This was part of Machine Learning and Mean-Field Games

Agency problem with mean field agents

Thibaut Mastrolia, University of California, Berkeley (UC Berkeley)
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.