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Welfare in the volunteer’s dilemma

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  • Battaglini, Marco
  • Palfrey, Thomas R.

Abstract

We study the volunteer’s dilemma with heterogeneous costs and private information. We characterize efficiency properties of equilibrium. While the probability of success – the focus of previous theoretical analysis – may be strictly decreasing in group size, per-capita welfare is always increasing for every possible cost, strictly for sufficiently high costs. As group size increases, the expected utility of every member, regardless of their cost, converges to the expected utility of a member with the lowest possible cost, which is the same expected utility when there is no free rider problem, i.e., with only a single player in the game who has the lowest possible cost. Convergence, however, is slower than the convergence to zero of 1/n, so the total inefficiency diverges at infinity, even if the lowest cost is zero.

Suggested Citation

  • Battaglini, Marco & Palfrey, Thomas R., 2025. "Welfare in the volunteer’s dilemma," Journal of Public Economics, Elsevier, vol. 245(C).
  • Handle: RePEc:eee:pubeco:v:245:y:2025:i:c:s0047272725000581
    DOI: 10.1016/j.jpubeco.2025.105360
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    1. McKelvey Richard D. & Palfrey Thomas R., 1995. "Quantal Response Equilibria for Normal Form Games," Games and Economic Behavior, Elsevier, vol. 10(1), pages 6-38, July.
    2. Andreas Diekmann, 1985. "Volunteer's Dilemma," Journal of Conflict Resolution, Peace Science Society (International), vol. 29(4), pages 605-610, December.
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    4. Marco Battaglini & Thomas R. Palfrey, 2024. "Organizing for Collective Action: Olson Revisited," Journal of Political Economy, University of Chicago Press, vol. 132(9), pages 2881-2936.
    5. Battaglini, Marco & Palfrey, Thomas R, 2024. "Dynamic Collective Action and the Power of Large Numbers," CEPR Discussion Papers 19102, C.E.P.R. Discussion Papers.
    6. Goeree, Jacob K. & Holt, Charles A. & Smith, Angela M., 2017. "An experimental examination of the volunteer's dilemma," Games and Economic Behavior, Elsevier, vol. 102(C), pages 303-315.
    7. Heifetz, Aviad & Heller, Ruth & Ostreiher, Roni, 2021. "Do Arabian babblers play mixed strategies in a “volunteer’s dilemma”?," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 91(C).
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    More about this item

    Keywords

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    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • C92 - Mathematical and Quantitative Methods - - Design of Experiments - - - Laboratory, Group Behavior
    • H41 - Public Economics - - Publicly Provided Goods - - - Public Goods
    • H54 - Public Economics - - National Government Expenditures and Related Policies - - - Infrastructures

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