Improving Policy Functions in High-Dimensional Dynamic Games

In this paper, we propose a method for finding policy function improvements for a single agent in high-dimensional Markov dynamic optimization problems, focusing in particular on dynamic games. Our approach combines ideas from literatures in Machine Learning and the econometric analysis of games to derive a one-step improvement policy over any given benchmark policy. In order to reduce the dimensionality of the game, our method selects a parsimonious subset of state variables in a data-driven manner using a Machine Learning estimator. This one-step improvement policy can in turn be improved upon until a suitable stopping rule is met as in the classical policy function iteration approach. We illustrate our algorithm in a high-dimensional entry game similar to that studied by Holmes (2011) and show that it results in a nearly 300 percent improvement in expected profits as compared with a benchmark policy.