Clustered networks protect cooperation against catastrophic collapse

Abstract

Assuming 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.