Predator-prey games on complex networks

Abstract We study the predator-prey game, an intriguing collective and dynamic process in nature, on complex networks. The game is over when the prey and the predator meet at the same node, where the associated mean first encounter time is used as the payoff value. We find that for a number of real networks, a saddle point will appear on the resultant payoff matrix, suggesting that each player has an optimal pure strategy. Interestingly, the prey and the predator exhibit distinct best responses. Specifically, the prey tends to move towards low-degree nodes to escape, while the predator chasing is more likely to hop to nodes with medium-degree. Moreover, in this situation, a scaling behavior of the value of the game indicates that the lifetime of the prey is very long in an infinite-size environment. Furthermore, we find that the saddle point of the predator-prey game occurs more readly on homogeneous networks rather than on heterogeneous ones. Our work provides a basic modeling framework for studying various collective behavior of interacting entities on complex networks.