title: Degree mixing in multilayer networks impedes the evolution of cooperation.
abstract: Traditionally, the evolution of cooperation has been studied on single, isolated networks. Yet a player, especially in human societies, will typically be a member of many different networks, and those networks will play different roles in the evolutionary process. Multilayer networks are therefore rapidly gaining on popularity as the more apt description of a networked society. With this motivation, we here consider two-layer scale-free networks with all possible combinations of degree mixing, wherein one network layer is used for the accumulation of payoffs and the other is used for strategy updating. We find that breaking the symmetry through assortative mixing in one layer and/or disassortative mixing in the other layer, as well as preserving the symmetry by means of assortative mixing in both layers, impedes the evolution of cooperation. We use degree-dependent distributions of strategies and cluster-size analysis to explain these results, which highlight the importance of hubs and the preservation of symmetry between multilayer networks for the successful resolution of social dilemmas.
authors.affiliation: Department of Physics, Hong Kong Baptist University, Kowloon Tong, Hong Kong and Center for Nonlinear Studies and Beijing-Hong Kong-Singapore Joint Center for Nonlinear and Complex Systems, Institute of Computational and Theoretical Studies, Hong Kong Baptist University, Kowloon Tong, Hong Kong.
authors.forename: Zhen
authors.initials: Z
authors.lastname: Wang
authors.affiliation: Centre for Chaos and Complex Networks, Department of Electronic Engineering, City University of Hong Kong, Kowloon, Hong Kong.
authors.forename: Lin
authors.initials: L
authors.lastname: Wang
authors.affiliation: Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška cesta 160, SI-2000 Maribor, Slovenia.
authors.forename: Matjaž
authors.initials: M
authors.lastname: Perc
mesh_terms: D003163:Competitive Behavior; D003198:Computer Simulation; D003299:Cooperative Behavior; D005716:Game Theory; D015233:Models, Statistical; D060756:Social Networking