Can Competition Outperform Collaboration? The Role of Misbehaving Agents

We investigate a novel approach to resilient distributed optimization with quadratic costs in a multiagent system prone to unexpected events that make some agents misbehave. In contrast to commonly adopted filtering strategies, we draw inspiration from phenomena modeled through the Friedkin–Johnsen dynamics and argue that adding competition to the mix can improve resilience in the presence of misbehaving agents. Our intuition is corroborated by analytical and numerical results showing that 1) there exists a nontrivial tradeoff between full collaboration and full competition and 2) our competition-based approach can outperform state-of-the-art algorithms based on weighted mean subsequence reduced. We also study the impact of communication topology and connectivity on resilience, pointing out insights into robust network design.