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Group size and collective action in a binary contribution game

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  • Nöldeke, Georg
  • Peña, Jorge

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

  • Nöldeke, Georg & Peña, Jorge, 2020. "Group size and collective action in a binary contribution game," Journal of Mathematical Economics, Elsevier, vol. 88(C), pages 42-51.
    • Handle: RePEc:eee:mateco:v:88:y:2020:i:c:p:42-51
    DOI: 10.1016/j.jmateco.2020.02.003
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    Cited by:

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    4. Ginzburg, Boris & Guerra, José-Alberto & Lekfuangfu, Warn N., 2023. "Critical Mass in Collective Action," MPRA Paper 117139, University Library of Munich, Germany.

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    More about this item

    Keywords

    Private provision of public goods; Group size effects; Collective action; Threshold games; Participation games; Teamwork dilemma;
    All these keywords.

    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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