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 …nd 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%.

No data? No problem! A Search-based Recommendation System with Cold Starts

“…For example, if in the past a consumer has visited vehicles from cluster 1 three times and has visited clusters 2 and 3 once each, the corresponding state variable is equal to A t = {0.6, 0.2, 0.2} . This approach is based on the work by Santos (2020). The advantage of keeping track of relative frequencies is that it reduces the size of the state space by generating the same number of support points as of a multinomial distribution.…”