Chimera and anticoordination states in learning dynamics

Lugo, Haydée; González-Avella, Juan Carlos; San Miguel, Maxi
Frontiers in Applied Mathematics and Statistics 5, 16 (2019)

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 different 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.

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