A game-theoretic attack-defense framework for the study of network resilience.

The rapid evolution of communication technologies and the Internet of Things has enhanced system interconnectivity, allowing localized disruptions to cascade into failures. Many such breakdowns are not purely accidental but emerge from intentional countermeasures that influence one another during disruptions. Capturing this interplay requires a framework describing how strategic behaviors coevolve and collectively determine the resilience of complex networks. Here we develop a game-theoretic framework that captures the coevolution of attacks and defenses through repeated interactions on a networked system. Attackers and defenders update strategies based on past outcomes, generating adaptive dynamics that link network structure with strategic behavior. We examine strategic unilateral control of payoffs and uncover a heterogeneity-dependent asymmetry: attackers dominate on heterogeneous networks, whereas defenders prevail on homogeneous ones. Remarkably, optimal attacker strategies converge on the network's percolation threshold, as confirmed across synthetic and empirical networks. Our results reveal how topology governs strategic coevolution and emergent resilience.