Groupe d’études et de recherche en analyse des décisions

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

Prashant Girdharilal Mehta

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 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 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.