Prior-Free Delegation

Abstract

We consider a robust delegation problem in which the principal does not know the distribution from which the underlying state is drawn. The principal can choose a general randomized mechanism and maximizes her worst-case expected payoff over all state distributions. Our main result characterizes the robustly optimal mechanism. The mechanism has up to three regions: (i) accommodation, where the agent's ideal action is taken, (ii) calibrated randomization, where each type receives a distinct lottery, and (iii) pooling, where all types receive the same lottery. We then extend our model to a multidimensional setting in which preferences are additively separable and satisfy a cross-dimensional symmetry condition, and show that delegating separately across dimensions is robustly optimal.