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 populations of volunteering types. Monomorphisms with the more volunteering types are more frequent if the populations have fewer members, and if the benefits from volunteering are larger. Such monomorphisms with volunteering cease to exist if the population becomes infinitely large. In contrast, the disadvantage of volunteering disappears if the ratio of individual benefits and costs of volunteering becomes infinitely large.

我们研究了有限人群中志愿服务策略的长期随机稳定性。我们允许采用混合策略，其特征在于玩家可能不会自愿参与。进化策略的成对比较表明，具有较低自愿性的策略是有优势的。但是，从长远来看，还有志愿服务类型的人群。如果群体中的成员人数较少，并且志愿服务的收益较大，则具有更多志愿服务类型的单态性会更加频繁。如果人口变得无限大，这种具有自愿性的单态性将不复存在。相反，如果个人利益和志愿服务成本之比变得无限大，则志愿服务的弊端就消失了。