Nash Certainty Equivalence in Large Population Stochastic Dynamic Games: Connections with the Physics

of Interacting Particle Systems

Professor Peter Caines

McGill University

joint work with M. Huang, The Australian National University

and R. P. Malhamé, Ecole Polytechnique de Montreal

Abstract

We consider large population dynamic games where the agents evolve according to their interacting non-uniform dynamics and are coupled by their individual cost functions. Starting with linear dynamics and quadratic costs, a state aggregation technique is employed to obtain a set of decentralized control laws for the individual that ensures closed-loop stability and a so-called Nash equilibrium property. In order to handle large populations of nonlinear systems (i.e., agents), the Nash Certainty Equivalence (NCE) methodology generalizes via an extension of the theory of uncontrolled interacting particle systems developed by McKean and Vlasov. The general NCE theory treats the controlled version of the particle system model in which each generic individual at a microscopic level interacts with the ensemble of other individuals of which it is itself, in a statistical sense, a representative. This general NCE theory entails the development of a Hamilton-Jacobi-Bellman equation whose coefficients depend upon the probability distribution of the population of agents. Applications to CDMA communications, economics and the schooling behavior of fish and birds will be indicated.

Friday, March 16. 2007

3:30 – 4:30 p.m.

Rm. 1500 EECS