Computational Methods for First-Order Nonlocal Mean Field Games with Applications

Abstract

We introduce a novel framework to model and solve first-order mean field game systems with nonlocal interactions, extending the results in [L. Nurbekyan and J. Saúde, Port. Math., 75 (2018), pp. 367--396]. Our approach relies on kernel-based representations of mean field interactions and feature-space expansions in the spirit of kernel methods in machine learning. We demonstrate the flexibility of our approach by modeling various interaction scenarios between agents. Additionally, our method yields a computationally efficient saddle-point reformulation of the original problem that is amenable to state-of-the-art convex optimization methods such as the primal-dual hybrid gradient method. We also discuss potential applications of our methods to multiagent trajectory planning problems.

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