  We investigate the resolution of second-order, potential, and monotone mean
field games with the generalized conditional gradient algorithm, an extension
of the Frank-Wolfe algorithm. We show that the method is equivalent to the
fictitious play method. We establish rates of convergence for the optimality
gap, the exploitability, and the distances of the variables to the unique
solution of the mean field game, for various choices of stepsizes. In
particular, we show that linear convergence can be achieved when the stepsizes
are computed by linesearch.
