Randomization and the Robustness of Linear Contracts

We consider a principal-agent model with moral hazard, bilateral risk-neutrality, and limited liability, where the principal knows only some of the agent's feasible actions. The principal evaluates contracts by their payoff guarantee over all possible sets of feasible actions. We show that the guarantee from any randomization over contracts can be weakly improved by randomizing over the same or smaller number of linear contracts. Thus, random linear contracts are robustly optimal as a class. We derive the optimal guarantee and characterize a maximizing sequence of random linear contracts attaining it in the limit as the size of their support tends to infinity; these contracts do not require commitment to randomization. The gain from randomization can be arbitrarily large.