Prashant Mehta

Coordinated Science Laboratory

Department of Mechanical Science & Engineering

University of Illinois at Urbana-Champaign

** 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 nonlinear 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 can exhibit phase
transitions with often undesireable 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 Koramoto control law can be obtained as an
approximation
of the game-theoretic solution. Approximate dynamic programming techniques to obtain the Kuramoto control law are
discussed.

This is joint work with Sean Meyn and Uday Shanbhag at the University of Illinois.

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