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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-03818329
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    References listed on IDEAS

    as
    1. Duddy, Conal, 2015. "Fair sharing under dichotomous preferences," Mathematical Social Sciences, Elsevier, vol. 73(C), pages 1-5.
    2. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    3. Foley, Duncan K, 1970. "Lindahl's Solution and the Core of an Economy with Public Goods," Econometrica, Econometric Society, vol. 38(1), pages 66-72, January.
    4. Bergstrom, Theodore & Blume, Lawrence & Varian, Hal, 1986. "On the private provision of public goods," Journal of Public Economics, Elsevier, vol. 29(1), pages 25-49, February.
    5. Le Breton, Michel & Weymark, John A., 2011. "Chapter Seventeen - Arrovian Social Choice Theory on Economic Domains," Handbook of Social Choice and Welfare, in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 2, chapter 17, pages 191-299, Elsevier.
    6. Aziz, Haris & Brandl, Florian & Brandt, Felix, 2015. "Universal Pareto dominance and welfare for plausible utility functions," Journal of Mathematical Economics, Elsevier, vol. 60(C), pages 123-133.
    7. Bogomolnaia, Anna & Moulin, Herve & Stong, Richard, 2005. "Collective choice under dichotomous preferences," Journal of Economic Theory, Elsevier, vol. 122(2), pages 165-184, June.
    8. Faruk Gul & Wolfgang Pesendorfer, 2020. "Lindahl Equilibrium as a Collective Choice Rule," Papers 2008.09932, arXiv.org, revised Aug 2020.
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    Cited by:

    1. Felix Brandt & Matthias Greger & Erel Segal-Halevi & Warut Suksompong, 2023. "Coordinating Charitable Donations," Papers 2305.10286, arXiv.org, revised Sep 2024.
    2. 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.

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