Phase Transitions in Stochastic Many-Player Games

My research addresses stochastic games with many players, optimal control with partial information, and, recently, optimization with random matrices. This seminar focuses on a stochastic game where the players exhibit qualitatively distinct behaviors in different parameter regimes. Inspired by the ‘Ising model’ of statistical physics, we call this stochastic game the ‘Ising game.’ We characterize the qualitative change in behavior as a phase transition where the ‘Ising game’ admits two stable constant equilibrium solutions in the super-critical parameter regime. In this talk, we consider a macroscopic limit for which Nash-equilibrium solutions to the ‘Ising game’ concentrate on the two stable constant equilibria. A sharp interface forms and minimizes an energy functional related to an anisotropic space-time minimal surface. This characterization of the interface contrasts with classical results on the ‘Ising model’ and requires us to address a new challenging mathematical problem. Our analysis contributes to understanding new phenomena of collective intelligent behavior, such as arising in finance, robotics, and machine learning.

Share this Event