Phase transition in large population games: An Application to synchronization of coupled oscillators

This talk is concerned with phase transition in non-cooperative dynamic games with a large number of nonlinear agents.

The talk is motivated by problems at the intersection of game theory and dynamical systems. Game theory provides a powerful set of tools for analysis and design of strategic behavior in controlled multi-agent systems. In economics, for example, game-theoretic techniques provide a foundation for analyzing the behavior of rational agents in markets. In practice, a fundamental problem is that controlled multi-agent systems frequently exhibit phase transitions with often undesirable outcomes. In economics, an example of this is the so-called “rational irrationality.”

A prototypical example of multi-agent system that exhibits phase transition is the coupled
oscillator model of Kuramoto. In this talk, a variant of the Kuramoto model is used albeit in a novel game-theoretic setting for control. The main conclusion is that the synchronization of the coupled oscillators can be interpreted as a solution of a non-cooperative dynamic game. The classical Kuramoto control law is shown to be “close to" such a game-theoretic solution.

Prashant G. Mehta is an Assistant Professor at the Department of Mechanical Science & Engineering, University of Illinois at Urbana-Champaign. He received his Ph.D. in Applied Mathematics from Cornell University in 2004. Prior to joining UIUC, he was a research engineer at the United Technologies Research Center (UTRC). At UTRC, he was recognized with an outstanding achievement award for his contributions in developing dynamical systems methods to obtain practical solutions to problems in aero-engines. His research interests are in development of stochastic methods for modeling and control of nonlinear systems, with applications to biology, integrated building systems and communication networks.