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arXiv · 2606.23288

Flow Games with Public Arcs: the Least Core and the Nucleolus

Tianhang Lu·Han Xiao·Qizhi Fang
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Abstract

We study flow games with public arcs, an extension of classical cooperative flow games that allows players to use public resources. In these games, a coalition corresponds to a set of arcs, while certain arcs, called public arcs, can be used freely by any coalition. The value of a coalition is the maximum flow value achievable using the arcs controlled by the coalition along with the public arcs. We investigate two solution concepts, the least core and the nucleolus. Both solution concepts provide fair ways to allocate the value of the grand coalition among individual players. We provide polynomial-size formulations of the least core of these games. We also give a deterministic polynomial-time algorithm for computing the nucleolus, whether or not the core is empty.

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Tianhang Lu, Han Xiao, Qizhi Fang. 2026-06-22. Flow Games with Public Arcs: the Least Core and the Nucleolus. https://arxiv.org/abs/2606.23288

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