Cluster Formation in Multiagent Consensus via Dynamic Resilient Graph Games

In this paper we formulate a two-player game-theoretic problem on resilient graphs representing communication channels that are vulnerable to attacks in multiagent consensus setting. An attacker is capable to disconnect part of the edges of the graph by emitting jamming signals while, in response, the defender recovers some of them by increasing the transmission power for the communication signals over the corresponding edges. It is also possible for the attacker to emit stronger jamming signals that cannot be overcome by the defender. We consider repeated games where the utilities of players in each game depend on attack/recovery performance measured over multiple intervals. The utilities of both players are mainly related to agents' states and the cluster formation, i.e., how the agents are divided. The players' actions are constrained by their energy for transmissions, with a less strict constraint for the attacker compared to the defender. Numerical examples of dynamic games played over time are provided to demonstrate the cluster formation.