A relative-entropy extragradient algorithm provably computes static mean field equilibria, with explicit trade-offs between grid fineness and iteration count.
Mean field games: convergence of a finite difference method.SIAM Journal on Numerical Analysis, 51(5):2585–2612, 2013
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Kullback-Leibler Mirror-Prox for Measure-Valued Variational Inequalities and Mean-Field Equilibria
A relative-entropy extragradient algorithm provably computes static mean field equilibria, with explicit trade-offs between grid fineness and iteration count.