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A Framework for Computing the Nucleolus via Dynamic Programming

A Framework for Computing the Nucleolus via Dynamic Programming This article defines a general class of cooperative games for which the nucleolus is efficiently computable. This class includes new members for which the complexity of computing their nucleolus was not previously known. We show that when the minimum excess coalition problem of a cooperative game can be formulated as a hypergraph dynamic program, its nucleolus is efficiently computable. This gives a general technique for designing efficient algorithms for computing the nucleolus of a cooperative game. This technique is inspired by a recent result of Pashkovich [27] on weighted voting games. However, our technique significantly extends beyond the capabilities of previous work. We demonstrate this by applying it to give an algorithm for computing the nucleolus of b-matching games in polynomial time on graphs of bounded treewidth. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png ACM Transactions on Economics and Computation Association for Computing Machinery

A Framework for Computing the Nucleolus via Dynamic Programming

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References (41)

Publisher
Association for Computing Machinery
Copyright
Copyright © 2023 Copyright held by the owner/author(s). Publication rights licensed to ACM.
ISSN
2167-8375
eISSN
2167-8383
DOI
10.1145/3580375
Publisher site
See Article on Publisher Site

Abstract

This article defines a general class of cooperative games for which the nucleolus is efficiently computable. This class includes new members for which the complexity of computing their nucleolus was not previously known. We show that when the minimum excess coalition problem of a cooperative game can be formulated as a hypergraph dynamic program, its nucleolus is efficiently computable. This gives a general technique for designing efficient algorithms for computing the nucleolus of a cooperative game. This technique is inspired by a recent result of Pashkovich [27] on weighted voting games. However, our technique significantly extends beyond the capabilities of previous work. We demonstrate this by applying it to give an algorithm for computing the nucleolus of b-matching games in polynomial time on graphs of bounded treewidth.

Journal

ACM Transactions on Economics and ComputationAssociation for Computing Machinery

Published: Jun 24, 2023

Keywords: Combinatorial optimization

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