Collective influence in evolutionary social dilemmas

TL;DR

This paper explores how collective influence, considering hierarchical network structures beyond simple degree, affects the resolution of social dilemmas in evolutionary games, revealing optimal influence depths vary with dilemma strength.

Contribution

It introduces the formalism of collective influence with hierarchical depth to better predict influential players in social dilemmas, surpassing degree-based measures.

Findings

Optimal hierarchical depth depends on social dilemma strength.

Degree is only optimal when temptation to defect is low.

Hierarchical influence structures enhance strategy spreading.

Abstract

When evolutionary games are contested in structured populations, the degree of each player in the network plays an important role. If they exist, hubs often determine the fate of the population in remarkable ways. Recent research based on optimal percolation in random networks has shown, however, that the degree is neither the sole nor the best predictor of influence in complex networks. Low-degree nodes may also be optimal influencers if they are hierarchically linked to hubs. Taking this into account leads to the formalism of collective influence in complex networks, which as we show here, has far-reaching implications for the favorable resolution of social dilemmas. In particular, there exists an optimal hierarchical depth for the determination of collective influence that we use to describe the potency of players for passing their strategies, which depends on the strength of the social dilemma. Interestingly, the degree, which corresponds to the baseline depth zero, is optimal only when the temptation to defect is small. Our research reveals that evolutionary success stories are related to spreading processes which are rooted in favorable hierarchical structures that extend beyond local neighborhoods.