A combat game model with inter-network confrontation and intra-network cooperation

Inter-network combat and intra-network cooperation among structured systems are likely to have been recurrent features of human evolutionary history; however, little research has investigated the combat mechanism between structured systems that the adversarial interactions will cause the disability of agents and agents are prone to seek cooperation with neighbors. Hence, the current study has proposed a two-network combat game model and designed the corresponding rules of how to attack, how to be disabled, how to cooperate, and how to win. First, within the framework of our model, we have simulated the combat among four common network structures—the Erdős–Rényi (ER) random network, the grid graph, the small-world network, and the scale-free network. We found that the grid network always holds the highest winning percentage, while the ER random graph is most likely to lose when combating with the other three network structures. For each structure, we have also simulated the combat between the same network structures with different generating parameters. The simulations reveal that the small-world property and heterogeneity can promote winning a combat. Besides, by broadening and deepening cooperation, we have found that broader cooperation helps defeat the opposite system on grid and scale-free networks, yet hinders it on ER and Watts–Strogatz (WS) networks, while deeper cooperation can benefit to winning except on scale-free networks. These findings inform our understanding of the effects of structure and cooperation in a combat.