Effects of relatedness on the evolution of cooperation in nonlinear public goods games

Evolution of cooperation has traditionally been studied by assuming that individuals adopt either of two pure strategies, to cooperate or defect. Recent work has considered continuous cooperative investments, turning full cooperation and full defection into two opposing ends of a spectrum and sometimes allowing for the emergence of the traditionally-studied pure strategies through evolutionary diversification. These studies have typically assumed a well-mixed population in which individuals are encountered with equal probability. Here, we allow for the possibility of assortative interactions by assuming that, with specified probabilities, an individual interacts with one or more other individuals of the same strategy. A closely related assumption has previously been made in evolutionary game theory and has been interpreted in terms of relatedness. We systematically study the effect of relatedness and find, among other conclusions, that the scope for evolutionary branching is reduced by either higher average degree of, or higher uncertainty in, relatedness with interaction partners. We also determine how different types of non-linear dependencies of benefits and costs constrain the types of evolutionary outcomes that can occur. While our results overall corroborate the conclusions of earlier studies, i.e. higher relatedness promotes the evolution of cooperation, our investigation gives a comprehensive picture of how relatedness affects the evolution of cooperation with continuous investments. In impunity games proposers, like allocators in dictator games, can take what they want; however, responders can refuse offers deemed unsatisfactory at own cost. We modify the impunity game via allowing offers to condition of another participant's counterfactual generosity intention. For a given pair of proposer candidates each states, via the strategy vector method, an intended and two adjusted offers: one (possibly) upward adjusted in case the intended offer of the other candidate is higher and one (possibly) downward adjusted in case it is lower. Additionally, each candidate determines an acceptance threshold for the responder role. Only one candidate in each pair is randomly selected and endowed as the actual proposer whose offer is either possibly upward or downward adjusted depending on the counterfactual offer of the other proposer candidate. The endowed proposer of one pair is matched with the non-endowed candidate of another pair in the responder role. The data confirm that counterfactual intentions of others often affect own generosity via substantial and significant average adjustments to the weakest social influence. Overall, offers seem correlated with acceptance thresholds. Furthermore, we find significant gender differences: female participants state lower intended and adjusted offers as well as acceptance thresholds and therefore appear to be less sensitive to social influence.