Distributed Convergence to Nash Equilibria in Two-network Zero-sum Games

Abstract:
Recent years have seen an increasing interest on networked strategic scenarios where individual agents may cooperate or compete with each other, interact across different layers and with dynamically changing neighbors, and have only access to limited information. This talk is a contribution to this growing body of work. We consider a class of strategic scenarios in which two networks of agents have opposing objectives with regards to the optimization of a common objective function. We assume this function is the result of aggregating individual objective functions, one per agent. Therefore, the network as a whole does not have access to the function to optimize, and individual agents only have a partial knowledge of it. In the resulting zero-sum game, individual agents collaborate with neighbors in their respective network and have only partial knowledge of the state of the agents in the other network. We synthesize distributed strategies for both the case when information among agents flows bi- or uni-directionally, and establish their convergence to Nash equilibria under suitable conditions on the objective functions. The technical approach combines concepts from algebraic graph theory, nonsmooth analysis, consensus algorithms, set-valued dynamical systems, and game theory.

Bio:
Jorge Cortes is an Associate Professor with the Department of Mechanical and Aerospace Engineering at the University of California, San Diego. Dr. Cortes is the author of "Geometric, Control and Numerical Aspects of Nonholonomic Systems" (New York: Springer-Verlag, 2002) and co-author of "Distributed Control of Robotic Networks" (Princeton: Princeton University Press, 2009). He received a NSF CAREER award in 2006 and was the recipient of the 2006 Spanish Society of Applied Mathematics Young Researcher Prize. He has co-authored papers that have won the 2008 IEEE Control Systems Outstanding Paper Award, the 2009 SIAM Review SIGEST selection from the SIAM Journal on Control and Optimization, and the 2012 O. Hugo Schuck Best Paper Award in the Theory category. He is a IEEE Control Systems Society Distinguished Lecturer (2010-2012). He currently serves in the Editorial Board of IEEE Transactions on Automatic Control, IEEE Control Systems Magazine, SIAM Journal on Control and Optimization, Systems and Control Letters, and Journal of Geometric Mechanics. His research interests include cooperative control, game theory, spatial estimation, distributed optimization, and geometric mechanics.