COMPUTATIONAL METHODS FOR FIRST-ORDER NONLOCAL MEAN FIELD GAMES WITH APPLICATIONS

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. Saude, 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.