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arXiv · 2401.13535

On the Approximate Core and Nucleon of Flow Games with Public Arcs

Pengfei Liu·Han Xiao·Tianhang Lu·Qizhi Fang
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Abstract

We investigate flow games featuring both private arcs owned by individual players and public arcs accessible cost-free to all coalitions. We explore two solution concepts within this framework: the approximate core and the nucleon. The approximate core relaxes core requirements by permitting a bounded relative payoff deviation for every coalition, and the nucleon is a multiplicative analogue of Schmeidler's nucleolus which lexicographically maximizes the vector consisting of relative payoff deviations for every coalition arranged in a non-decreasing order. By leveraging a decomposition property for paths and cycles in a flow network, we derive complete characterizations for the approximate core and demonstrate that the nucleon can be computed in polynomial time.

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Pengfei Liu, Han Xiao, Tianhang Lu, Qizhi Fang. 2024-01-24. On the Approximate Core and Nucleon of Flow Games with Public Arcs. https://arxiv.org/abs/2401.13535

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