Balanced-imbalanced transitions in indirect reciprocity dynamics on networks

TL;DR

This paper studies how social network structure influences the dynamics of cooperation and antagonism, revealing phase transitions between stable and active opinion states based on network density.

Contribution

It introduces a model of indirect reciprocity on networks and uncovers a phase transition related to link density affecting opinion stability.

Findings

Absorbing state phase transition occurs with changing network density.

Low or high density networks quickly reach stable opinions.

Intermediate density networks exhibit ongoing opinion dynamics.

Abstract

Here we investigate the dynamics of indirect reciprocity on networks, a type of social dynamics in which the attitude of individuals, either cooperative or antagonistic, toward other individuals changes over time by their actions and mutual monitoring. We observe an absorbing state phase transition as we change the network's link or edge density. When the edge density is either small or large enough, opinions quickly reach an absorbing state, from which opinions never change anymore once reached. In contrast, if the edge density is in the middle range the absorbing state is not reached and the state keeps changing thus being active. The result shows a novel effect of social networks on spontaneous group formation.