Contract DesignUnderApproximate Best Responses

2025-02-21

AI Summary

This paper studies optimal contract design in principal-agent problems with hidden actions, where the agent responds with bounded suboptimality (i.e., approximately optimal actions). Addressing the computational intractability of conventional Stackelberg approximate-response models, we establish the first theoretical framework for delegation under approximate optimality. We develop the first polynomial-time algorithm for computing optimal contracts—overcoming the long-standing belief that such problems are computationally infeasible. Further integrating game-theoretic modeling, polynomial optimization, and no-regret online learning, we design an adaptive contract mechanism that is both efficiently solvable and robust to unknown environments. Our results provide computationally tractable, robust theoretical foundations and algorithmic tools for applications including blockchain incentive mechanisms and distributed machine learning.

Technology Category

• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Mechanism Design
• Search and Optimization: Learning to Search

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

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.

Problem

• Studies hidden-action principal-agent problems.
• Develops polynomial-time optimal contract algorithm.
• Explores contract learnability with no-regret algorithm.

Innovation

• Polynomial-time optimal contract algorithm
• No-regret learning for contracts
• Approximate best responses analysis