Traditionally, the evolution of cooperation has been studied on single,isolated networks. Yet a player, especially in human societies, will typicallybe a member of many different networks, and those networks will play adifferent role in the evolutionary process. Multilayer networks are thereforerapidly gaining on popularity as the more apt description of a networkedsociety. With this motivation, we here consider 2-layer scale-free networkswith all possible combinations of degree mixing, wherein one network layer isused for the accumulation of payoffs and the other is used for strategyupdating. We find that breaking the symmetry through assortative mixing in onelayer and/or disassortative mixing in the other layer, as well as preservingthe symmetry by means of assortative mixing in both layers, impedes theevolution of cooperation. We use degree-dependent distributions of strategiesand cluster-size analysis to explain these results, which highlight theimportance of hubs and the preservation of symmetry between multilayer networksfor the successful resolution of social dilemmas.
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