Sharing Supermodular Costs
Name
Schulz-Uhan-.pdf
Size
316.12 KB
Format
Adobe PDF
Checksum (MD5)
aaaca06556fecdf6fab9f2db883e4d1c
Author(s)
Schulz, Andreas S.
Uhan, Nelson A.
Date Issued
July 2010
Journal
Operations Research
Publisher
INFORMS
Citation
Schulz, A. S., and N. A. Uhan. “Sharing Supermodular Costs.” Operations Research 58.4-Part-2 (2010) : 1051-1056.
Version
Author's final manuscript
Abstract
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 inapproximable 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.
MIT Department
Sloan School of Management
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike 3.0
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1287/opre.1100.0841
