Secure coordination with a two-sided helper

We investigate the problem of secure source coding with a two-sided helper in a game-theoretic framework. Alice (A) and Helen (H) view iid correlated information sequences Xⁿ and Yⁿ respectively. Alice communicates to Bob (B) at rate R, while H broadcasts a message to both A and B at rate R_H. Additionally, A and B share secret key K at rate R₀ that is independent of (Xⁿ, Yⁿ). An active adversary, Eve (E) sees all communication links while having access to a (possibly degraded) version of the past information. We characterize the rate-payoff region for this problem. We also solve the problem when the link from A to B is private. Our work recovers previous results of Schieler-Cuff and Kittichokechai et al.