Cooperation in the snowdrift game on directed small-world networks under self-questioning and noisy conditions

TL;DR

This study investigates how self-questioning and noise influence cooperation in the snowdrift game on directed small-world networks, revealing mechanisms that promote or hinder cooperation depending on network structure and parameters.

Contribution

It introduces a self-questioning updating mechanism in the snowdrift game on directed small-world networks and analyzes its effects under noisy and noise-free conditions.

Findings

Self-questioning promotes cooperation at high payoff ratios.

Rewired networks facilitate cooperation for low payoff ratios.

Noise disrupts symmetry and weakens cooperation at large payoffs.

Abstract

Cooperation in the evolutionary snowdrift game with a self-questioning updating mechanism is studied on annealed and quenched small-world networks with directed couplings. Around the payoff parameter value $r=0.5$, we find a size-invariant symmetrical cooperation effect. While generally suppressing cooperation for $r>0.5$ payoffs, rewired networks facilitated cooperative behavior for $r<0.5$. Fair amounts of noise were found to break the observed symmetry and further weaken cooperation at relatively large values of $r$. However, in the absence of noise, the self-questioning mechanism recovers symmetrical behavior and elevates altruism even under large-reward conditions. Our results suggest that an updating mechanism of this type is necessary to stabilize cooperation in a spatially structured environment which is otherwise detrimental to cooperative behavior, especially at high cost-to-benefit ratios. Additionally, we employ component and local stability analyses to better understand the nature of the manifested dynamics.