Can Competition Outperform Collaboration? The Role of Malicious Agents

We investigate a novel approach to resilient distributed optimization with quadratic costs in a Networked Control System prone to exogenous attacks that make agents misbehave. In contrast with commonly adopted filtering strategies, we draw inspiration from a game-theoretic formulation of the consensus problem and argue that adding competition to the mix can improve resilience in the presence of malicious agents. Our intuition is corroborated by analytical and numerical results showing that (i) our strategy reveals a nontrivial performance trade-off between full collaboration and full competition, and (ii) such competitionbased approach can outperform state-of-the-art algorithms based on Mean Subsequence Reduced. Finally, we study impact of communication topology and connectivity on performance, pointing out insights to robust network design.