Linear Contracts in Multitasking: Robustness, Uniformity, and Learning

2024-05-31

AI Summary

This paper studies linear contract design in a multi-task principal–agent framework under realistic constraints: incomplete signal observation, unknown agent cost structure, and data-driven deployment. Methodologically, it integrates game-theoretic modeling, robust optimization, homogeneous function analysis, and instrumental variable (IV) regression, framing contract learning as a counterfactual estimation problem with measurement error. Its contributions are threefold: (1) it establishes worst-case robust optimality guarantees under ambiguity—i.e., under an adversarial uncertainty set over cost and signal distributions; (2) it proves uniqueness and structural simplicity of optimal contract parameters under homogeneous agent costs, enabling explicit design solely via the degree of homogeneity; and (3) it proposes IV-based offline and online learning algorithms that recover optimal linear contracts from observational data with finite-sample theoretical guarantees. Empirical and theoretical results demonstrate strong optimality and practical implementability even under severe information scarcity.

Technology Category

• Multiagent Systems: Mechanism Design
• Intelligent Robots: Learning & Optimization for ROB
• Game Theory and Economic Paradigms: Mechanism Design

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
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

In this work, we study the multitasking principal-agent problem. The agent performs several task for the principal, and the principal posts a contract incentivizing the agent to exert effort. The principal can observe a signal for each task, and the contract is a mapping from the space of possible signals to a payment. We study the special class of linear contracts from three perspectives: robustness, uniformity, and learning. Firstly, we show a robustness result: in an ambiguous setting when only first moment information is known, there is a linear contract maximizing the principal's payoff in a worst-case scenario. Secondly, we show a uniformity result: when the agent's cost function is homogeneous to a certain degree and the the principal's utility takes a linear form across tasks, then the optimal contract depends on the agent's cost function only through its homogeneuity degree. Thirdly, we study the problem of learning an optimal linear contract through observational data. We identify this as an measurement error model, and propose instrumental regression methods to estimate the optimal contract parameters in an offline setting, or to learn the optimal contract in an online setting.

Problem

• Study multitasking principal-agent problem with linear contracts.
• Analyze robustness, uniformity, and learning in contract design.
• Propose methods to estimate optimal contract parameters using data.

Innovation

• Linear contracts maximize payoff in ambiguous settings.
• Optimal contracts depend on agent's cost homogeneity.
• Instrumental regression estimates optimal contract parameters.