Abstract
Social animals vary in their ability to compete with group members over shared resources and also vary in their cooperative efforts to produce these resources. Competition among groups can promote within-group cooperation, but many existing models of intergroup cooperation do not explicitly account for observations that group members invest differentially in cooperation and that there are often within-group competitive or power asymmetries. We present a game theoretic model of intergroup competition that investigates how such asymmetries affect within-group cooperation. In this model, group members adopt one of two roles, with relative competitive efficiency and the number of individuals varying between roles. Players in each role make simultaneous, coevolving decisions. The model predicts that although intergroup competition increases cooperative contributions to group resources by both roles, contributions are predominantly from individuals in the less competitively efficient role, whereas individuals in the more competitively efficient role generally gain the larger share of these resources. When asymmetry in relative competitive efficiency is greater, a group's per capita cooperation (averaged across both roles) is higher, due to increased cooperation from the competitively inferior individuals. For extreme asymmetry in relative competitive efficiency, per capita cooperation is highest in groups with a single competitively superior individual and many competitively inferior individuals, because the latter acquiesce and invest in cooperation rather than within-group competition. These predictions are consistent with observed features of many societies, such as monogynous Hymenoptera with many workers and caste dimorphism.