# Chimera and anticoordination states in learning dynamics

## TL;DR

This paper models complex social dynamics using a two-layer network, revealing new states like chimera and anticoordination, driven by agents' skepticism and risk considerations in strategic interactions.

## Contribution

It introduces a novel two-layer network model capturing chimera and anticoordination states in social and strategic dynamics, extending single-network analyses.

## Key findings

- Discovery of chimera states with coexisting coordination and coexistence
- Identification of global anticoordination with opposite strategies in layers
- Analysis of agents' skepticism and risk as key factors in emergent states

## Abstract

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.