The purpose of this conference is to bring together mathematicians and economists interested in studying dynamic stochastic systems in which interactions among large numbers of people influence aggregates that in turn affect the decisions of each individual. Mean field games and optimal control theories cast in continuous time are promising tools for studying such settings. The conference aims to be a forum to meet new ideas and new people and to exchange ideas. Over the years, economics has profitably imported ideas and methods from applied mathematics and control theory. We believe that this conference will foster net imports to economics in this way once again.
Agenda:
May 14
08:30 Depart from Hotel
08:45-09:00 Registration
09:00-09:10 Opening speech by Thomas J. Sargent
09:10-10:10 Thomas J. Sargent: Income and wealth inequality
10:10-11:10 Diogo Gomes: An Introduction to Mean Field Games
11:10-11:25 Break
11:25-12:25 Philip Yam: Calculus on Space of Random Variables and Mean Field Theory
12:25-13:30 Lunch and break
13:30-14:30 Fabio Camilli: Partial Differential Equations and Mean Field Games on Networks
14:30-14:45 Break
14:45-15:45 Marco Cirant: Periodic Patterns Arising in Non-monotone Mean-Field Games
15:45- 16:45 Hanbing Liu: Optimal Control Problem of Parabolic Systems with State Constraints
16:45-17:00 Group Photo
17:00-18:30 Dinner
18:30 Depart to Hotel
May 15
08:45 Depart from Hotel
09:00-10:00 Diogo Gomes: A Mean-field Game Price Model
10:00-11:00 Philip Yam: Optimal Savings and the Value of Population under Stochastic Environment
11:00-11:15 Break
11:15-12:15 Xue Dong He: On the Equilibrium Strategies for Time Inconsistent Problems in Continuous Time
12:15-13:30 Lunch and break
13:30-14:30 Qian Lin: Nash equilibrium payoffs for stochastic differential games
14:30-14:45 Break
14:45-15:45 Jonathan Payne: Application of Mean Field Game Theory to economics
15:45-17:00 Free discussion and addtional talks
17:00-18:30 Dinner
18:30 Depart to Hotel
May 16
08:45 Depart from Hotel
09:00-10:00 Fabio Camilli: A Mean Field Games Approach to Clustering
10:00-11:00 Qing Tang: On Some Nonlocal Mean Field Games
11:00-11:45 Free discussion and addtional talks
11:45-12:00 Closing speech by Thomas J. Sargent
12:00-13:00 Lunch
Invited Speakers
1、Fabio Camilli，
Department of Basic and Applied Sciences for Engineering (SBAI) ，Sapienza Università di Roma
Talk 1: Partial differential equations and Mean Field Games on networks
In this talk, we will discuss basic aspect of the theory of PDE defined on networks and then, the specific example of the MFG system on networks.
Presented paper: [1] F. Camilli, R. D. Maio, and A. Tosin. Measure-valued solutions to nonlocal transport equations on networks. Journal of Differential Equations, 264(12):7213 – 7241, 2018.
[2] S. Cacace, F. Camilli, Fabio C. Marchi. A numerical method for mean field games on networks. ESAIM: M2AN, 51(1):63–88, 2017.
[3] F. Camilli, C. Marchi, Stationary Mean Field Games systems defined on networks, SIAM J. of Control & Optimization, 54 (2016), no. 2, 1085–1103.
Talk 2: A Mean Field Games approach to clustering In this talk, we will discuss the study of some multi-population MFG systems which mimic the classical EM algorithm in cluster theory.
Presented paper: A Mean Field Games approach to clustering, work in progress.
2、Philip Yam，
Department of Statistics，The Chinese University of HongKong
1) Title: Calculus on Space of Random Variables and Mean Field Theory
Abstract: Mean field games and mean field type control problems (Bensoussan et al. 2013), which aims at searching for the Nash equilibrium of differential games among a large number of players, have become so vital to disciplines ranging from engineering to economics and finance. In this talk, we shall introduce a new calculus technique to study the (infinite- dimensional) forward-backward stochastic differential equations of McKean-Vlasov type arisen from mean field games and mean field type problems. More specifically, after explaining this Hilbert space framework of random variables, we shall provide a sketch of proof of the global unique existence of the solution to mean field systems when the mean field effect is not too large.
Reference: Bensoussan, A., Frehse, J., and Yam, P. (2013). Mean Field Games and Mean Field Type Control Theory (2013). New York: Springer Verlag.
2) Title: Optimal Savings and the Value of Population under Stochastic Environment
Abstract: In the work of Arrow et al. (2007, PNAS), they studied a macroeconomic growth model so that the population dynamic was involved in both the total utility (objective function) of the whole population and in the capital investment process. In essence, they assumed the deterministic evolution for both dynamics, such that the labor force of the population is also incurred through the Cobb–Douglas production function. In this talk, we shall discuss the well-posedness of the extension of their problem, particularly over a finite time horizon, in which we also allow more realistic and generic population growth and incorporate a stochastic environment for both the demography and capital investment. Technically, some novel PDE methodologies have been developed in our work, and we believe that this can be of parallel use in various sophisticated modeling in economic growth theory.
Reference: Arrow, K., Bensoussan, A., Feng, Q., and Sethi, S.P. (2007). Optimal savings and the value of population, Proceedings of the National Academy of Sciences, 47: 18421-6.
3、Qing Tang，
Department of Mathematics，China University of Geosciences (Wuhan)
Talk: On some nonlocal mean field games
In this talk, I will discuss some time-fractional mean field games. We consider the variational structure and optimal transport formulation of a time-fractional second order Mean Field Games (MFG) system with local coupling. The MFG system consists of time-fractional Fokker-Planck and Hamilton-Jacobi-Bellman equations. In such a situation the individual agent follows a non-Markovian dynamics given by a subdiffusion process. Hence, the results of this paper extend the theory of variational MFG to the subdiffusive situation, providing an Eulerian interpretation of timefractional MFG systems.This is joint work with Fabio Camilli. I will also discuss some of my own recent work in progress regarding mean field games with jump diffusion and applications to finance.
Reference: Q. Tang, F. Camilli, Variational time-fractional Mean Field Games, arXiv:1812.05431math.AP.
4、Marco Cirant，
Dipartimento di Scienze Matematiche, Fisiche e Informatiche Università di Parma
Title: Periodic patterns arising in non-monotone Mean-Field Games Abstract: This talk will be devoted to the discussion of some Mean-Field Games models where agents have a tendency to aggregate. In these models the typical uniqueness and stability of equilibria fails in the long time regime. It will be shown the existence of solutions that exhibit a periodic behaviour in time. A description of the analytic techniques involved will be presented, together with some numerical experiments.
Reference: M. Cirant, On the existence of oscillating solutions in non-monotone Mean-Field Games. To appear in J. Differential Equations, 2019.
5、Diogo Gomes，
Professor, Applied Mathematics and Computational Science， Computer, Electrical and Mathematical Science and Engineering Division， King Abdullah University (KAUST)
Talk 1: An introduction to mean field games
Talk 2: TBA
6、Xue Dong He，
Department of Systems Engineering and Engineering Management，The Chinese University of Hong Kong
Paper: He, Xue Dong and Jiang, Zhaoli, On the Equilibrium Strategies for TimeInconsistent Problems in Continuous Time (January 30, 2019). Available at SSRN: https://ssrn.com/abstract=3308274 or http://dx.doi.org/10.2139/ssrn.3308274
