Approximate Optimality of Linear Contracts Under Uncertainty

TL;DR

This paper demonstrates that linear contracts are nearly optimal in principal-agent models with uncertainty, especially when the uncertainty is high, outperforming other simple contracts like debt contracts.

Contribution

It establishes approximation guarantees for linear contracts in uncertain settings and compares their performance to other contract formats.

Findings

Linear contracts are near-optimal under high uncertainty.

Other simple contracts like debt contracts can perform poorly with many actions.

Approximation guarantees improve with the degree of uncertainty.

Abstract

We consider a hidden-action principal-agent model, in which actions require different amounts of effort, and the agent privately knows his ability that determines his cost of effort. We show that linear contracts admit approximation guarantees that improve with a natural metric that captures the degree of uncertainty in the contracting setting. We thus show that linear contracts are near-optimal whenever there is enough uncertainty. In contrast, other simple contract formats such as debt contracts may suffer from a loss linear in the number of possible actions, even when there is sufficient uncertainty.