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hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorElie, Romuald*
hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorMastrolia, Thibaut*
hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorPossamaï, Dylan*
dc.subjectMoral hazard
dc.subjectmean field games
dc.subjectMcKean–Vlasov SDEs
dc.subjectmean field FBSDEs
dc.subjectinfinite dimensional HJB equations
dc.titleA tale of a Principal and many many Agents
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenIn this paper, we investigate a moral hazard problem in finite time with lump–sum and continuous 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 (FBSDE for short), we are able to rewrite the Principal's problem as a control problem of McKean–Vlasov SDEs. We review two general approaches to tackle it: the first one introduced recently in [2, 66, 67, 68, 69] using dynamic programming and Hamilton–Jacobi– Bellman (HJB for short) equations, the second based on the stochastic Pontryagin maximum principle, which follows [16]. We solve completely and explicitly the problem in special cases, going beyond the usual linear–quadratic framework. 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 goes to +∞, this illustrating in our specific setting the general results of [12].
dc.relation.isversionofjnlnameMathematics of Operations Research
dc.subject.ddclabelProbabilités et mathématiques appliquéesen

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