Clustered networks protect cooperation against catastrophic collapse

Gwen Spencer

doi:10.1017/nws.2018.5

Abstract

AbstractAssuming a society of conditional cooperators (or moody conditional cooperators), this computational study proposes a new perspective on the structural advantage of social network clustering. Previous work focused on how clustered structure might encourage initialoutbreaks of cooperationor defend against invasion by a few defectors. Instead, we explore the ability of a societal structure to retain cooperative norms in the face of widespread disturbances. Such disturbances may abstractly describe hardships like famine and economic recession, or the random spatial placement of a substantial numbers ofpure defectors(orround-1 defectors) among a spatially structured population of players in a laboratory game, etc.As links in tightly clustered societies are reallocated to distant contacts, we observe that a society becomes increasingly susceptible tocatastrophic cascades of defection: mutually-beneficial cooperative norms can be destroyed completely by modest shocks of defection. In contrast, networks with higher clustering coefficients can withstand larger shocks of defection before being forced to catastrophically low levels of cooperation. We observe a remarkably linearprotective effect of clusteringcoefficient that becomes active above acritical level of clustering. Notably, both the critical level and the slope of this dependence is higher for decision-rule parameterizations that correspond to highercosts of cooperation. Our modeling framework provides a simple way to reinterpret the counter-intuitive and widely cited human experiments of Suri and Watts (2011) while also affirming the classical intuition that network clustering and higher levels of cooperation should be positively associated.

Highlights

Introduction and MotivationThe ubiquity of short average path lengths in social networks is often explained as reflecting the advantage of fast diffusion of information (starting from the foundational work of Granovetter (1973))
This protective effect is still strongly apparent at 20% Generous-type Moody Conditional Cooperation (MCC), but appears to dissipate as an increasing number of Generous-type MCCs are added to the distribution
As Stingy-type MCCs are added to the distribution we obtain a series of heterogeneous player distributions that exhibit a very strong protective effect of clustering

Summary

Introduction

The ubiquity of short average path lengths in social networks is often explained as reflecting the advantage of fast diffusion of information (starting from the foundational work of Granovetter (1973)). In graphs with low density, “weak ties” that reach to otherwise-distant members of the network are key to obtaining short average path lengths, giving rise to a “small world” property (Granovetter (1973); Watts & Strogatz (1998)). Observations of significant network clustering (which requires many short ties to neighbors of neighbors) are ubiquitous in real data about social networks. What advantages might contribute to the popularity of short ties?

Methods

Results

Conclusion