Dynamic resilient graph games for state-dependent jamming attacks analysis on multi-agent systems

A cybersecurity problem for a multi-agent consensus problem is investigated through a dynamic game formulation. Specifically, we consider a game repeatedly played between a jamming attacker and a defender. The attacker attempts to jam the links between a number of agents to delay their consensus. On the other hand, the defender tries to maintain the connection between agents by attempting to recover some of the jammed links with the goal of achieving faster consensus. In each game, the players decide which links to attack/recover and for how long to continue doing so based on a Lyapunov-like function representing the largest difference between the states of the agents. We analyze the subgame perfect equilibrium of the game and obtain an upper bound of the consensus time that is influenced by the strategies of the players. The results are illustrated with a numerical example.