  We present a continuous-time contract whereby a top-level player can
incentivize a hierarchy of players below him to act in his best interest
despite only observing the output of his direct subordinate. This paper extends
Sannikov's approach from a situation of asymmetric information between a
principal and an agent to one of hierarchical information between several
players. We develop an iterative algorithm for constructing an incentive
compatible contract and define the correct notion of concavity which must be
preserved during iteration. We identify conditions under which a dynamic
programming construction of an optimal dynamic contract can be reduced to only
a one-dimensional state space and one-dimensional control set, independent of
the size of the hierarchy. In this sense, our results contribute to the
applicability of dynamic programming on dynamic contracts for a large-scale
principal-agent hierarchy.
