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Funding public projects: A case for the Nash product rule

Author

Listed:
  • Florian Brandl

    (HCM - Hausdorff Center for Mathematics - Rheinische Friedrich-Wilhelms-Universität Bonn)

  • Felix Brandt

    (TUM - Technische Universität Munchen - Technical University Munich - Université Technique de Munich)

  • Matthias Greger

    (TUM - Technische Universität Munchen - Technical University Munich - Université Technique de Munich)

  • Dominik Peters

    (LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique)

  • Christian Stricker

    (TUM - Technische Universität Munchen - Technical University Munich - Université Technique de Munich)

  • Warut Suksompong

    (NUS - National University of Singapore)

Abstract

We study a mechanism design problem where a community of agents wishes to fund public projects via voluntary monetary contributions by the community members. This serves as a model for public expenditure without an exogenously available budget, such as participatory budgeting or voluntary tax programs, as well as donor coordination when interpreting charities as public projects and donations as contributions. Our aim is to identify a mutually beneficial distribution of the individual contributions. In the preference aggregation problem that we study, agents with linear utility functions over projects report the amount of their contribution, and the mechanism determines a socially optimal distribution of the money. We identify a specific mechanism-the Nash product rule-which picks the distribution that maximizes the product of the agents' utilities. This rule is Pareto efficient and incentivizes agents to contribute their entire budget while spending each agent's contribution only on projects the agent finds acceptable.

Suggested Citation

  • Florian Brandl & Felix Brandt & Matthias Greger & Dominik Peters & Christian Stricker & Warut Suksompong, 2022. "Funding public projects: A case for the Nash product rule," Post-Print hal-03818329, HAL.
    • Handle: RePEc:hal:journl:hal-03818329
    DOI: 10.1016/j.jmateco.2021.102585
    Note: View the original document on HAL open archive server: https://hal.science/hal-03818329v1
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    References listed on IDEAS

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    Cited by:

    1. Beikverdi, Majid & Tehrani, Nasim Ghanbar & Shahanaghi, Kamran, 2024. "A Bi-level model for district-fairness participatory budgeting: Decomposition methods and application," European Journal of Operational Research, Elsevier, vol. 314(1), pages 340-362.
    2. Haris Aziz & Patrick Lederer & Xinhang Lu & Mashbat Suzuki & Jeremy Vollen, 2024. "Approximately Fair and Population Consistent Budget Division via Simple Payment Schemes," Papers 2412.02435, arXiv.org, revised Jul 2025.
    3. Felix Brandt & Matthias Greger & Erel Segal-Halevi & Warut Suksompong, 2023. "Coordinating Charitable Donations," Papers 2305.10286, arXiv.org, revised Sep 2024.

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