Improving Policy Functions in High-Dimensional Dynamic Games

NBER Working Paper No. 21124

Issued in April 2015

NBER Program(s):Industrial Organization, Technical Working Papers



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.

Acknowledgments

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Document Object Identifier (DOI): 10.3386/w21124

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