Stochastic Networks, Applied Probability, and Performance Seminar

  • Remote Access Enabled - Webinar
  • Virtual Presentation
  • BRUCE HAJEK
  • Professor, Department of Electrical and Computer Engineering,
  • Research Professor, Coordinated Science Laboratory, Hoeft Chair, College of Engineering
  • University of Illinois at Urbana-Champaign
Seminars

On non-unique solutions in mean field games

The theory of mean field games has arisen as a tool to understand noncooperative dynamic stochastic games with a large number of agents. Much of the theory has evolved under conditions ensuring uniqueness of the mean field game Nash equilibrium. However, in some situations, typically involving symmetry breaking, non-uniqueness of solutions is an important feature. To investigate the nature of non-unique solutions, we focus on the technically simple setting where agents have one of two states, with continuous time dynamics, and the game is symmetric in the players, and players are restricted to using Markov strategies. We identify all the mean field game Nash equilibria. Such equilibria correspond to symmetric ϵ-Nash Markov equilibria for the large N finite systems such that ϵ→0 as N→∞. In contrast to the mean field game, for the finite systems there is a unique Nash equilibrium. We focus on the problem of identifying which mean field game equilibria correspond to the limit of the Nash equilibria for the finite N system.

This is joint work with Michael Livesay.

Bruce Hajek is a Center for Advanced Study Professor and Head of Electrical and Computer Engineering, Hoeft Chair of Engineering, and Research Professor in the Coordinated Science Laboratory at the University of Illinois at Urbana-Champaign, where he has been on the faculty since 1979. He received a BS in Mathematics and MS in Electrical Engineering from the University of Illinois and the Ph. D. in Electrical Engineering from the University of California at Berkeley. Prof. Hajek's research interests include communication networks, auction theory, stochastic analysis, combinatorial optimization, machine learning, information theory, and bioinformatics. He served as Editor-in-Chief for the IEEE Transactions on Information Theory, and as President of the IEEE Information Theory Society. He received the Institute of Electrical and Electronics Engineers (IEEE) Kobayashi Award for Computer Communication and the ACM SIGMETRICS Achievement Award and he is a member of the US National Academy of Engineering.

REGISTER:  Remote Participation Enabled. See announcement.

The seminar series is broadly focused on theoretical topics spanning the areas of applied probability, including but not limited to stochastic networks, computer networks, stochastic processes, performance analysis, statistical analysis, mathematical modeling, simulation, optimization, and queueing theory.

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