Distributed Team Orchestration via Supervisor Networks: Convergence, Optimality, and Resilience

Abstract

In this paper, we study zero-sum potential team games with a supervisor network, where agents rely on supervisor-provided belief information rather than accurate common beliefs. The main challenge is that such belief information can be inaccurate because of supervisors' belief-estimation errors and the misreporting of joint actions by Byzantine teams. We propose the distributed team-orchestrating algorithm (DTOA), which combines team fictitious play with supervisor-based distributed belief learning. We prove the convergence of supervisors' belief estimates and establish that the induced learning dynamics converge to a near team-Nash equilibrium (TNE) in terms of the team-Nash gap (TNG). In the Byzantine setting, we consider a misreporting attack model and develop a Byzantine-resilient DTOA. We further provide probabilistic guarantees for Byzantine-team identification and establish an asymptotic bound on the honest TNG. Numerical experiments illustrate the theoretical findings, compare DTOA with baseline learning methods, and evaluate its performance in a Markov decision process setting.