A Complete Characterization of Convexity in Flow Games
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.
Cite
@article{arxiv.2604.04729,
title = {A Complete Characterization of Convexity in Flow Games},
author = {Han Xiao and Luying Zhang and Qizhi Fang},
journal= {arXiv preprint arXiv:2604.04729},
year = {2026}
}