  We investigate a novel approach to resilient distributed optimization with
quadratic costs in a multi-agent 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 (i) there exists a nontrivial trade-off between
full collaboration and full competition and (ii) our competition-based approach
can outperform state-of-the-art algorithms based on Weighted Mean Subsequence
Reduced. We also study impact of communication topology and connectivity on
resilience, pointing out insights to robust network design.
