Kernel-based potential mean-field games with unbiased random Fourier $U$-statistics

ArXi:2605.29371v1 Announce Type: cross We study the subclass of potential mean-field games in which the running interaction cost and the terminal target cost are both expressed through reproducing-kernel maximum mean discrepancy (MMD) penalties, and develop a computational framework that exploits this kernel structure. Both costs are estimated from finite-sample empirical distributions using a random Fourier U-statistic representation that is unbiased and has linear cost in the batch size.