Approximation of $ N $-player stochastic games with singular controls by mean field games

This paper establishes that a class of $ N $-player stochastic games with singular controls, either bounded velocity or finite variation, can both be approximated by mean field (MFGs) controls velocity. More specifically, it shows (i) the optimal control to an MFG \theta is shown \epsilon_N $-NE game velocity, = O(\frac{1}{\sqrt{N}}) $, and (ii) this (\epsilon_N + \epsilon_{\theta}) where \epsilon_{\theta} error term depends on $. work generalizes classical result approximation MFGs, allowing for discontinuous controls.