Stochastic Algorithms, Symmetric Markov Perfect Equilibrium, and the 'curse' of Dimensionality
提出一种随机算法，通过近似积分和单点更新避免维数诅咒，用于计算对称马尔可夫完美均衡，在产业组织问题中可大幅提升速度并降低内存需求。
This paper introduces a stochastic algorithm for computing symmetric Markov perfect equilibria. The algorithm computes equilibrium policy and value functions, and generates a transition kernel for the (stochastic) evolution of the state of the system. It has two features that together imply that it need not be subject to the curse of dimensionality. First, the integral that determines continuation values is never calculated; rather it is approximated by a simple average of returns from past outcomes of the algorithm, an approximation whose computational burden is not tied to the dimension of the state space. Second, iterations of the algorithm update value and policy functions at a single (rather than at all possible) points in the state space. Random draws from a distribution set by the updated policies determine the location of the next iteration's updates. This selection only repeatedly hits the recurrent class of points, a subset whose cardinality is not directly tied to that of the state space. Numerical results for industrial organization problems show that our algorithm can increase speed and decrease memory requirements by several orders of magnitude.