Thresholds in the resilience of modular social networks to invasion by defectors. (7th January 2019)

• Record Type: Journal Article
• Authors: Wechsler, Daniel; Bascompte, Jordi
• Is Part Of: Journal of theoretical biology. Volume 460(2019)
• Page Start: 56
• Page End: 63
• Publication Date: 2019-01-07
• Subjects: Evolution of cooperation -- Game theory -- Non-linear transition -- Complex networks; Biology -- Periodicals; Biological Science Disciplines -- Periodicals; Biology -- Periodicals; Biologie -- Périodiques; Theoretische biologie; Biology; Periodicals; 571.05
• DOI: 10.1016/j.jtbi.2018.10.018
• Languages: English
• ISSNs: 0022-5193

Abstract

Highlights: Highly modular societies are resilient to the spreading of invasive defectors. There is a well-defined threshold in modularity separating invasion from resistance. The threshold in modularity is reminiscent of an epidemic threshold in SIR models. Our results can provide rules of thumb on how to build resilient cooperative networks. Abstract: Cooperative interactions constitute the backbone of many biological and social systems. Since cooperation is prone to exploitation, these systems must incorporate mechanisms that prevent the spreading of defective behaviors. One such mechanism is modularity, i.e., the tendency of a social network to be organized in modules, where individuals within a module tend to interact strongly among themselves while avoiding interacting with individuals from other modules. This structure allows cooperation to prevail by having modules of cooperative individuals with a limited exposure to defectors. To address the rate and shape of the effect of modularity on the resilience of cooperation, here we study a variant of the Prisoner's Dilemma on modular networks. Our simulations reveal a sharp transition between a resilient and a vulnerable regime as modularity exceeds a critical threshold. By using a simplified mathematical model, we show that the observed threshold is equivalent to the epidemic threshold found in a certain class of SIR models. This allows us to derive an explicit condition under which a cooperative society is expected to be resilient to invasive defectors.