Many-strategy games in groups with relatives and the evolution of coordinated cooperation.

Humans often cooperate in groups with friends and family members with varying degrees of genetic relatedness. Past kin selection can also be relevant to interactions between strangers, explaining how the cooperation first arose in the ancestral population. However, modelling the effects of relatedness is difficult when the benefits of cooperation scale nonlinearly with the number of cooperators (e.g., economies of scale). Here, we present a direct fitness method for rigorously accounting for kin selection in n-player interactions with m discrete strategies, where a genetically homophilic group-formation model is used to calculate the necessary higher-order relatedness coefficients. Our approach allows us to properly account for non-additive fitness effects between relatives (synergy). Analytical expressions for dynamics are obtained, and they can be solved numerically for modestly sized groups and numbers of strategies. We illustrate with an example where group members can verbally agree (cheap talk) to contribute to a public good with a sigmoidal benefit function, and we find that such coordinated cooperation is favoured by kin selection. As interactions switched from family to strangers, in order for coordinated cooperation to persist and for the population to resist invasion by liars, either some level of homophily must be maintained or following through on the agreement must be in the self-interests of contributors. Our approach is useful for scenarios where fitness effects are non-additive and the strategies are best modelled in a discrete way, such as behaviours that require a cognitive 'leap' of insight into the situation (e.g., shared intentionality, punishment).