  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 It\^o 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.
