Structure and equilibrium
In Diekmann's (1985) model, each of n players decides whether to volunteer at cost K; if at least one volunteers, everyone receives benefit U, and if no one does, everyone gets 0. There are n asymmetric equilibria in which one person volunteers and the rest free-ride, but nothing determines who that person should be, so the symmetric mixed-strategy equilibrium is the focus of analysis. In it, each individual's probability of not volunteering is (K/U)^(1/(n−1)); as the group grows, each person is less likely to volunteer, and the probability that no one does actually rises. This sharpens the free-rider problem in large groups described by Olson (1965). Bliss and Nalebuff (1984) analyzed the same structure in the private supply of public goods with their dragon-slaying analogy.
The bystander effect and diffusion of responsibility
The model offers a game-theoretic account of the bystander effect documented by Darley and Latané (1968), whose experiments showed that the more people witnessed an emergency, the less often and more slowly any individual helped; Latané and Nida (1981) summarized this as diffusion of responsibility. A meta-analysis by Fischer et al. (2011) found that the bystander effect weakens in clearly dangerous emergencies. Weesie (1993) showed that once differences in costs and the timing of action are taken into account, equilibria emerge in which the lowest-cost player volunteers first, and Diekmann's (1993) asymmetric experiments supported this.
Experimental evidence and applications
In experiments by Murnighan, Kim and Metzger (1993) and Franzen (1995), individual volunteering fell as groups grew, but stayed above the levels theory predicts. Goeree, Holt and Smith (2017) confirmed that individual volunteering declines with group size but found that the probability of no one volunteering rises less than theory implies. Otsubo and Rapoport (2008) tested a dynamic version in which players choose over time, a waiting structure resembling the war of attrition. Archetti (2009) applied the framework to cooperation in microbial and animal groups and discussed optimal group size.
FAQ
- What is the volunteer's dilemma in simple terms?
- If just one person steps up, everyone benefits, but since each hopes someone else will do it, it's possible that nobody steps up at all.
- Why do bigger groups make it less likely anyone helps?
- In a bigger group, each person figures someone else will handle it, so each is less likely to act. Game theory shows this effect can be strong enough that the chance of nobody acting actually goes up.
Sources reviewed: 2026-10-26
References
- Diekmann, A. (1985). Volunteer's dilemma. Journal of Conflict Resolution, 29(4), 605–610.
- Diekmann, A. (1993). Cooperation in an asymmetric volunteer's dilemma game: Theory and experimental evidence. International Journal of Game Theory, 22(1), 75–85.
- Darley, J. M., & Latané, B. (1968). Bystander intervention in emergencies: Diffusion of responsibility. Journal of Personality and Social Psychology, 8(4), 377–383.
- Latané, B., & Nida, S. (1981). Ten years of research on group size and helping. Psychological Bulletin, 89(2), 308–324.
- Olson, M. (1965). The Logic of Collective Action. Cambridge, MA: Harvard University Press.
- Bliss, C., & Nalebuff, B. (1984). Dragon-slaying and ballroom dancing: The private supply of a public good. Journal of Public Economics, 25(1–2), 1–12.
- Murnighan, J. K., Kim, J. W., & Metzger, A. R. (1993). The volunteer dilemma. Administrative Science Quarterly, 38(4), 515–538.
- Franzen, A. (1995). Group size and one-shot collective action. Rationality and Society, 7(2), 183–200.
- Weesie, J. (1993). Asymmetry and timing in the volunteer's dilemma. Journal of Conflict Resolution, 37(3), 569–590.
- Otsubo, H., & Rapoport, A. (2008). Dynamic volunteer's dilemmas over a finite horizon: An experimental study. Journal of Conflict Resolution, 52(6), 961–984.
- Goeree, J. K., Holt, C. A., & Smith, A. M. (2017). An experimental examination of the volunteer's dilemma. Games and Economic Behavior, 102, 303–315.
- Fischer, P., Krueger, J. I., Greitemeyer, T., et al. (2011). The bystander-effect: A meta-analytic review on bystander intervention in dangerous and non-dangerous emergencies. Psychological Bulletin, 137(4), 517–537.
- Archetti, M. (2009). The volunteer's dilemma and the optimal size of a social group. Journal of Theoretical Biology, 261(3), 475–480.
