Optimal delegation with a finite number of states

This paper studies delegation without monetary transfers when the number of possible states is small, and therefore finite. To do so, we fully characterize the class of optimal delegation sets in the finite-state version of Holmstrom's (1984) seminal model and analyze their properties. Our finite state assumption entails the following results: (i) the agent never takes her ideal decision, and takes a decision strictly between her and the principal's ideal (thus compromising with the latter) in low enough states; (ii) the agent takes the same decision in high enough states, and is indifferent between the decision she takes and the next highest decision in every other state; (iii) the agent may be induced to take decisions outside the support of the principal's ideal decisions; (iv) marginal increases in the agent's bias do not (generically) cause optimal delegation sets to shrink, and may increase the variance of the decision taken by the agent. We also show that the principal and the agent may both be better off if the latter cannot distinguish between some states.