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Can one solve a mean field game numerically with a finite number of players?

I am analyzing the following problem: given a set of players $x^i_t$ for $i=1,\dots,N$ satisfying the SDE $$ dx^i_t = \alpha^i_t dt + \sigma dW^i_t $$ where $W^i_t$ are independent Brownian Motions, ...
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