A Framework for Computing the Nucleolus via Dynamic Programming
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Published:2023-03-31
Issue:1-2
Volume:11
Page:1-21
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ISSN:2167-8375
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Container-title:ACM Transactions on Economics and Computation
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language:en
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Short-container-title:ACM Trans. Econ. Comput.
Author:
Koenemann Jochen1ORCID,
Toth Justin1ORCID
Affiliation:
1. University of Waterloo, Canada
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.
Funder
Natural Sciences and Engineering Research Council of Canada
Publisher
Association for Computing Machinery (ACM)
Subject
Computational Mathematics,Marketing,Economics and Econometrics,Statistics and Probability,Computer Science (miscellaneous)
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