Game among Interdependent Networks: The Impact of Rationality on System Robustness

TL;DR

This paper models the strategic interactions among entities managing interdependent networks, revealing how rational behaviors influence system robustness and identifying factors to improve resilience.

Contribution

It introduces a mathematical framework for analyzing interdependent network games and compares Nash equilibrium with social welfare, highlighting conditions for cooperation and system vulnerability.

Findings

Cooperation maximizes social welfare when average degree is constant.

Nash equilibrium often diverges from optimal social welfare, reducing system robustness.

Adjusting network coupling and topology can mitigate vulnerabilities.

Abstract

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 payoffs. There exists a game among these entities when designing their own networks. In this paper, we study the game investigating how the rational behaviors of entities impact the system robustness. We first introduce a mathematical model to quantify the interacting payoffs among varying entities. Then we study the Nash equilibrium of the game and compare it with the optimal social welfare. We reveal that the cooperation among different entities can be reached to maximize the social welfare in continuous game only when the average degree of each network is constant. Therefore, the huge gap between Nash equilibrium and optimal social welfare generally exists. The rationality of entities makes the system inherently deficient and even renders it extremely vulnerable in some cases. We analyze our model for two concrete systems with continuous strategy space and discrete strategy space, respectively. 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 the system vulnerability.