  In this work we assess the role played by the dynamical adaptation of the
interactions network, among agents playing Coordination Games, in reaching
global coordination and in the equilibrium selection. Specifically, we analyze
a coevolution model that couples the changes in agents' actions with the
network dynamics, so that while agents play the game, they are able to sever
some of their current connections and connect with others. We focus on two
update rules: Replicator Dynamics (RD) and Unconditional Imitation (UI). We
investigate a Pure Coordination Game (PCG), in which choices are equivalent,
and on a General Coordination Game (GCG), for which there is a risk-dominant
action and a payoff-dominant one. The network plasticity is measured by the
probability to rewire links. Changing this plasticity parameter, there is a
transition from a regime in which the system fully coordinates in a single
connected component to a regime in which the system fragments in two connected
components, each one coordinated on a different action (either if both actions
are equivalent or not). The nature of this fragmentation transition is
different for different update rules. Second, we find that both for RD and UI
in a GCG, there is a regime of intermediate values of plasticity, before the
fragmentation transition, for which the system is able to fully coordinate in a
single component network on the payoff-dominant action, i. e., coevolution
enhances payoff-dominant equilibrium selection for both update rules.
