Going with the Flow: Approximating Banzhaf Values via Graph Neural Networks
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arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866908601373687808 |
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| author | Kempinski, Benjamin Kachman, Tal |
| author_facet | Kempinski, Benjamin Kachman, Tal |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_13391 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Going with the Flow: Approximating Banzhaf Values via Graph Neural Networks Kempinski, Benjamin Kachman, Tal Machine Learning Computer Science and Game Theory 91A12, 68T07, 05C21 I.2.6; F.2.2; C.2.1 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. |
| title | Going with the Flow: Approximating Banzhaf Values via Graph Neural Networks |
| topic | Machine Learning Computer Science and Game Theory 91A12, 68T07, 05C21 I.2.6; F.2.2; C.2.1 |
| url | https://arxiv.org/abs/2510.13391 |