A combat game model between hierarchical networks

Inter-network combat between hierarchical systems plays an essential role in shaping the landscape of everyone's surroundings, influencing fields such as sports tournaments, business competitions, military conflicts, and trade wars. In response, this study proposes a hierarchical combat game model to analyze the dynamics of leader-follower networks engaged in adversarial interactions. Within this model, leaders are motivated by the collective goals, framing the strategic dilemmas faced by followers, who must balance adherence to leadership strategies against minimizing personal risk. Utilizing the leader-follower game as a theoretical framework, the study investigates the impact of leader characteristics on overall success, measured by the winning percentage (WP). The key findings reveal that increasing the number of leaders consistently enhances WP, with the effect being more pronounced in larger populations. However, higher aspiration level and rationality among leaders may impede their chances of winning the game. Additionally, the analysis uncovers strong correlations between the differences in the number of surviving followers, differences in payoffs, and differences in the proportion of followers adopting the Attack strategy, highlighting critical factors that drive success in combat scenarios. Furthermore, our investigation into follower dynamics reveals that the side making the first sacrifice often wins.