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Portugaliae Mathematica

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Volume 75, Issue 3/4, 2018, pp. 367–396
DOI: 10.4171/PM/2023

Published online: 2019-06-06

Fourier approximation methods for first-order nonlocal mean-field games

Levon Nurbekyan[1] and João Saúde[2]

(1) McGill University, Montreal, Canada
(2) Carnegie Mellon University, Pittsburgh, USA

In this note, we develop Fourier approximation methods for the solutions of first-order nonlocal mean-field games (MFG) systems. Using Fourier expansion techniques, we approximate a given MFG system by a simpler one that is equivalent to a convex optimization problem over a finite-dimensional subspace of continuous curves. Furthermore, we perform a time-discretization for this optimization problem and arrive at a finite-dimensional saddle point problem. Finally, we solve this saddle-point problem by a variant of a primal dual hybrid gradient method.

Keywords: Infinite-dimensional differential games, mean-field games, nonlocal interactions, Fourier expansions

Nurbekyan Levon, Saúde João: Fourier approximation methods for first-order nonlocal mean-field games. Port. Math. 75 (2018), 367-396. doi: 10.4171/PM/2023