  This paper proposes a novel approach to resilient distributed optimization
with quadratic costs in a networked control system (e.g., wireless sensor
network, power grid, robotic team) prone to external attacks (e.g., hacking,
power outage) that cause agents to misbehave. Departing from classical
filtering strategies proposed in literature, we draw inspiration from a
game-theoretic formulation of the consensus problem and argue that adding
competition to the mix can enhance resilience in the presence of malicious
agents. Our intuition is corroborated by analytical and numerical results
showing that i) our strategy highlights the presence of a nontrivial tradeoff
between blind collaboration and full competition, and ii) such
competition-based approach can outperform state-of-the-art algorithms based on
Mean Subsequence Reduced.
