Distributed aggregative games on graphs in adversarial environments

Existing solutions to aggregative games assume that all players are fully trustworthy for cooperative tasks or, in a worst-case scenario, are selfish players with no intent to intentionally harm the network. Nevertheless, the need to believe that players will behave consistently exposes the network to vulnerabilities associated with cyber-physical attacks. This paper investigates the effects of cyber-physical attacks on the outcome of distributed aggregative games (DAGs). More specifically, we are seeking to answer two main questions: (1) how a stealthy attack can deviate the game outcome from a cooperative Nash equilibrium, and by doing so, (2) by how much efficiency of a DAG degrades. To this end, we first show that adversaries can stealthily manipulate the outcome of a DAG by compromising the Nash equilibrium solution and consequently lead to an emergent misbehavior or no emergent behavior. This study will intensify the urgency of designing novel resilient solutions to DAGs so that the overall network sustains some notion of acceptable global behavior in the presence of malicious agents. Finally, we corroborate and illustrate our results by providing simulation examples. Simulations reveal that the adverse effect of a compromised agent is considerably worse than that of a selfish agent.