Stochastic incentive problems with partial dynamic information and multiple levels of hierarchy

We formulate and solve a class of three-agent incentive decision problems with strict hierarchy and decentralized information. The agent at the top of the hierarchy (leader) observes a random linear combination of the decisions of the other two agents and constructs his policy based on this, as well as some static information. We show that for general concave utility functions, and under some reasonable conditions on the random variables involved, the leader has an optimal incentive policy which is linear in the partial dynamic measurement and which induces the desired behavior on the two followers.