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**Machine Learning and Mean-Field Games**## Agency problem with mean field agents

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Thibaut Mastrolia, University of California, Berkeley (UC Berkeley)
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**Tuesday, May 24, 2022**

**Abstract**: We investigate a moral hazard problem in finite time with lump-sum payments, involving infinitely many Agents with mean field type interactions, hired by one Principal. By reinterpreting the mean-field game faced by each Agent in terms of a mean field forward backward stochastic differential equation (driven by a Brownian motion or more generally a Lévy process), we are able to rewrite the Principal’s problem as a control problem of McKean-Vlasov SDEs. We solve the problem completely and explicitly in special cases. We finally show in our examples that the optimal contract in the N-players model converges to the mean-field optimal contract when the number of agents is infinite.