Groupe d’études et de recherche en analyse des décisions

Mean Field Games: A Paradigm for Individual-Mass Interactions

Roland P. Malhamé Professeur titulaire, Département de génie électrique, Polytechnique Montréal, Canada

In this talk, I shall argue that Mean Field Games are the natural framework for understanding the peculiar equilibria that might emerge when dynamic agents with vanishing individual influence, interact cooperatively or non cooperatively with a likewise mass of other agents as their numbers become very large. This framework is prevalent in many situations: markets in the absence of monopolies, societal dynamics, many industry dynamics, animal groups from herds to fish schools, social insect societies such as bees and ants, and large scale engineering systems such as the Internet, or currently envisioned so-called smart electrical grids.

I shall present some of the initial theoretical results in the field both in the linear and non linear stochastic dynamic framework. I shall discuss some of the different mathematical approaches that can be followed in analyzing the usefulness of an infinite population Nash or Pareto equilibrium inducing feedback control strategy when applied to a finite but large population. I will then present an illustrative mean field based fish schooling model. Recent generalizations within the linear framework will be discussed, as well as potential directions for future research.

This talk was first given at the 15th International Symposium on Dynamic Games in the Czech Republic (with GERAD as cosponsor). My work in this area was joint with GERAD’s Peter Caines and Minyi Huang, as well as ex McGill- CIM-GERAD Ph.D. student, Mojtaba Nourian.