Cooperation in an asymmetric volunteer's dilemma game with relatedness

What motivates some members of a social group to voluntarily incur costs in order to provide for the common good? This question lies at the heart of theoretical and empirical studies of cooperative behavior. This is also the question that underlies the classic volunteer's dilemma model, which has been previously explored in scenarios where group members are related or interact asymmetrically. Here we present a model that combines asymmetry and relatedness, showing that the probability of volunteerism in such systems depends closely on both the degree of asymmetry and level of relatedness between interacting individuals. As has been shown in previous volunteer's dilemma models, the payoff ratio and overall group size also influence the probability of volunteerism. The probability of volunteerism decreases with increasing group size or decreasing cost-to-benefit ratio of the co-players; in the presence of asymmetrical interactions, subordinate players were more likely to offer public goods than the dominant player. More asymmetrical interactions decrease the probability of volunteerism of the dominant player; overall volunteerism increases with increasing relatedness.