Affine Incentive Schemes for Stochastic Systems with Dynamic Information

In this paper we study the derivation of optimal incentive schemes in two-agent stochastic decision problems with a hierarchical decision structure, in a general Hilbert space setting. The agent at the top of the hierarchy is assumed to have access to the value of other agent´s decision variable as well as to some common and private information, and the second agent´s loss function is taken to be strictly convex. In this set-up, it is shown that there exists, under some fairly mild structural restrictions, an optimal incentive policy for the first agent, which is affine in the dynamic information and generally nonlinear in the static (common and private) information. Certain special cases are also discussed and a numerical example is solved.