Dynamic instabilities induced by asymmetric influence: Prisoners' dilemma game on small-world networks

TL;DR

This study investigates how asymmetric influence from an influential node affects cooperation dynamics in small-world networks playing the Prisoner's Dilemma, revealing sudden cooperation breakdowns and variable recovery times.

Contribution

It introduces a model with an influential node in small-world networks and analyzes its impact on cooperation stability and dynamics.

Findings

Cooperation exhibits punctuated equilibrium with sudden breakdowns.

Breakdowns are linked to imitation of the influential node's strategy.

Recovery times vary depending on network connectivity and cooperation levels.

Abstract

A two-dimensional small-world type network, subject to spatial prisoners' dilemma dynamics and containing an influential node defined as a special node with a finite density of directed random links to the other nodes in the network, is numerically investigated. It is shown that the degree of cooperation does not remain at a steady state level but displays a punctuated equilibrium type behavior manifested by the existence of sudden breakdowns of cooperation. The breakdown of cooperation is linked to an imitation of a successful selfish strategy of the influential node. It is also found that while the breakdown of cooperation occurs suddenly, the recovery of it requires longer time. This recovery time may, depending on the degree of steady state cooperation, either increase or decrease with an increasing number of long range connections.