  Understanding the role of network structure in the evolution of cooperation
is a key research goal at the intersection between physics and biology. Recent
studies have particularly focused on multiplex networks given that multiple
social domains are interrelated and cannot be represented by single-layer
networks. However, the role of network multiplexity is not fully understood
when combined with another important network characteristic: network dynamics.
In the present study, we investigated evolutionary prisoner's dilemma games
played on dynamic two-layer multiplex networks in which the payoff combined
across the two layers determined strategy evolution. In addition, we introduced
network dynamics where agents can sever links with defecting neighbors and
construct new links. Our simulation showed that link updating enhances
cooperation but the resultant states are far from those of full cooperation.
This modest enhancement in cooperation was related to symmetry breaking whereby
the cooperation frequency in one layer disproportionately increased while that
in the other layer remained the same or even diminished. However, this broken
symmetry disappeared with sufficiently fast link updating. Our results show
that the introduction of network dynamics enhances cooperation in the
prisoner's dilemma as previously reported, but this enhancement is accompanied
by significant asymmetry once network multiplexity is considered.
