{"ID":2833980,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.02690","arxiv_id":"2512.02690","title":"Monotone Near-Zero-Sum Games: A Generalization of Convex-Concave Minimax","abstract":"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.","short_abstract":"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 monoto...","url_abs":"https://arxiv.org/abs/2512.02690","url_pdf":"https://arxiv.org/pdf/2512.02690v1","authors":"[\"Ruichen Luo\",\"Sebastian U. Stich\",\"Krishnendu Chatterjee\"]","published":"2025-12-02T12:21:38Z","proceeding":"cs.GT","tasks":"[\"cs.GT\",\"math.OC\"]","methods":"[]","has_code":false}