Game Over Interdependent Networks: Rationality Makes the System Inherent Deficient

Many real-world systems are composed of interdependent networks that rely on one another. Such networks are typically designed and operated by different entities, who aim at maximizing their own interest. In this paper, we study the game over interdependent networks, investigating how the rational behaviors of entities impact the whole system. We first introduce a mathematical model to quantify the interacting payoffs among varying entities. Then we study the Nash equilibrium and compare it with the optimal social welfare. We reveal that the cooperation between different entities can be reached to maximize the social welfare only when the average degree of each network is constant. Otherwise, there may be a huge gap between the Nash equilibrium and optimal social welfare. Therefore, the rationality of different entities that operates these networks makes the system inherently deficient and even extremely vulnerable in some cases. Furthermore, we uncover some factors (such as weakening coupled strength of interdependent networks, designing suitable topology dependency of the system) that help reduce the gap and improve the system vulnerability.