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October 16, 2025Open Access

Contract Design Under Approximate Best Responses

FBFrancesco BacchiocchiPolitecnico di Milano JGJiarui Gan MCMatteo CastiglioniPolitecnico di Milano

Key Points

An optimal contract can be computed in polynomial time, indicating a breakthrough in solving principal-agent issues.
The main result shows efficiency contrary to previous findings in Stackelberg games, where similar computations are challenging.
A no-regret learning algorithm is proposed for applications where the principal lacks prior knowledge, enhancing contract learnability.
The study extends the understanding of payments and hidden actions in various fields, including blockchain and machine learning tasks.

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.

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