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Welfare in the Volunteer’s Dilemma

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  • Marco Battaglini
  • Thomas R. Palfrey

Abstract

We study the volunteer’s dilemma in environments with heterogeneous preferences and private information. We characterize the efficiency properties of equilibrium, which is a departure from all the previous literature that focuses only on the probability of group success. While the probability of success may be non-monotonic in the size of the group, we show that per-capita welfare is always increasing for all types, strictly for sufficiently high types. As group size increases, the expected utility of every type converges to the expected utility of the type with the lowest possible cost, which is the same expected utility when there is no free rider problem, i.e., when there is only a single player in the game and that player has the lowest possible cost.

Suggested Citation

  • Marco Battaglini & Thomas R. Palfrey, 2024. "Welfare in the Volunteer’s Dilemma," NBER Working Papers 32999, National Bureau of Economic Research, Inc.
    • Handle: RePEc:nbr:nberwo:32999
    Note: PE POL
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    References listed on IDEAS

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    1. Marco Battaglini & Thomas R. Palfrey, 2024. "Dynamic Collective Action and the Power of Large Numbers," NBER Working Papers 32473, National Bureau of Economic Research, Inc.
    2. 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.
    3. Hillenbrand, Adrian & Winter, Fabian, 2018. "Volunteering under population uncertainty," Games and Economic Behavior, Elsevier, vol. 109(C), pages 65-81.
    4. Andreas Diekmann, 1985. "Volunteer's Dilemma," Journal of Conflict Resolution, Peace Science Society (International), vol. 29(4), pages 605-610, December.
    5. 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).
    6. 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.
    7. 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.
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    More about this item

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • 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
    • H41 - Public Economics - - Publicly Provided Goods - - - Public Goods

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