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

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 costto-benefit ratios. Additionally, we employ component and local stability analyses to better understand the nature of the manifested dynamics.