A two-network adversarial game: Model, strategy, and structure

Adversarial games between two groups offering a spectrum of mixed cooperative-adversarial scenarios have been extensively focused on and studied, like video games and swarm confrontation, while comparably limited attention has been paid to the role and impact of structures of groups. Complex networks are widely employed to characterize the various relationships and structures among diverse individuals. In this context, we present a two-network adversarial game model, encompassing both in-network cooperation and between-network attacks, to explore adversarial strategies and examine the effects of network structures on game outcomes. The decision-making process of adversarial strategies is decomposed into the target selection and team organization procedures. We find that prioritizing the assault on high-attack nodes in the target selection procedure increases the winning probability. Furthermore, we propose a two-step framework of cooperative attack strategies combining the two procedures to realize team-to-node attacks, thus increasing the total attack damage. Moreover, we investigate the impact of degree heterogeneity and long-range connections on structural efficiency, which characterizes the ability of structures to win the game. Heterogeneous networks are susceptible to fragmentation under attacks, which hinders cooperation. However, regular networks with totally homogeneous structures are not the strongest, and small-world networks featuring a small proportion of long-range connections exhibit even higher structural efficiency.