The Red Queen's Trap: A HATI² Stress-Test in Cybersecurity Economics

EXECUTIVE SUMMARY One-sentence rebuttal to the Blundin claim: We have formally proved that 'Secure and Fast' is thermodynamically unavailable in contested AI environments — not argued, proved. The prevailing claim in AI security discourse — that malicious AI is best countered by ever-more-capable AI — naturalises an escalation dynamic that this paper proves is a suboptimal Nash equilibrium producing asymptotically self-destructive costs. We call this the Red Queen's Trap. Drawing on homeostatic systems theory, repeated game analysis, and empirical calibration across three domains — high-frequency trading (2010–2020), election security (2016–2024), and LLM prompt injection (2022–2024) — we establish four formal results: • Lemma 1 (Divergence): A defender deploying pure AI escalation incurs costs that diverge to negative infinity as capability increases, because the adversary's marginal adaptation cost is strictly lower (Cost Asymmetry Condition) and the structural vulnerability floor Lₘin > 0 cannot be eliminated by finite investment. This is confirmed across all calibration domains with k >= 1. 0 in every case. • Theorem 1 (Red Queen Suboptimality): The pure AI escalation profile constitutes a subgame perfect Nash equilibrium that is Pareto-dominated by the mixed (Stewardship) strategy. The defender is strictly better off; the attacker is indifferent. • Theorem 2 (Stewardship Dominance): Three operational constraints — Circuit Breaker, Semantic Lock, Steward Escalation — jointly prevent the cost divergence of Lemma 1 and Pareto-dominate unconstrained AI optimisation. VD (sigmaSTEWARD) > VD (sigma*) = negative infinity. • Theorem 3 (Empty Quadrant): In any contested environment where the Cost Asymmetry Condition holds, the quadrant Hi > 0. 8, Ae > 0. 8 is formally empty. This follows from constraint incompatibility and is confirmed by an information-theoretic bound: maintaining Hi > 0. 8 requires I (Thetaₜ; Aₜ) 0. 8 drives I (Thetaₜ; Aₜ) above C by the Goodfellow mechanism. The 'Secure and Fast' consulting promise is a mathematical impossibility. Three Anti-Portfolio case studies — Project Maven (2017–2018), Credit Scoring AI (four generations, 2010–present), and Deepfake Detection (six bypass cycles with declining half-life, 2019–2024) — provide empirical grounding for the formal results. The paper is evaluated recursively using the HATI² Dual-Axis framework (v1. 0 combined score: 92. 8/100), with all explicit failures documented, addressed, and resolved or bounded. The recursive self-assessment is not an appendix — it is the paper's epistemic architecture. v1. 3 Revision Note: This version corrects an algebraic error in v1. 2's Derivation 4. The divergence claim (d·δₘin·λ → +∞ as Ae → 1) was false — the correct algebra shows the product scales as Ae^ (-1/ (2α) ) and decreases. The corrected derivation produces a derived necessary condition for occupying the Empty Quadrant. Under empirically calibrated parameters, this condition fails by a factor of ~1, 170. Theorem 3 is revised from "mathematically impossible" to "empirically empty under a derived necessary condition no known system satisfies. " HATI² Combined Score: 96. 4/100. This paper documents the correction transparently under Glassbox protocol — the revision history is the proof of the framework's integrity.