Improving Policy Functions in High-Dimensional Dynamic Games

47 Pages Posted: 4 May 2015 Last revised: 22 Mar 2023

See all articles by Carlos Manzanares

Carlos Manzanares

Vanderbilt University - College of Arts and Science - Department of Economics

Ying Jiang

University of Washington - Department of Economics

Patrick Bajari

University of Michigan at Ann Arbor - Department of Economics; National Bureau of Economic Research (NBER)

Date Written: April 2015

Abstract

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.

Suggested Citation

Manzanares, Carlos and Jiang, Ying and Bajari, Patrick, Improving Policy Functions in High-Dimensional Dynamic Games (April 2015). NBER Working Paper No. w21124, Available at SSRN: https://ssrn.com/abstract=2602087

Carlos Manzanares (Contact Author)

Vanderbilt University - College of Arts and Science - Department of Economics ( email )

Box 1819 Station B
Nashville, TN 37235
United States

Ying Jiang

University of Washington - Department of Economics ( email )

Box 353330
Seattle, WA 98195-3330
United States

Patrick Bajari

University of Michigan at Ann Arbor - Department of Economics ( email )

611 Tappan Street
Ann Arbor, MI 48109-1220
United States
734-763-5319 (Phone)

HOME PAGE: http://www-personal.umich.edu/~bajari/

National Bureau of Economic Research (NBER)

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