Contract Design Under Approximate Best Responses

TL;DR

This paper studies principal-agent problems with approximate best responses, providing a polynomial-time algorithm for optimal contract design and a no-regret learning method for unknown environments.

Contribution

It introduces the first polynomial-time algorithm for optimal contracts under approximate best responses and explores learnability in unknown settings.

Findings

Polynomial-time algorithm for optimal contract design.

Feasibility of learning contracts with no prior knowledge.

Contrast with intractability in Stackelberg games.

Abstract

Principal-agent problems model scenarios where a principal incentivizes an agent to take costly, unobservable actions through the provision of payments. Such problems are ubiquitous in several real-world applications, ranging from blockchain to the delegation of machine learning tasks. In this paper, we initiate the study of hidden-action principal-agent problems under approximate best responses, in which the agent may select any action that is not too much suboptimal given the principal's payment scheme (a.k.a. contract). Our main result is a polynomial-time algorithm to compute an optimal contract under approximate best responses. This positive result is perhaps surprising, since, in Stackelberg games, computing an optimal commitment under approximate best responses is computationally intractable. We also investigate the learnability of contracts under approximate best responses, by providing a no-regret learning algorithm for a natural application scenario where the principal has no prior knowledge about the environment.