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, which is played repeatedly over time, 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 multi-agent consensus problem. 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：

---

具有多代理共识应用的动态弹性网络游戏

网络系统中的网络安全问题被视为基于博弈论方法的弹性图问题。攻击者移除了一些边，而防御者试图恢复它们，从而降低了网络系统底层图的连通性。双方球员都受到能量限制，因此他们的行动受到限制，不能连续进行。对于这个随着时间重复进行的两阶段博弈，我们根据边缘连通性和图的连通分量的数量来表征攻击者和防御者的最佳策略。然后将弹性图游戏应用于多代理共识问题。我们研究边缘的攻击和恢复如何影响共识过程。最后，