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竞赛理论模型，其中攻击方和防御方在多个攻击面上分配资源以增强人工智能能力。攻击方的投资通过两个渠道发挥作用：无条件提升攻击效能，并有条件地削弱防御效果，从而产生一种随防御方自身投资而内生性加深的对抗性折扣。我们推导出一个封闭形式的军备竞赛比率，将攻击与防御投资的相对边际效能分解为六个结构性基元，并证明了在连续最佳反应动态下的均衡唯一性与全局收敛性。核心结果涉及信号互相关性——即一个攻击面上的威胁情报在多大程度上增强另一攻击面上的检测能力。当存在完全互相关时，军备竞赛比率与攻击面数量无关：攻击方因攻击面扩张而获得的优势被彻底中和。在基准的完全稀释情形下，若缺乏互相关性，每个攻击面的防御效能将随攻击面增加而消失。将分析拓展至面临按期望值选择目标的攻击方的异质性防御者时，我们认为该模型揭示了双重低效率：私人防御的过度投资（一种零和转移性外部性）与共享信号关联的投资不足（一种公共物品）。这些形式化结果，连同基本模型之外的公共品推理，共同刻画了在对抗性竞争中，集体信息聚合何时能够超越私人能力投资成为决定性因素。