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3rd International Conference on Game Theory for Networks

May 24–26, 2012 | Vancouver, Canada

Prof. Peter E. Caines - McGill University

"The Mean Field Control of Large Population Networks of Economic and Communicating Agents"

Abstract

Multi-agent competitive and cooperative systems occur in a vast range of designed and natural settings such as communication, economic, environmental, epidemiological, transportation and energy systems. However, the complexity of such large population stochastic dynamic systems often makes centralized control infeasible and standard game theoretic analysis intractable.

The principal notion of Mean Field stochastic control is that when the agent population is infinite individual feedback strategies (i.e. control laws) exist for all of the agents so that each agent will be in a Nash equilibrium with the precomputable behaviour of the mass of other agents. However for a wide range of situations it may be shown that when such control laws are applied to finite population systems the Nash equilibrium error vanishes as the population grows without bound.

This talk will introduce the key ideas of this rapidly developing field and will outline recent developments of the methodology to (i) auctions over networks of large populations of agents and (ii) the admission control of call requests on loss networks of large populations of communicating agents.

Bio

Peter Caines received the BA in mathematics from Oxford University in 1967 and the PhD in systems and control theory in 1970 from Imperial College, University of London, under the supervision of David Q. Mayne, FRS.

After periods as a postdoctoral researcher and faculty member at UMIST, Stanford, UC Berkeley, Toronto and Harvard, he joined McGill University, Montreal, in 1980, where he is James McGill Professor and Macdonald Chair in the Department of Electrical and Computer Engineering. In 2000 the adaptive control paper he coauthored with G. C. Goodwin and P. J. Ramadge (*IEEE Transactions on Automatic Control*, 1980) was recognized by the IEEE Control Systems Society as one of the 25 seminal control theory papers of the 20th century.

He is a Life Fellow of the IEEE, a Fellow of SIAM, the Institute of Mathematics and its Applications (UK) and the Canadian Institute for Advanced Research and was elected to the Royal Society of Canada in 2003. In 2009 he received the IEEE Control Systems Society Bode Lecture Prize.

Peter Caines is the author of *Linear Stochastic Systems*}, John Wiley, 1988, and his research interests include stochastic, multi-agent and hybrid systems theory together with their links to renewable energy generation and transmission, communications, physics, economics and biology.