The volunteer's dilemma and the optimal size of a social group

If one or few individuals are enough to perform an action that produces a collective good and if this action has a cost, living in group can be beneficial because the cost can be shared with other individuals. Without coordination, however, the production of a collective good by the contribution of one or few individuals is inefficient and can be modelled as a volunteer's dilemma. In the volunteer's dilemma the individuals that pay the cost for the production of the collective good benefit from their action if nobody else volunteers, but the cost is wasted if too many individuals volunteer. Increasing group size reduces the need of volunteering for each member of the group; the overall benefit for the group, however, decreases too because the larger the group is, the less likely it is that the collective good is produced. This problem persists even with a high degree of relatedness between group members; an optimal, intermediate group size exists that maximizes the probability to produce the collective good.