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 networks with broad-scale degree distributions favor the emergence of robust cooperative clusters, and that temporal networks might 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 to multilayer and interdependent networks. This has revealed new paths to cooperation, but also opened up new questions 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 to what extent payoffs in one network influence the payoffs in the other network. We show that assortative linking between the layers-connecting hubs of one network with the hubs in the other-does enhance cooperation under adverse conditions, but does so with a relatively modest margin in comparison to random matching or disassortative matching between the two layers. We also confirm previous results, showing that the bias in the payoffs in terms of contributions from different layers can help public cooperation to prevail, and in fact more so than the assortativity between layers. These results are robust to variations in the network structure and average degree, and they can be explained well by the distribution of strategies across the networks and by the suppression of individual success levels that is due to the payoff interdependence.