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Principal-agent problem with multiple principals

Hu, Kaitong; Ren, Zhenjie; Yang, Junjian (2022), Principal-agent problem with multiple principals, Stochastics: An International Journal of Probability and Stochastic Processes, p. 18. 10.1080/17442508.2022.2125808

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Type
Article accepté pour publication ou publié
Date
2022
Journal name
Stochastics: An International Journal of Probability and Stochastic Processes
Publisher
Taylor & Francis
Published in
Paris
Pages
18
Publication identifier
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Author(s)
Hu, Kaitong
Centre de Mathématiques Appliquées - Ecole Polytechnique [CMAP]
Ren, Zhenjie
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Yang, Junjian
Fakultät für Mathematik und Geoinformation [Wien] [TU Wien]
Abstract (EN)
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.
Subjects / Keywords
Moral hazard; contract theory; backward SDE; optimal switching; mean field games; propagation of chaos