Sharing Supermodular Costs

• 成果类型: Article
• 署名作者: Schulz, Andreas S.; Uhan, Nelson A.
• 署名单位: Massachusetts Institute of Technology (MIT); Massachusetts Institute of Technology (MIT); Purdue University System; Purdue University
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.1100.0841
• 发表日期: 2010
• 页码: 1051-1056
• 关键词: spanning tree games; least core; Nucleolus

摘要

We study cooperative games with supermodular costs. We show that supermodular costs arise in a variety of situations; in particular, we show that the problem of minimizing a linear function over a supermodular polyhedron-a problem that often arises in combinatorial optimization-has supermodular optimal costs. In addition, we examine the computational complexity of the least core and least core value of supermodular cost cooperative games. We show that the problem of computing the least core value of these games is strongly NP-hard and, in fact, is in approximable within a factor strictly less than 17/16 unless P = NP. For a particular class of supermodular cost cooperative games that arises from a scheduling problem, we show that the Shapley value-which, in this case, is computable in polynomial time-is in the least core, while computing the least core value is NP-hard.