 刊物名称: QUANTITATIVE ECONOMICS
• ISSN/ISSBN: 1759-7323
• DOI: 10.3982/QE153
• 发表日期: 2012
• 页码: 53-93
• 关键词: Dynamic stochastic games; continuous time; Markov perfect equilibrium; numerical methods

摘要

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.