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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.02380 |
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Table of Contents:
- The nucleolus is a central solution concept in cooperative game theory. While its computation is NP-hard in general, it can be computed in polynomial time for convex games; however, the only published polynomial-time algorithm relies on the ellipsoid method. We develop a combinatorial alternative based on reduced games and iterative least-core value computations. Leveraging submodular function minimization and polyhedral structure in a novel way, we obtain a faster combinatorial algorithm for computing the least-core value, improving the oracle complexity by a factor $n^3$ over previous approaches. As a consequence, we obtain a new strongly polynomial-time and combinatorial algorithm for computing the nucleolus in convex games. Preliminary analysis indicates an improved oracle complexity compared to the ellipsoid-based algorithm.