A cyber security problem in a networked system formulated as a resilient graph problem based on a game-theoretic approach is considered. The connectivity of the underlying graph of the network system is reduced by an attacker who removes some of the edges, whereas the defender attempts to recover them. Both players are subject to energy constraints so that their actions are restricted and cannot be performed continuously. For this two-stage game, we characterize the optimal strategies for the attacker and the defender in terms of edge connectivity and the number of connected components of the graph. The resilient graph game is then applied to a multiagent consensus problem, where the game is played repeatedly over time. In this article, we study how the attacks and the recovery on the edges affect the consensus process. Finally, we also provide numerical simulation to illustrate the results.

中文翻译：

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动态弹性网络游戏及其在多主体共识中的应用

考虑了基于博弈论方法的网络系统中的网络安全问题，该网络安全问题被制定为弹性图问题。攻击者删除了一些边缘，而防御者则试图恢复这些边缘，从而降低了网络系统基础图的连通性。两名玩家都受到能量的限制，因此他们的行为受到限制，无法连续执行。对于此两阶段游戏，我们根据边缘连接性和图形的连接组件数来描述针对攻击者和防御者的最佳策略。然后将弹性图博弈应用于多主体共识问题，该博弈随时间反复进行。在本文中，我们研究边缘的攻击和恢复如何影响共识过程。最后，