We investigated a two-layered multiplex network in which players interact depending on the social distance between them. The aim of this study is to clarify the effects of multi-layered structure on emergence of cooperation in the prisoner's dilemma game including social distances, interactions, and learning distances. We found that the increase of learning distance promotes cooperation even on a multiplex network, and a cooperative strategy tends to vanish away with the parameters, which is contract to the Seltzer's result.
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