Steganography and probabilistic risk analysis: a game theoretical framework for quantifying adversary advantage and impact

In environments where adversaries engage in active surveillance and covert communication, defenders face the dual challenge of when to deploy steganography and whether it yields measurable operational benefit. We present a game-theoretic model of steganographic operations that captures the strategic interaction between a defender and an adversary through calibrated monetary primitives and nonlinear utility mappings. The model derives mixed-strategy equilibria that determine conditional and unconditional success rates for hiding and detection, and introduces a time-varying adversarial advantage metric that quantifies when an attacker's incentive exceeds the defender's effective concealment or detection capability. By linking this advantage to a currency-unit risk measure, we extend the classical risk formulation into a decision-aware, monetised framework. The quantitative evaluation combines nonlinear equilibrium analysis, a Monte Carlo ensemble of 10,000 draws, and empirical calibration on Break Our Steganographic System database (BOSSbase) 1.01 using four spatial-domain adaptive steganographic methods: Wavelet Obtained Weights (WOW), Spatial Universal Wavelet Relative Distortion (S-UNIWARD), High-pass, Low-pass and Low-pass (HILL), and Minimising the Probability of Detection (MiPOD). The payloads are 0.100, 0.200, and 0.400 bits per pixel. Two lightweight convolutional neural-network steganalysis back-ends are used to estimate the defender signal, defined as 1 - TPR@FPR = 0.10. The aggregated trajectories show persistent positive adversarial advantage in most configurations, with mean normalised advantage reaching 0.22 and maximum normalised risk reaching 0.20. Lower-risk cases show average positive advantage of approximately 0.01, while higher-risk regimes reach approximately 0.18 to 0.19. In the monetary setting, the maximum epoch-level risk reaches £210,375, high-risk configurations produce mean risks close to £196,000, and the maximum observed security benefit is £11,250. Detector performance further shows best-epoch area under the curve (AUC) values of at least 0.95 for the more stable detector, while the more volatile detector produces defender-signal values spanning approximately 0.015 to 0.915. These results show that adversarial advantage can be translated into interpretable monetary risk estimates for assessing whether steganographic defences decrease, amplify, or only marginally affect organisational exposure.