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Group size and collective action in a binary contribution game

Author

Listed:
  • Georg Nöldeke

    (Unibas - Université de Bâle = University of Basel = Basel Universität)

  • Jorge Peña

    (IAST - Institute for Advanced Study in Toulouse)

Abstract

We consider how group size affects the private provision of a public good with non-refundable binary contributions. A fixed amount of the good is provided if and only if the number of contributors reaches an exogenous threshold. The threshold, the group size, and the identical, non-refundable cost of contributing to the public good are common knowledge. Our focus is on the case in which the threshold is larger than one, so that teamwork is required to produce the public good. We show that both expected payoffs and the probability that the public good is obtained in the best symmetric equilibrium are decreasing in group size. We also characterize the limit outcome when group size converges to infinity and provide precise conditions under which the expected number of contributors is decreasing or increasing in group size for sufficiently large groups.

Suggested Citation

  • Georg Nöldeke & Jorge Peña, 2020. "Group size and collective action in a binary contribution game," Post-Print hal-02923973, HAL.
    • Handle: RePEc:hal:journl:hal-02923973
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    Cited by:

    1. Peña, Jorge & Heifetz, Aviad & Nöldeke, Georg, 2024. "The shirker’s dilemma and the prospect of cooperation in large groups," Theoretical Population Biology, Elsevier, vol. 155(C), pages 10-23.
    2. Jorge Peña & Georg Nöldeke, 2023. "Cooperative Dilemmas with Binary Actions and Multiple Players," Dynamic Games and Applications, Springer, vol. 13(4), pages 1156-1193, December.
    3. Jann, Ole & Schottmüller, Christoph, 2021. "Regime change games with an active defender," Games and Economic Behavior, Elsevier, vol. 129(C), pages 96-113.
    4. Ginzburg, Boris & Guerra, José-Alberto & Lekfuangfu, Warn N., 2023. "Critical Mass in Collective Action," MPRA Paper 117139, University Library of Munich, Germany.
    5. Gerard Domènech-Gironell & Dimitrios Xefteris, 2025. "Buying elections for peanuts," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 80(2), pages 565-593, September.

    More about this item

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • H41 - Public Economics - - Publicly Provided Goods - - - Public Goods

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