The Volunteer's Dilemma in Finite Populations

We study the long-run stochastic stability properties of volunteering strategies in finite populations. We allow for mixed strategies, characterized by the probability that a player may not volunteer. A pairwise comparison of evolutionary strategies shows that the strategy with a lower probability of volunteering is advantaged. However, in the long run there are also groups of volunteering types. Homomorphisms with the more volunteering types are more frequent if the groups have fewer members, and if the benefits from volunteering are larger. Such homomorphisms with volunteering cease to exist if the group becomes infinitely large. In contrast, the disadvantage of volunteering disappears if the ratio of individual benefits and costs of volunteering becomes infinitely large.