Mean Field Control of Large Population Stochastic Systems
Final rept. 1 May 2009-30 Apr 2012
ROYAL INSTITUTION FOR THE ADVANCEMENT OF LEARNING MONTREAL (CANADA)
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Multi-agent competitive and cooperative systems occur in a vast range of designed and natural settings such as communication, economic, energy and transportation systems. However, the complexity of such large population stochastic dynamic systems, and frequently their inherent nature, make centralized control infeasible or irrelevant and standard game theoretic analysis intractable. The key idea of Mean Field MF stochastic control or Nash Certainty Equivalence NCE control is that when the agent population is very large individual feedback strategies exist for all of the agents so that each agent will be in an approximate Nash equilibrium with the pre-computable behaviour of the mass of other agents. During the period of receipt of this award significant progress in this research area has been made in this subject area. In particular, as planned, the following topics have been analyzed and computational methodologies generated i a fundamental theory and computational methodology of adaptive MF Stochastic systems, ii a MF Games theory of Consensus and Flocking Systems, iii MF Leader-Follower and Egoist-Altruist systems, iv applications to power markets, and v a fundamental analysis of non-linear Mean Field Systems with Major and Minor players. In this Final Report the main sections are devoted to the five topics listed above. This comprehensive summary of the significant work accomplished within this research program is followed by bibliography of the publications which have been generated by the PI and his collaborators.
- Statistics and Probability