Stochastic Games on Large Graphs in Mean Field and Sparse Regimes

Explore stochastic games on large graphs in mean field and sparse regimes in this SIAM Activity Group on Financial Mathematics and Engineering virtual talk. Delve into the theory of mean field games and its limitations in modeling stochastic dynamic games with many interacting players. Examine recent efforts to overcome these limitations by incorporating heterogeneous interactions, particularly those governed by networks. Focus on a case study of linear-quadratic stochastic differential games where players are labeled by graph vertices and interact symmetrically with nearest neighbors. Investigate large-scale asymptotics for various graph sequences, emphasizing the differences between sparse and dense regimes. Learn about the basic model setup, mean field games and control, large graphs, approximate equilibrium, and automorphisms. Gain insights into this complex topic from speaker Daniel Lacker of Columbia University in this hour-long presentation.

Introduction
Acknowledgements
What is the initiative
How did this start
The mentoring initiative
How to participate
Mentor and mentee forms
Questions
Rules
Motivation
Guiding questions
Related literature
Basic model setup
Mean field game
Mean field control
Large graphs
Approximate equilibrium
Automorphisms
Conclusion