Abstract
Cooperation is crucial for all levels of living systems. The last two decades have seen progress in revealing the mechanisms for cooperation in structured populations. Most of those analytical works have an explicit assumption, i.e., weak rationality or high temperature in statistical physical terms. It is still far from known how rationality alters the fate of cooperation, although simulation results have provided some intuitions. To be specific, the analytical insight is still lacking under what conditions cooperation can still be promoted, given that it cannot be favored by weak rationality. To this end, we investigate a coevolutionary model where both strategy and network evolve simultaneously. We give a sufficient condition under which cooperation cannot be favored for weak-selection limit, but it can be rescued by enhancing rationality alone. Furthermore, we give the critical rationality analytically. Counterintuitively, we show that the critical rationality can be larger if cooperator–defector links are more fragile, indicating that robust cooperator–defector social relationships can rescue cooperation. We, thus, show that increasing rationality intensity alone can rescue cooperation, where it cannot be present under weak-selection limit. Our work calls for an extrapolation from weak rationality in evolutionary game theory.