Exploring Centrality Dynamics for Epidemic Control in Complex Networks: An Asymmetrical Centralities Game Approach

The Distributed Denial-of-Service (DDoS) attack, a notorious threat to the Internet, gained widespread attention in July 1999 due to its significant impact on major organizations. Originally emerging in 1998, this type of attack involves mass infection of a network’s devices. To take control of numerous devices, the attacker’s strategy centers on injecting malicious code from an infected device into one or more vulnerable neighboring devices. In response, the network administrator, known as the defender, engages in a conflictual interaction to limit the attacker’s control and influence. Within this adversarial landscape, intelligent agents (the defender and the attacker), strategically compete within the network, aiming to control crucial devices identified through centrality measures. The complexity arises from varied roles, information accessibility, resources, and diverse perspectives on risks, prompting agents to adopt distinct centrality measures. Our analysis emphasizes the critical importance of recognizing these variations in centrality measures and their impact on each agent’s objectives, as we introduce a novel approach that integrates this asymmetry, wherein the cost of agents’ actions depends on the centrality values of the involved devices. We thus propose a non-zero-sum game model to determine the Nash equilibrium strategy profile for agents at each stage of the game in such a context. Through numerical experiments, we demonstrate that integrating these differences in centrality measures within our game model effectively enables defenders to mitigate the impact of epidemics initiated by malicious attackers.