We study a contest-theoretic model of adversarial investment in which an attacker and a defender allocate resources to AI-augmented capabilities across multiple attack surfaces. The attacker's investment operates through two channels: it amplifies offensive potency unconditionally and erodes defensive effectiveness conditionally, generating an adversarial discount that deepens endogenously with the defender's own investment. We derive a closed-form arms race ratio decomposing the relative marginal effectiveness of offensive and defensive investment into six structural primitives and establish equilibrium uniqueness and global convergence under a continuous best-response dynamic. The central result concerns signal cross-correlation, the degree to which threat intelligence on one surface informs detection on another. With full cross-correlation, the arms race ratio is independent of the number of attack surfaces: the attacker's structural advantage from surface proliferation is completely neutralized. Under the benchmark full-dilution case, without cross-correlation, per-surface defense effectiveness vanishes as the attack surface grows. Extending the analysis to heterogeneous defenders facing an attacker who targets by expected value, we argue that the model points to a dual inefficiency: overinvestment in private defense (a zero-sum redirective externality) and underinvestment in shared signal correlation (a public good). These formal results, together with public-good reasoning outside the base model, characterize when collective information aggregation can dominate private capability investment as the decisive margin in adversarial contests.

翻译：我们研究了一个对抗性投资的理论模型，在该模型中，攻击方与防御方将资源分配至跨多个攻击面的人工智能增强能力。攻击方的投资通过两个渠道发挥作用：它无条件提升攻击效能，并条件性地削弱防御效力，从而产生一种随着防御方自身投资内生性加深的对抗折价。我们推导出一个封闭形式的军备竞赛比率，将进攻与防御投资的相对边际效益分解为六个结构性基元，并在连续最优反应动态下确立了均衡的唯一性与全局收敛性。核心结果涉及信号交叉关联，即一个攻击面的威胁情报在多大程度上促进另一攻击面的检测。在完全交叉关联下，军备竞赛比率与攻击面数量无关：攻击方因攻击面扩散而获得的结构性优势被完全中和。在基准的完全稀释情形下，若无交叉关联，随着攻击面增加，单个攻击面的防御效力将趋于消失。将分析扩展至面临按预期价值瞄准的攻击方的异质性防御者时，我们认为该模型指向双重低效：私人防御的过度投资（一种零和转移外部性）与共享信号关联的投资不足（一种公共品）。这些形式化结果，连同基础模型之外的公共品推理，共同刻画了在对抗性博弈中，集体信息聚合何时能够超越私人能力投资，成为决定性边际。