Cooperation in an asymmetric volunteer’s dilemma game with relatedness

Abstract

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 coplayers; 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. asymmetric interaction, cooperation, volunteer's dilemma, relatedness, public goods, kin selection, inclusive fitness Citation:He J Z, Wang R W, Christopher X J J, et al. Cooperation in an asymmetric volunteer's dilemma game with relatedness.

Asymmetric interaction paired with a super-rational strategy might resolve the tragedy of the commons without requiring recognition or negotiation

“…In both the IPD and VoD groups of cooperators outperform groups of defectors, but defectors have the potential to outperform cooperators in groups: this paradox defines the social dilemma. The key difference between these two games is that the probability of cooperation in the IPD is strictly dependent on the cost-to-benefit discount ratio 2 25 whereas in the VoD the probability of cooperation also depends on the size of the group 19 20 26 27 28 29 . In analyzing the outcome of such games, one consideration is whether a “pure” strategy exists which can displace all other strategies.…”

Asymmetry within social groups: division of labour and intergroup competition

“…Previous theory has investigated both within‐group asymmetry and between‐group competition, but the asymmetric nested tug‐of‐war model we present here brings together both components explicitly and stands out from prior models in several ways. For example, previous models of public goods provision without intergroup competition have allowed variation in the amount of resources that each group member has, and variation in the benefits and costs to each group member of contribution to the public good (Diekmann, ; Frank, , ; Crowley & Baik, ; He et al ., ). Gavrilets & Fortunato () do explicitly investigate how intergroup competition affects cooperation via the coevolution of within‐group traits, but their model similarly considers groups with asymmetry in resource holdings, rather than the asymmetry in power that we investigate.…”

“…These previous models differ from ours in an additional key respect: with asymmetries in the amount of resources, ‘dominant’ individuals are better able to invest in both cooperation and competition, yielding the result that higher‐ranking individuals contribute more to group productivity (Frank, , ; He et al ., ; Gavrilets & Fortunato, ). This seeming contradiction with our results arises because in our model, individuals in each role are unequal in their abilities to invest in within‐group competition but equally able to invest in within‐group cooperation.…”

Spatial games and the maintenance of cooperation in an asymmetric Hawk-Dove game

“…This unique cooperating strategy for any players in IPD model does not, in fact, conform to real cooperation systems. In almost all real cooperation systems, ranging from the eusocial-society of insects to inter-specific cooperation systems, almost all cooperative partners take a mixed strategy of either cooperating or competing with their counter-partners [13,18,[20][21][22][23]; as the same is true in the genetic expression of a coherent cell [24].…”

“…The interacting players may be different in size or strength, influencing the outcome of the game [21,24]. In asymmetric cooperation systems, the payoff for the players may depend on their strength and the strength ratio of the two players, k:(1k) therefore describes the degree of asymmetry between the interacting players, here k and 1k can be the percentage of resources dominated by each player, the probability of winning the fight with others, or any other parameters similarly characterized by an interaction between a dominate and sub-ordinates.…”