Multi-agent Contracts

Paul Dütting, Tomer Ezra, Michal Feldman, Thomas Kesselheim

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


We study a natural combinatorial single-principal multi-agent contract design problem, in which a principal motivates a team of agents to exert effort toward a given task. At the heart of our model is a reward function, which maps the agent efforts to an expected reward of the principal. We seek to design computationally efficient algorithms for finding optimal (or near-optimal) linear contracts for reward functions that belong to the complement-free hierarchy. Our first main result gives constant-factor approximation algorithms for submodular and XOS reward functions, with value and demand oracles, respectively. It relies on an unconventional use of "prices"and (approximate) demand queries for selecting the set of agents that the principal should contract with, and exploits a novel scaling property of XOS functions and their marginals, which may be of independent interest. Our second main result is an ω(n) impossibility for settings with n agents and subadditive reward functions, even with demand oracle access. A striking feature of this impossibility is that it applies to subadditive functions that are constant-factor close to submodular. This presents a surprising departure from previous literature, e.g., on combinatorial auctions.

Original languageEnglish
Title of host publicationSTOC 2023 - Proceedings of the 55th Annual ACM Symposium on Theory of Computing
EditorsBarna Saha, Rocco A. Servedio
PublisherAssociation for Computing Machinery
Number of pages14
ISBN (Electronic)9781450399135
StatePublished - 2 Jun 2023
Event55th Annual ACM Symposium on Theory of Computing, STOC 2023 - Orlando, United States
Duration: 20 Jun 202323 Jun 2023

Publication series

NameProceedings of the Annual ACM Symposium on Theory of Computing
ISSN (Print)0737-8017


Conference55th Annual ACM Symposium on Theory of Computing, STOC 2023
Country/TerritoryUnited States


FundersFunder number
European Research Council
European Union’s Horizon 2020 research and innovation program866132
Israel Science Foundation317/17
NSF-BSF788893, 2020788


    • XOS
    • contract theory
    • moral hazard
    • submodularity


    Dive into the research topics of 'Multi-agent Contracts'. Together they form a unique fingerprint.

    Cite this