Stochastic games on large graphs in mean field and sparse regimes
Abstract
The now-widespread theory of mean field games provides a systematic framework for modeling stochastic dynamic games with many interacting players. It is fundamentally limited, however, to models in which players view each other as exchangeable. This talk discusses some recent efforts to push past this limitation by incorporating heterogeneous interactions, such as those governed by networks. I will focus on a recent case study, joint with Agathe Soret, on linear-quadratic stochastic differential games in which each player is labeled by a vertex in a graph and interacts symmetrically with its nearest neighbors. Large-scale asymptotics are developed for various graph sequences, with an emphasis on the difference between sparse and dense regimes.
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