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Understanding the role of network structure in the evolution of cooperationis a key research goal at the intersection between physics and biology. Recentstudies have particularly focused on multiplex networks given that multiplesocial domains are interrelated and cannot be represented by single-layernetworks. However, the role of network multiplexity is not fully understoodwhen combined with another important network characteristic: network dynamics.In the present study, we investigated evolutionary prisoner's dilemma gamesplayed on dynamic two-layer multiplex networks in which the payoff combinedacross the two layers determined strategy evolution. In addition, we introducednetwork dynamics where agents can sever links with defecting neighbors andconstruct new links. Our simulation showed that link updating enhancescooperation but the resultant states are far from those of full cooperation.This modest enhancement in cooperation was related to symmetry breaking wherebythe cooperation frequency in one layer disproportionately increased while thatin the other layer remained the same or even diminished. However, this brokensymmetry disappeared with sufficiently fast link updating. Our results showthat the introduction of network dynamics enhances cooperation in theprisoner's dilemma as previously reported, but this enhancement is accompaniedby significant asymmetry once network multiplexity is considered.

Symmetry breaking in the prisoner's dilemma on two-layer dynamic multiplex networks