BRAID: Learning Equilibrium Maps in Interdependent Security Games via Weight-Tied Iterative Graph Neural Networks

[2608.14856] BRAID: Learning Equilibrium Maps in Interdependent Security Games via Weight-Tied Iterative Graph Neural Networks Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Computer Science > Computer Science and Game Theory arXiv:2608.14856 (cs) [Submitted on 14 Aug 2026] Title: BRAID: Learning Equilibrium Maps in Interdependent Security Games via Weight-Tied Iterative Graph Neural Networks Authors: Elnaz Nowrouzi , Zhiqun Zuo , Xueru Zhang , Mohammad Mahdi Khalili View a PDF of the paper titled BRAID: Learning Equilibrium Maps in Interdependent Security Games via Weight-Tied Iterative Graph Neural Networks, by Elnaz Nowrouzi and 3 other authors View PDF HTML (experimental) Abstract: 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. Comments: 20 pages, 2 figures, Accepted at GameSec 2026 Subjects: Computer Science and Game Theory (cs.GT) ; Machine Learning (cs.LG) Cite as: arXiv:2608.14856 [cs.GT] (or arXiv:2608.14856v1 [cs.GT] for this version) https://doi.org/10.48550/arXiv.2608.14856 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Elnaz Nowrouzi [ view email ] [v1] Fri, 14 Aug 2026 19:53:34 UTC (2,071 KB) Full-text links: Access Paper: View a PDF of the paper titled BRAID: Learning Equilibrium Maps in Interdependent Security Games via Weight-Tied Iterative Graph Neural Networks, by Elnaz Nowrouzi and 3 other authors View PDF HTML (experimental) TeX Source view license Current browse context: cs.GT < prev | next > new | recent | 2026-08 Change to browse by: cs cs.LG References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... 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