The cost of moral hazard and limited liability in the principal-agent problem

In this paper we quantify the potential social-welfare loss due to the existence of limited liability in the principal-agent problem. The worst-case welfare loss is defined as the largest possible ratio between the social welfare when the agent chooses the effort that is optimal for the system and that of the sub-game perfect equilibrium of the game. Our main result establishes that under the monotone likelihood-ratio property and a limited liability constraint, the worst-case welfare loss (also known as the Price of Anarchy) is exactly equal to the number of efforts available.