Optimal Dynamic Contracts for a Large-Scale Principal-Agent Hierarchy: A Concavity-Preserving Approach
It addresses the computational challenge of designing optimal dynamic contracts in large-scale principal-agent hierarchies, which is a known bottleneck in contract theory.
The paper extends Sannikov's continuous-time contract framework to hierarchical principal-agent settings, developing an iterative algorithm that preserves concavity and reduces the dynamic programming problem to one dimension regardless of hierarchy size, enabling optimal contract design for large-scale hierarchies.
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.