Online Contract Design

2026-02-07

AI Summary

This study addresses the problem of dynamic team formation and incentive contract design for a principal facing an online sequence of adversarial agents, with the goal of maximizing the principal’s utility. Integrating economic contract theory with online algorithms, the work models agents’ rational effort decisions under performance-based contracts after team assignment and selects the optimal team under irrevocable elimination constraints. The paper innovatively bridges contract theory and online algorithms by introducing a “balance point” technique, establishing—for the first time—the existence of a randomized online algorithm achieving a competitive ratio of 1/2 under additive rewards, which is provably optimal among all randomized algorithms. Furthermore, it demonstrates that no deterministic algorithm can guarantee a bounded competitive ratio in this setting.

Technology Category

• Multiagent Systems: Mechanism Design
• Machine Learning: Online Learning & Bandits
• 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
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

We initiate the study of online contracts, which integrate the game-theoretic considerations of economic contract theory, with the algorithmic and informational challenges of online algorithm design. Our starting point is the classic online setting with preemption of Buchbinder et al. [SODA'15], in which a hiring principal faces a sequence of adversarial agent arrivals. Upon arrival, the principal must decide whether to tentatively accept the agent to their team, and whether to dismiss previous tentative choices. Dismissal is irrevocable, giving the setting its online decision-making flavor. In our setting, the agents are rational players: once the team is finalized, a game is played where the principal offers contracts (performance-based payment schemes), and each agent decides whether or not to work. Working agents reward the principal, and the goal is to choose a team that maximizes the principal's utility. Our main positive result is a 1/2-competitive algorithm when agent rewards are additive, which matches the best-possible competitive ratio. Our algorithm is randomized and this is necessary, as we show that no deterministic algorithm can attain a bounded competitive ratio. Moreover, if agent rewards are allowed to exhibit combinatorial structure known as XOS, even randomized algorithms might fail. En route to our competitive algorithm, we develop the technique of balance points, which can be useful for further exploration of online contracts in the adversarial model.

Problem

• online contracts
• algorithmic game theory
• competitive ratio
• adversarial arrivals
• principal-agent problem

Innovation

• online contract design
• competitive ratio
• randomized algorithm
• balance points
• adversarial arrivals