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

Tianhang Lu, Han Xiao and Qizhi Fang

Papers from arXiv.org

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. These games have significant applications in financial, communication, and supply-chain networks. We investigate two solution concepts, the least core and the nucleolus. Both solution concepts provide principled ways to allocate the value of the grand coalition among individual players. We provide characterizations of the least core of these games. We also give a polynomial-time algorithm to compute the nucleolus when the core is non-empty.

Date: 2026-06
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