Unilateral Payoff Control is Infeasible in Network Attack-Defense Interactions

Network resilience generally refers to the ability of a network to maintain normal operation in the face of various failures and disturbances, which has many applications in social, financial, communication, and transportation systems. There is a large amount of research on designing strategies to disrupt the network from the perspective of attack and to protect the network from the defense standpoint. However, attacks and defenses in the real world often occur simultaneously and repeatedly. The study of network resilience should not be limited to the structural characteristics but should consider the functional characteristics of the network. We develop a general game-theoretic framework to study attack-defense repeated interactions on complex net-works and examine the possibility of achieving precise control over the payoffs of attackers and defenders. Our findings reveal that neither the attacker nor the defender can unilaterally control their own payoff, the opponent's payoff, or any linear combination thereof. This work highlights the limitations of unilateral payoff control in real-world interaction scenarios, a consideration often overlooked in numerous theoretical studies.