ONE-DIMENSIONAL, NON-LOCAL, FIRST-ORDER STATIONARY MEAN-FIELD GAMES WITH CONGESTION: A FOURIER APPROACH

摘要

Here, we study a one-dimensional, non-local mean-field game model with congestion. When the kernel in the non-local coupling is a trigonometric polynomial we reduce the problem to a finite dimensional system. Furthermore, we treat the general case by approximating the kernel with trigonometric polynomials. Our technique is based on Fourier expansion methods.