Cascade of elimination and emergence of pure cooperation in coevolutionary games on networks

We propose a coevolutionary game to study cooperative behavior in the presence of catastrophic phenomenon. We incorporate tolerance to elimination of individuals in network games where individuals update their strategies synchronously, and there are no birth of individuals and stochastic effects. We find that an avalanche-like death process can arise when defection strategies exist and individuals are vulnerable to deficiency of profits. Strikingly, we observe that, after such a cascading process terminates, cooperators are the sole survivors regardless of the game types and of the connection patterns among individuals as determined by the network topology. Cooperation thus becomes the optimal strategy and absolutely outperforms defection. Our results can yield insights into evolution of cooperation in the presence of catastrophic events in social and natural systems.