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| Format: | Preprint |
| Published: |
2026
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| Online Access: | https://arxiv.org/abs/2604.12558 |
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| _version_ | 1866914471227686912 |
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| author | Hou, Yuqing |
| author_facet | Hou, Yuqing |
| contents | Nash equilibrium is a fundamental solution concept in extensive-form games, while its efficient computation is still far from straightforward. This paper considers finite $n$-player extensive-form games with perfect recall under the sequence-form representation. Unlike existing approaches, which mainly treat the sequence form as a compact computational reformulation, we develop a direct sequence-form definition of Nash equilibrium. Building on this, we rigorously establish the associated sequence-form Nash equilibrium system through an equivalence proof with mixed-strategy Nash equilibrium. On this basis, we propose a single-stage interior-point differentiable path-following method for equilibrium computation. The method uses logarithmic-barrier regularization to generate a differentiable equilibrium path in the interior of the realization-plan space, leading to favorable numerical stability and convergence properties. Numerical results show that the proposed method is effective and computationally efficient. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_12558 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Two Sequence-Form Interior-Point Differentiable Path-Following Method to Compute Nash Equilibria Hou, Yuqing Computer Science and Game Theory Nash equilibrium is a fundamental solution concept in extensive-form games, while its efficient computation is still far from straightforward. This paper considers finite $n$-player extensive-form games with perfect recall under the sequence-form representation. Unlike existing approaches, which mainly treat the sequence form as a compact computational reformulation, we develop a direct sequence-form definition of Nash equilibrium. Building on this, we rigorously establish the associated sequence-form Nash equilibrium system through an equivalence proof with mixed-strategy Nash equilibrium. On this basis, we propose a single-stage interior-point differentiable path-following method for equilibrium computation. The method uses logarithmic-barrier regularization to generate a differentiable equilibrium path in the interior of the realization-plan space, leading to favorable numerical stability and convergence properties. Numerical results show that the proposed method is effective and computationally efficient. |
| title | Two Sequence-Form Interior-Point Differentiable Path-Following Method to Compute Nash Equilibria |
| topic | Computer Science and Game Theory |
| url | https://arxiv.org/abs/2604.12558 |