Monotone Near-Zero-Sum Games: A Generalization of Convex-Concave Minimax
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912743175487488 |
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| author | Luo, Ruichen Stich, Sebastian U. Chatterjee, Krishnendu |
| author_facet | Luo, Ruichen Stich, Sebastian U. Chatterjee, Krishnendu |
| contents | Zero-sum and non-zero-sum (aka general-sum) games are relevant in a wide range of applications. While general non-zero-sum games are computationally hard, researchers focus on the special class of monotone games for gradient-based algorithms. However, there is a substantial gap between the gradient complexity of monotone zero-sum and monotone general-sum games. Moreover, in many practical scenarios of games the zero-sum assumption needs to be relaxed. To address these issues, we define a new intermediate class of monotone near-zero-sum games that contains monotone zero-sum games as a special case. Then, we present a novel algorithm that transforms the near-zero-sum games into a sequence of zero-sum subproblems, improving the gradient-based complexity for the class. Finally, we demonstrate the applicability of this new class to model practical scenarios of games motivated from the literature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_02690 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Monotone Near-Zero-Sum Games: A Generalization of Convex-Concave Minimax Luo, Ruichen Stich, Sebastian U. Chatterjee, Krishnendu Computer Science and Game Theory Optimization and Control Zero-sum and non-zero-sum (aka general-sum) games are relevant in a wide range of applications. While general non-zero-sum games are computationally hard, researchers focus on the special class of monotone games for gradient-based algorithms. However, there is a substantial gap between the gradient complexity of monotone zero-sum and monotone general-sum games. Moreover, in many practical scenarios of games the zero-sum assumption needs to be relaxed. To address these issues, we define a new intermediate class of monotone near-zero-sum games that contains monotone zero-sum games as a special case. Then, we present a novel algorithm that transforms the near-zero-sum games into a sequence of zero-sum subproblems, improving the gradient-based complexity for the class. Finally, we demonstrate the applicability of this new class to model practical scenarios of games motivated from the literature. |
| title | Monotone Near-Zero-Sum Games: A Generalization of Convex-Concave Minimax |
| topic | Computer Science and Game Theory Optimization and Control |
| url | https://arxiv.org/abs/2512.02690 |