Optimum/near-optimum incentive policies for stochastic decision problems involving parametric uncertainty

In this paper we consider a general class of stochastic incentive decision problems in which the leader has access to the control value of the follower and to private as well as common information on the unknown state of nature. The follower's cost function depends on a finite number of parameters whose values are not known accurately by the leader, and in spite of this parametric uncertainty the leader seeks a policy which would induce the desired behavior on the follower. We obtain such policies for the leader, which are smooth, induce the desired behavior at the nominal values of these parameters, and furthermore make the follower's optimal reaction either minimally sensitive or totally insensitive to variations in the values of these parameters from the nominals. The general solution is determined by some orthogonality relations in some appropriately constructed (probability) measure spaces, and leads to particularly simple incentive policies. The features presented here are intrinsic to stochastic decision problems and have no counterparts in deterministic incentive problems.