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Monotone Near-Zero-Sum Games

ICLR 2026 Conference SubmissionAnonymous Authors
OpenReview Score: 6.0Download Report PDF
Non-zero-sum games; monotone games
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.

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This report is AI-GENERATED using Large Language Models and WisPaper (A scholar search engine). It analyzes academic papers' tasks and contributions against retrieved prior work. While this system identifies POTENTIAL overlaps and novel directions, ITS COVERAGE IS NOT EXHAUSTIVE AND JUDGMENTS ARE APPROXIMATE. These results are intended to assist human reviewers and SHOULD NOT be relied upon as a definitive verdict on novelty.
NOTE that some papers exist in multiple, slightly different versions (e.g., with different titles or URLs). The system may retrieve several versions of the same underlying work. The current automated pipeline does not reliably align or distinguish these cases, so human reviewers will need to disambiguate them manually.
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Overview

Overall Novelty Assessment

The paper introduces monotone near-zero-sum games as an intermediate class between zero-sum and general-sum settings, proposing an Iterative Coupling Linearization algorithm that transforms these games into sequences of zero-sum subproblems. Within the taxonomy, it resides in the 'Transformation-Based Approaches for Near-Zero-Sum Games' leaf, which contains only two papers total. This sparse population suggests the research direction is relatively unexplored, with few prior works explicitly addressing intermediate game classes through transformation methods.

The taxonomy reveals two main branches: algorithmic frameworks for intermediate game classes and gradient-based convergence in monotone/zero-sum games. The original paper's leaf sits within the first branch, focusing on transformation techniques rather than direct gradient methods. Neighboring work in the second branch (accelerated gradient methods, mirror descent variants) emphasizes convergence guarantees in standard zero-sum or monotone settings without exploiting near-zero-sum structure. This positioning indicates the paper bridges a gap between specialized transformation approaches and broader convergence analysis.

Among nineteen candidates examined across three contributions, no refutable prior work was identified. The definition of monotone near-zero-sum games examined five candidates with zero refutations, the algorithm examined four candidates with zero refutations, and practical applications examined ten candidates with zero refutations. This limited search scope suggests that within the top-K semantic matches and citation expansion, no overlapping prior work was detected, though the analysis does not claim exhaustive coverage of the entire field.

Based on the sparse taxonomy leaf and absence of refutable candidates among nineteen examined papers, the work appears to occupy a relatively novel position within the limited search scope. The transformation-based approach to near-zero-sum games represents a specialized direction with minimal prior exploration, though the analysis acknowledges it covers top semantic matches rather than the complete literature landscape.

Taxonomy

Core-task Taxonomy Papers
3
3
Claimed Contributions
19
Contribution Candidate Papers Compared
0
Refutable Paper

Research Landscape Overview

Core task: gradient complexity of monotone near-zero-sum games. The field structure suggested by the taxonomy divides into two main branches. The first branch, 'Algorithmic Frameworks for Near-Zero-Sum and Intermediate Game Classes,' focuses on designing methods that handle games lying between purely cooperative and purely adversarial settings, often employing transformation-based techniques to exploit near-zero-sum structure. The second branch, 'Gradient-Based Convergence in Monotone and Zero-Sum Games,' emphasizes convergence guarantees for gradient-based algorithms in monotone or zero-sum environments, where classical notions like last-iterate convergence become tractable. Together, these branches capture the tension between exploiting special game structure and ensuring robust convergence properties. Within the transformation-based approaches, a small handful of works explore how to leverage near-zero-sum assumptions to improve gradient complexity bounds. Monotone Near Zero Sum[0] sits squarely in this cluster, proposing a transformation that reduces near-zero-sum games to monotone variational inequalities, thereby enabling faster convergence rates. Its closest neighbor, Monotone Near Zero Sum Generalization[2], extends similar ideas to broader game classes, suggesting that transformation-based methods remain an active line of inquiry. Meanwhile, works like Last Iterate Convergence[1] and Doubly Optimal No Regret[3] emphasize convergence guarantees in zero-sum or monotone settings without necessarily exploiting near-zero-sum structure, highlighting a trade-off between generality and the ability to exploit problem-specific assumptions. The original paper's emphasis on transformation techniques positions it as a specialized approach within the broader landscape of gradient-based game-solving methods.

Claimed Contributions

Definition of monotone near-zero-sum games

The authors introduce a new class of games characterized by a smoothness parameter delta that interpolates between monotone zero-sum games (delta equals zero) and monotone general-sum games (delta equals L). This class partially bridges the gap between these two existing classes.

5 retrieved papers
Iterative Coupling Linearization algorithm

The authors develop a new algorithm that transforms near-zero-sum games into a sequence of zero-sum subproblems. This algorithm achieves improved gradient complexity compared to existing variational inequality methods when the near-zero-sum parameter delta is small.

4 retrieved papers
Practical applications of near-zero-sum games

The authors show that the new class of near-zero-sum games can model practical scenarios such as regularized matrix games and competitive games with small additional incentives, where their methods achieve provably faster convergence rates.

10 retrieved papers

Core Task Comparisons

Comparisons with papers in the same taxonomy category

Contribution Analysis

Detailed comparisons for each claimed contribution

Contribution

Definition of monotone near-zero-sum games

The authors introduce a new class of games characterized by a smoothness parameter delta that interpolates between monotone zero-sum games (delta equals zero) and monotone general-sum games (delta equals L). This class partially bridges the gap between these two existing classes.

Contribution

Iterative Coupling Linearization algorithm

The authors develop a new algorithm that transforms near-zero-sum games into a sequence of zero-sum subproblems. This algorithm achieves improved gradient complexity compared to existing variational inequality methods when the near-zero-sum parameter delta is small.

Contribution

Practical applications of near-zero-sum games

The authors show that the new class of near-zero-sum games can model practical scenarios such as regularized matrix games and competitive games with small additional incentives, where their methods achieve provably faster convergence rates.

Table of Contents