An Aggregation Method for Large-Scale Dynamic Games

50 Pages Posted: 10 Mar 2020

See all articles by Carlos Daniel Santos

Carlos Daniel Santos

New University of Lisbon - Nova School of Business and Economics

Date Written: January 17, 2020

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%.

Keywords: Aggregation, Curse of Dimensionality, Dynamic Games, Reputation, Markov Perfect Equilibrium

Suggested Citation

Santos, Carlos Daniel, An Aggregation Method for Large-Scale Dynamic Games (January 17, 2020). Available at SSRN: https://ssrn.com/abstract=3521302 or http://dx.doi.org/10.2139/ssrn.3521302

Carlos Daniel Santos (Contact Author)

New University of Lisbon - Nova School of Business and Economics ( email )

Campus de Campolide
Lisbon, 1099-032
Portugal

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