An Aggregation Method for Large-Scale Dynamic Games

Abstract

It is a well known fact that many dynamic games are subject to the curse of dimensionality, limiting the ability to use them in the study of real-world problems. I propose a new method to solve complex large-scale dynamic games using aggregation as an approximate solution. I obtain two fundamental characterization results. First, approximations with small within-state variation in the primitives have a smaller maximum error bound. I provide numerical results which compare the exact errors and the bound. Second, I find that for monotone games, order preserving aggregation is a necessary condition of any optimal aggregation. I suggest using quantiles as a straightforward implementation of an order preserving aggregation architecture for industry distributions. I conclude with an illustration, by solving and estimating a stylized dynamic reputation game for the hotel industry. Simulation results show maximal errors between the exact and approximated solutions below 6%, with average errors below 1%.