A two-player game-theoretic problem on resilient graphs is formulated. An attacker is capable to disable some of the edges of the network with the objective to divide the agents into clusters by emitting jamming signals while, in response, the defender recovers some of the edges by increasing the transmission power for the communication signals. We consider repeated games between the attacker and the defender where the optimal strategies for the two players are derived in a rolling horizon fashion by taking account of the sizes of the clusters. The players’ actions at each discrete-time step are constrained by their energy for transmissions of signals. We derive several theoretical results to characterize the properties of the two-player game under some specific conditions of the agents’ communication network and the players’ energy parameters. In order to investigate more general cases, we provide some numerical evaluations to show the effects of the values of horizon lengths and game periods on the players’ performance.
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