  In many real-life situations, individuals are dared to simultaneously achieve
social objectives of acceptance or approval and strategic objectives of
coordination. Since these two objectives may take place in dfferent
environments, a two-layer network is the simple and natural framework for the
study of such kind of dynamical situations. In this paper we present a model in
which the state of the agents corresponds to one of two possible strategies.
They change their states by interaction with their neighbors in the network.
Inside each layer the agents interact by a social pressure mechanism, while
between the layers the agents interact via a coordination game. From an
evolutionary approach, we focus on the asymptotic solutions for all-to-all
interactions across and inside the layers and for any initial distribution of
strategies. We find new asymptotic configurations which do not exist in a
single isolated social network analysis. We report the emergence and existence
of chimera states in which two different collective states coexist in the
network. Namely, one layer reaches a state of full coordination while the other
remains in a dynamical state of coexistence of strategies. In addition, the
system may also reach a state of global anticoordination where a full
coordination is reached inside each layer but with opposite strategies in each
of the two network layers. We trace back the emergence of chimera states and
global anticoordination states to the agents inertia against social pressure,
referred here to as the level of skepticism, along with the degree of risk
taken into account in a general coordination game.
