Optimal Robust Contract Design

TL;DR

This paper characterizes the optimal randomized linear contract in a robust principal-agent setting with limited information, showing it can significantly outperform deterministic contracts and generalizes to team contracting models.

Contribution

It provides a closed-form characterization of the optimal randomized linear contract, extending previous results and demonstrating its advantages over deterministic contracts.

Findings

Randomized contracts can outperform deterministic ones arbitrarily.

Optimal randomized contracts remain linear with a closed-form density.

Results extend to team contracting models.

Abstract

We consider the robust contract design problem when the principal only has limited information about the actions the agent can take. The principal evaluates a contract according to its worst-case performance caused by the uncertain action space. Carroll (AER 2015) showed that a linear contract is optimal among deterministic contracts. Recently, Kambhampati (JET 2023) showed that the principal's payoff can be strictly increased via randomization over linear contracts. In this paper, we characterize the optimal randomized contract, which remains linear and admits a closed form of its cumulative density function. The advantage of randomized contracts over deterministic contracts can be arbitrarily large even when the principal knows only one non-trivial action of the agent. Furthermore, our result generalizes to the model of contracting with teams, by Dai and Toikka (Econometrica 2022).