Coordination problems on networks revisited: statics and dynamics

Simple binary-state coordination models are widely used to study collective socio-economic phenomena such as the spread of innovations or adoption products on social networks. The common trait these systems is occurrence large-scale events taking place abruptly, in form a cascade process, consequence small perturbations an apparently stable state. conditions for instabilities have been largely analysed literature, however same no sufficient attention was given relation between structural properties (Nash) equilibria and possible outcomes dynamical equilibrium selection. Using methods from statistical physics disordered systems, present work investigates both analytically numerically, Nash networks, focusing mostly random graphs. We provide accurate description properties, which then exploited shed light mechanisms behind onset coordination/miscoordination large This done studying most processes selection, best response, bounded-rational dynamics learning processes. In particular, we show that well beyond instability region, full still globally stochastically stable, selection with low stochasticity (e.g. response) strong memory effects reinforcement learning) can be prevented achieving by being trapped into (exponentially number agents) set locally at low/medium (inefficient equilibria). These results should useful allow better understanding general problems complex