The subject of my presentation is motivated by problems at the intersection of game theory and nonlinear dynamical systems. Game theory provides a powerful set of tools for analysis and design of strategic behavior in controlled multi-agent networked systems. In practice, a fundamental problem is that such systems can exhibit phase transitions with often undesirable outcomes. In economics, an example of this is the so-called rational irrationality: "behavior that, on the individual level, is perfectly reasonable but that, when aggregated in the marketplace, produces calamity." Some of these concepts are discussed in my presentation with the aid of a coupled oscillator network model. The main conclusion is that the synchronization of the coupled oscillators can be interpreted as a solution of a non-cooperative dynamic game. The rich theory surrounding the classical Kuramoto model is extended to the dynamic game setting, and used to explain phase transitions in these systems. Applications of the methodology to neuroscience are also briefly outlined. This work is in collaboration with Huibing Yin, Sean Meyn and Uday Shanbhag (Yin, H., P. G. Mehta, S. P. Meyn and U. V. Shanbhag, "Synchronization of Coupled Oscillators is a Game," IEEE Transactions on Automatic Control, 57:4, 920-935, April 2012).
Prashant Mehta is an Associate Professor in the Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign. He received his Ph.D. in Applied Mathematics from Cornell University in 2004. Prior to joining Illinois, he was a Research Engineer at the United Technologies Research Center (UTRC). His research interests are at the intersection of dynamical systems and control theory, including mean-field games, model reduction, and nonlinear control. He has received several awards including an Outstanding Achievement Award for his research contributions at UTRC, several Best Paper awards with his students at Illinois, and numerous teaching and advising honors at Illinois.