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.Comment: 12 pages, 13 figure