Abstract:This paper establishes that a class of N -player stochastic games with singular controls, either of bounded velocity or of finite variation, can both be approximated by mean field games (MFGs) with singular controls of bounded velocity. More specifically, it shows (i) the optimal control to an MFG with singular controls of a bounded velocity θ is shown to be an ǫ N -NE to an N -player game with singular controls of the bounded velocity, with ǫ N = O( 1 √ N ), and (ii) the optimal control to this MFG is an (ǫ N… Show more
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