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We consider a moral hazard problem with multiple principals in acontinuous-time model. The agent can only work exclusively for one principal ata given time, so faces an optimal switching problem. Using a randomizedformulation, we manage to represent the agent's value function and his optimaleffort by an It\^o process. This representation further helps to solve theprincipals' problem in case we have infinite number of principals in the senseof mean field game. Finally the mean field formulation is justified by anargument of propagation of chaos.

Principal-agent problem with multiple principals