Capacitated Network Bargaining Games: Stability and Structure
成果类型：
Article; Early Access
署名作者：
Sanita, Laura; Verberk, Lucy
署名单位：
Bocconi University; Eindhoven University of Technology
刊物名称：
MATHEMATICS OF OPERATIONS RESEARCH
ISSN/ISSBN：
0364-765X
DOI：
10.1287/moor.2024.0668
发表日期：
2025
关键词：
摘要：
Capacitated network bargaining games are popular combinatorial games that involve the structure of matchings in graphs. We show that it is always possible to stabilize unit weight instances of this problem (that is, ensure that they admit a stable outcome) via capacity reduction and edge removal operations without decreasing the total value that the players can get. Furthermore, for general weighted instances, we show that computing a minimum amount of vertex capacity to reduce to make an instance stable is a polynomial time solvable problem. We then exploit this to give approximation results for the NP-hard problem of stabilizing a graph via edge removal operations. Our work extends and generalizes previous results in the literature that deal with a unit capacity version of the problem, using several new arguments. In particular, whereas previous results mainly used combinatorial techniques, we here rely on polyhedral arguments and, more specifically, on the notion of circuits of a polytope.
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