Approximating the least core value and least core of cooperative games with supermodular costs
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Author(s)
Schulz, Andreas S.
Uhan, Nelson A.
Date Issued
March 2013
Journal
Discrete Optimization
Publisher
Elsevier
Citation
Schulz, Andreas S., and Nelson A. Uhan. “Approximating the Least Core Value and Least Core of Cooperative Games with Supermodular Costs.” Discrete Optimization 10, no. 2 (May 2013): 163–180.
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Author's final manuscript
Abstract
We study the approximation of the least core value and the least core of supermodular cost cooperative games. We provide a framework for approximation based on oracles that approximately determine maximally violated constraints. This framework yields a 3-approximation algorithm for computing the least core value of supermodular cost cooperative games, and a polynomial-time algorithm for computing a cost allocation in the 2-approximate least core of these games. This approximation framework extends naturally to submodular profit cooperative games. For scheduling games, a special class of supermodular cost cooperative games, we give a fully polynomial-time approximation scheme for computing the least core value. For matroid profit games, a special class of submodular profit cooperative games, we give exact polynomial-time algorithms for computing the least core value as well as a least core cost allocation.
MIT Department
Sloan School of Management
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DOI of Published Version
https://doi.org/10.1016/j.disopt.2013.02.002
