Generalized conditional gradient and learning in potential mean field\n games

We investigate the resolution of second-order, potential, and monotone mean\nfield games with the generalized conditional gradient algorithm, an extension\nof the Frank-Wolfe algorithm. We show that the method is equivalent to the\nfictitious play method. We establish rates of convergence for the optimality\ngap, the exploitability, and the distances of the variables to the unique\nsolution of the mean field game, for various choices of stepsizes. In\nparticular, we show that linear convergence can be achieved when the stepsizes\nare computed by linesearch.\n