Over the years, economics has profitably imported ideas and methods from applied mathematics and control theory. Mean field games and optimal control theories cast in continuous time are promising tools for studying dynamic stochastic systems in which interactions among large numbers of people influence aggregates that in turn affect the decisions of each individual.
From May 14th to 16th, the 2019 PHBS Conference on Mean Field Games and Control Theory was held at Peking University HSBC Business School (PHBS), providing a platform for mathematicians and economists to exchange ideas on frontier fields. Internationally renowned scholars, such as Diogo Gomes, Philip Yam, Fabio Camilli, Marco Cirant, and Jonathan Payne, were invited to present papers and discuss with participating scholars. These papers covered the main fields of mean field games, control theory, equilibrium strategy, pricing model and stochastic model.
Professor Thomas Sargent
Professor Thomas Sargent, the 2011 Nobel laureate in economics and the director of the Sargent Institute of Quantitative Economics and Finance of PHBS, said in the opening speech that the mean field games and control theory have broad prospects in economics, and he hopes that the conference will promote interdisciplinary exchanges.
Dr. Jonathan Payne
Jonathan Payne, PhD Candidate of Economics at New York University, talked on the application of mean field games theory to economics. He first outlined which economics models are mean field games and the general form of the relevant equations. And then he discussed existence, unique and stability results in the economics literature. Finally, he provided an overview of the computation techniques that economists use to solve Stochastic Mean Field Games.
Professor Diogo Gomes
Diogo Gomes, professor of applied Mathematics and computational science in King Abdullah University, introduced the latest developments in the theory of mean field games and the current main techniques by giving some simple and computation-friendly examples. Then he introduced a price-formation model, a constrained mean-field game, where a large number of small players can store and trade electricity.
Professor Fabio Camilli
Professor Fabio Camilli, from Department of Basic and Applied Sciences for Engineering (SBAI) at Sapienza University of Rome, focused on the application of the mean field games approach to cluster analysis, an important topic in the field of machine learning. Based on the mean field games theory, Dr. Camilli proposed two unsupervised clustering analysis methods, which is different from the classical algorithms.
Professor Marco Cirant
Marco Cirant, research assistant professor of department of Mathematics, Physics and Computer Science at University of Parma, focused on Periodic patterns arising in non-monotone Mean-Field Games. He discussed some mean field games models where agents have a tendency to aggregate. In these models the typical uniqueness and stability of equilibria fail in the long time regime. Then he showed the existence of solutions that exhibit a periodic behavior in time, presented a description of the analytic techniques involved in some numerical experiments.
Professor Philip Yam
Philip Yam, associate professor of Department of Statistics at the Chinese University of Hong Kong, talked on Calculus on Space of Random Variables and Mean Field Theory. He introduced a stochastic model of economic growth to explore optimal savings and population values in a random environment: in a limited time interval, population growth affects the utility of the entire population and capital investment in a random environment. In addition, he explained how to find the Nash equilibrium of differential games among a large number of players, which is vital to disciplines ranging from engineering, economics and finance.
Participants listen to the keynote speech
Scholars from universities such as Wuhan University and China University of Geosciences also delivered lectures and participated in the seminar. Dr. Qing Tang and Dr. Hanbing Liu of China University of Geosciences discussed nonlocal mean field games and optimal control problem of parabolic systems with state constraints. Dr. Qian Lin, who came from School of Economics and Management at Wuhan University, presented on Nash equilibrium payoffs for stochastic differential games.
The group photo of participants
The conference was hosted by the Sargent Institute of Quantitative Economics and Finance (SIQEF) at PHBS was jointly held by Sargent Institute of Quantitative Economics and Finance and Peking University Research Center for Macroeconomics and Finance. SIQEF strives to put mathematics and statistics at the service of quantitative analysis of questions about economics, finance, and government policy. The conference is currently one of the few academic conferences focusing on the frontiers of interdisciplinary majors, attracting scholars from universities, research institutions in the United States, Europe, and Hong Kong to explore the latest trends through academic exchanges.
By Mingming Cao
Edited by Cai Rong and Annie Jin
