Fast-response and low-tolerance promotes cooperation in cascading system collapse

In this paper, we investigate the impact of cascading exit on the evolution of cooperation in structured populations. Specifically, we introduce “rational choice” and “community of interest” in evolutionary games to define the exit rules. Exit behavior is determined by (i) an edge tolerance threshold when being exploited and (ii) the triangle exit rule that a focal player interrupts the interaction with its neighbor’s opponent which belongs to the joint neighborhood set. Results from Monte Carlo simulation show that the edge-based exit can promote the short-term cooperation, but it ultimately goes to extinction. At the same time, this process also triggers the effect of the second-order exit rule, which destroys the network topology completely. The fast-response and low-tolerance not only slows down the decomposition of network structures, but also delays the extinction of cooperation. Moreover, we find that the termination time of the network evolution exhibits an exponential distribution while the proportion of the remaining nodes exhibits a decreasing non-linear relationship. Our results shed some new lights on the coupling effects of the evolution of cooperation in the structured population with the network cascading process.