发表机构
The Ohio State University（俄亥俄州立大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对网络上相互依存安全博弈中纳什均衡计算成本高的问题，提出BRAID模型，用权重绑定迭代图神经网络学习均衡映射，速度提升43倍，可预测均衡并恢复参数扰动下的均衡变化，经实验验证有效。
AI 中文摘要
在网络上的相互依存安全（IDS）博弈中计算纳什均衡的计算成本很高：每个实例的最佳响应动态可能需要数百次迭代，而审计、压力测试和激励设计等下游任务通常需要在参数扰动下反复求解该博弈。我们提出BRAID，即最佳响应摊销迭代动态模型，该模型使用权重绑定迭代图神经网络学习从博弈参数到纳什均衡努力配置的直接映射，用单次前向传递替代迭代最佳响应计算，每个实例的速度可提升多达43倍。BRAID源于IDS博弈的最佳响应不动点结构：其SUM聚合反映了加性邻域耦合，而权重绑定门控循环单元（GRU）则模拟了阻尼最佳响应更新。该架构适用于投资成本曲率和邻域聚合不同的IDS规范，包括对数线性、二次成本和对数不变替代弹性（CES）效用。除了均衡预测外，BRAID还能恢复博弈参数（包括成本和网络边权重）扰动下均衡努力的变化情况。我们将这种敏感性恢复设为明确的评估目标，并引入两种训练策略——内部均衡训练和输入噪声正则化，在不使用敏感性标签的情况下改善学习到的均衡映射的局部行为。实验表明，BRAID可在各类效用规范和网络规模下有效预测纳什均衡并恢复均衡敏感性。
英文摘要
Computing Nash equilibria in interdependent security (IDS) games on networks is computationally expensive: best-response dynamics may need hundreds of iterations per instance, and downstream tasks such as auditing, stress-testing, and incentive design often require repeatedly re-solving the game under parameter perturbations. We propose BRAID, a Best-Response Amortized Iterative Dynamics model that uses a weight-tied iterative graph neural network to learn a direct map from game parameters to Nash equilibrium effort profiles, replacing iterative best response computation with a single forward pass that is up to 43X faster per instance. BRAID is derived from the best-response fixed-point structure of IDS games: its SUM aggregation reflects additive neighbor coupling, and a weight-tied gated recurrent unit (GRU) mirrors a damped best-response update. The same architecture applies across IDS specifications that vary investment-cost curvature and neighborhood aggregation, including log-linear, quadratic-cost, and log constant-elasticity-of-substitution (CES) utilities. Beyond equilibrium prediction, BRAID also recovers how equilibrium efforts change under perturbations to game parameters, including costs and network edge weights. We make this sensitivity recovery an explicit evaluation target and introduce two training strategies, interior-equilibrium training and input-noise regularization, that improve the local behavior of the learned equilibrium map without using sensitivity labels. Experiments show that BRAID effectively predicts Nash equilibria and recovers equilibrium sensitivities across utility specifications and network sizes.
Comments20 pages, 2 figures, Accepted at GameSec 2026
