用图神经网络快速估算网络中各节点的影响力，比传统方法快上百倍。
Going with the Flow: Approximating Banzhaf Values via Graph Neural Networks
- 用图神经网络将影响力计算转化为图级预测任务，直接学习拓扑结构中的模式。
- 在20万张合成图上测试，模型预测精度高，速度比精确算法快一个数量级。
- 训练后可零样本推广到新网络结构，无需重新训练，适合动态系统应用。
在网络流博弈中计算巴恩扎夫值是量化多智能体系统中个体影响力的基石，应用涵盖网络安全与基础设施规划。然而，当智能体数超过约20个时，精确计算因指数复杂度（$/mathcal{O}(2^m)$）变得不可行。尽管蒙特卡洛采样可提供统计估计，但样本需求高且无法跨不同网络配置迁移知识，难以应用于大规模或动态系统。本文提出一种基于图神经网络（GNN）的新学习方法，用于近似基数型网络流博弈中的巴恩扎夫值。通过将问题建模为图级预测任务，该方法直接从网络拓扑和控制结构中学习可泛化的影响力模式。我们在包含20万张图的大型合成数据集上进行了全面实验，配置涉及节点数（20–100）、智能体数（5–20）和边概率（0.5–1.0）。结果表明，训练后的GNN模型在精度与速度上均表现优异，相比精确法和采样法实现数量级加速。最显著的是，模型在特定规模与拓扑下训练后，可零样本准确预测全新网络结构的巴恩扎夫值，无需重新训练。本工作确立了GNN在复杂联网系统合作博弈分析中的实用价值。
原文摘要 · Abstract (English)
Computing the Banzhaf value in network flow games is fundamental for quantifying agent influence in multi-agent systems, with applications ranging from cybersecurity to infrastructure planning. However, exact computation is intractable for systems with more than $\sim20$ agents due to exponential complexity $\mathcal{O}(2^m)$. While Monte Carlo sampling methods provide statistical estimates, they suffer from high sample complexity and cannot transfer knowledge across different network configurations, making them impractical for large-scale or dynamic systems. We present a novel learning-based approach using Graph Neural Networks (GNNs) to approximate Banzhaf values in cardinal network flow games. By framing the problem as a graph-level prediction task, our method learns generalisable patterns of agent influence directly from network topology and control structure. We conduct a comprehensive empirical study comparing three state-of-the-art GNN architectures-Graph Attention Networks (GAT), Graph Isomorphism Networks with Edge features (GINE), and EdgeConv-on a large-scale synthetic dataset of 200,000 graphs per configuration, varying in size (20-100 nodes), agent count (5-20), and edge probability (0.5-1.0). Our results demonstrate that trained GNN models achieve high-fidelity Banzhaf value approximation with order-of-magnitude speedups compared to exact and sampling-based methods. Most significantly, we show strong zero-shot generalisation: models trained on graphs of a specific size and topology accurately predict Banzhaf values for entirely new networks with different structural properties, without requiring retraining. This work establishes GNNs as a practical tool for scalable cooperative game-theoretic analysis of complex networked systems.
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