Leader selection games under link noise injection attacks

In a leader-follower multi-agent system, the states of a set of leader agents are controlled directly by the system owner and used to influence the behavior of the remaining follower agents. When deployed in hostile environments, leaderfollower systems may be disrupted by adversaries introducing noise in the communication links between agents through interference or false packet insertion, thus corrupting the states of the follower agents. In this paper, we study the problem of mitigating the effect of noise injection attacks by selecting leader agents. We address two cases within a supermodular game-theoretic framework. In the first case, a fixed set of leaders is chosen when the system is initialized. We model this case as a Stackelberg game, in which the system moves first by choosing leaders in order to minimize the worst-case error and the adversary responds by introducing noise. In the second case, the set of leaders varies over time. We study the second case as a simultaneous-move game between the system and an adversary. We show that the game formulations for both cases have equilibria that can be approximated up to a provable bound using supermodular optimization techniques. We illustrate our approach via simulations.