Assortativity provides a narrow margin for enhanced cooperation on multilayer networks

Research at the interface of statistical physics, evolutionary game theory, and network science has in the past two decades significantly improved our understanding of cooperation in structured populations.We know that networkswith broad-scale degree distributions favor the emergence of robust cooperative clusters, and that temporal networksmight preclude defectors to exploit cooperators, provided the later can sever their bad ties soon enough. In recent years, however, research has shifted from single and isolated networks tomultilayer and interdependent networks. This has revealed newpaths to cooperation, but also opened up newquestions that remain to be answered.We here study how assortativity in connections between two different network layers affects public cooperation. The connections between the two layers determine towhat extent payoffs in one network influence the payoffs in the other network.We show that assortative linking between the layers— connecting hubs of one networkwith the hubs in the other—does enhance cooperation under adverse conditions, but does sowith a relativelymodestmargin in comparison to randommatching or disassortativematching between the two layers.We also confirmprevious results, showing that the bias in the payoffs in terms of contributions fromdifferent layers can help public cooperation to prevail, and in factmore so than the assortativity between layers. These results are robust to variations in the network structure and average degree, and they can be explainedwell by the distribution of strategies across the networks and by the suppression of individual success levels that is due to the payoff interdependence.