Optimal Honeypot Ratio and Convergent Fictitious-Play Learning in Signaling Games for CPS Defense

Cyber-Physical Systems (CPSs) are facing a fast-growing wave of attacks. To achieve effective proactive defense, this paper models honeypot deployment as a gamma-fixed signaling game in which node liveness serves as the only signal and normal-node signal gamma is exogenously fixed. We define the gamma-perfect Bayesian-Nash equilibrium (gamma-PBNE). Analytical expressions are obtained for all gamma-PBNEs, revealing three distinct equilibrium regimes that depend on the priori honeypot ratio. Furthermore, the optimal honeypot ratio and signaling strategy that jointly maximize the network average utility are obtained. To capture strategic interaction over time, we develop a discrete-time fictitious-play algorithm that couples Bayesian belief updates with empirical best responses. We prove that, as long as the honeypot ratio is perturbed within a non-degenerate neighbourhood of the optimum, every fictitious-play path converges to the defender-optimal gamma-PBNE. Numerical results confirm the effectiveness of the proposed method and demonstrate its applicability to CPS defense.