Frustrated opinion dynamics on real networks and its predictors

Indirect reciprocity is a type of social dynamics in which the attitude of an individual toward another individual is either cooperative or antagonistic, and it can change over time through their actions and mutual monitoring. This opinion dynamics is found to be frustrating in certain edge density regimes on random graphs when all the components adopt the Kandori rule, which is one of the norms of indirect reciprocity. In this study, we conducted an exhaustive analysis of so-called “leading-eight” norms of indirect reciprocity dynamics and found that three of them (the Kandori and other two rules) keep the opinion dynamics frustrated on random graphs. We investigated the frustrated opinion dynamics of these three norms on real acquaintance networks and observed that the degree of frustration of the system can be inferred when the network properties such as the number of triangular connections and number of quads are properly taken into account. This study also reveals that the closeness centrality of a triangular representation is a good predictor of the degree of local frustration. Furthermore, it is also found that better prediction is achieved when we do not consider all the reachable triads in the calculation of a focal triad’s closeness centrality. This result suggests that it is sufficient to predict the opinion dynamics by considering only the proximity triads within a certain observation radius from that triad. This finding may facilitate the analysis of real-world cooperative relationships consisting of a vast number of triads.