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arXiv · 2604.04729

A Complete Characterization of Convexity in Flow Games

Han Xiao·Luying Zhang·Qizhi Fang
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Abstract

Flow games coincide precisely with the fundamental class of non-negative totally balanced games. However, the conditions for their convexity have remained elusive. In this paper, we resolve this challenge by providing a complete characterization. Specifically, we show that a flow game is convex if and only if its underlying network satisfies three structural conditions: acyclicity, bottleneck exclusivity, and capacity sufficiency. These structural conditions are also equivalent to dual separability, which resolves the apparent paradox between cycle orientations and game-theoretic convexity by decoupling path contributions via bottleneck exclusivity. Furthermore, our characterization yields an efficient recognition procedure, establishing that flow game convexity is verifiable in polynomial time.

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Han Xiao, Luying Zhang, Qizhi Fang. 2026-04-06. A Complete Characterization of Convexity in Flow Games. https://arxiv.org/abs/2604.04729

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