Relatedness and economies of scale in the provision of different kinds of collective goods

Many models proposed to study the evolution of collective action rely on a formalism that represents social interactions as n-player games between individuals adopting discrete actions such as cooperate and defect. Despite the importance of relatedness as a solution to collective action problems in biology and the fact that most social interactions unavoidably occur between relatives, incorporating relatedness into these models has so far proved elusive. We address this problem by considering mixed strategies and by integrating discrete-action n-player games into the direct fitness approach of social evolution theory. As an application, we use our mathematical framework to investigate the provision of three different kinds of collective goods, paradigmatic of a vast array of helping traits in nature: “public goods” (both providers and shirkers can use the good, e.g., alarm calls), “club goods” (only providers can use the good, e.g., participation in collective hunting), and “charity goods” (only shirkers can use the good, e.g., altruistic sacrifice). We show that relatedness relaxes the collective action problems associated to the provision of these goods in different ways depending on the kind of good (public, club, or charity) and on its economies of scale (constant, diminishing, or increasing returns to scale). Our findings highlight the importance of explicitly accounting for relatedness, the kind of good, and economies of scale in theoretical and empirical studies of collective action.