Optimal Dynamic Contracts for a Large-Scale Principal-Agent Hierarchy: A Concavity-Preserving Approach

TL;DR

This paper develops a scalable method for designing optimal dynamic contracts in large hierarchical principal-agent settings, ensuring incentive compatibility while preserving key concavity properties, thus enabling efficient dynamic programming solutions.

Contribution

It introduces an iterative algorithm that maintains concavity during contract construction and reduces the problem to a one-dimensional state space, facilitating large-scale hierarchical contract design.

Findings

The algorithm preserves concavity during iteration.

Dynamic programming reduces to one-dimensional control.

Applicable to large-scale hierarchies with multiple players.

Abstract

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.