On stochastic incentive control problems with partial dynamic information

In this paper we consider a stochastic incentive decision problem with N > 1 followers and decentralized static information, where the leader's dynamic information comprises only a linear combination of the followers' actions. We obtain an incentive policy, affine in this dynamic information, which yields the same overall performance as the one the leader would obtain if he had observed the followers' actions separately. The existence conditions involved have been obtained explicitly for the case of finite probability spaces, and some challenging issues have been identified when the random variables are infinite valued.