Principal-agent problem with multiple principals

Kaitong Hu (1) , Zhenjie Ren (2) , Junjian Yang (3)

1 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
2 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
3 TU Wien - Fakultät für Mathematik und Geoinformation [Wien]

We consider a moral hazard problem with multiple principals in a continuous-time model. The agent can only work exclusively for one principal at a given time, so faces an optimal switching problem. Using a randomized formulation, we manage to represent the agent's value function and his optimal effort by an Itô process. This representation further helps to solve the principals' problem in case we have infinite number of principals in the sense of mean field game. Finally the mean field formulation is justified by an argument of propagation of chaos.

Mots clés: Moral hazard; contract theory; backward SDE; optimal switching; mean field games; propagation of chaos

Domaines: Probabilités [math.PR]; Économie et finance quantitative [q-fin]

Kaitong Hu, Zhenjie Ren, Junjian Yang. Principal-agent problem with multiple principals. 2019. ⟨hal-02088486⟩