On the 1-nucleolus

M.A. Estevez Fernandez; Peter Borm; M.G. Fiestras-Janeiro; M.A. Mosquera; E. Sánchez-Rodríguez

doi:10.1007/s00186-017-0597-x

On the 1-nucleolus

M.A. Estevez Fernandez, Peter Borm, M.G. Fiestras-Janeiro, M.A. Mosquera, E. Sánchez-Rodríguez

Tinbergen Institute

Research output: Contribution to Journal › Article › Academic › peer-review

Abstract

This paper analyzes the 1-nucleolus and, in particular, its relation to the nucleolus. It is seen that, contrary to the nucleolus, the 1-nucleolus can be computed in polynomial time due to a characterization using a combination of standard bankruptcy rules for associated bankruptcy problems. Sufficient conditions on a compromise stable game are derived such that the 1-nucleolus and the nucleolus coincide.

Original language	English
Pages (from-to)	309-329
Number of pages	21
Journal	Mathematical Methods of Operations Research
Volume	86
Issue number	2
DOIs	https://doi.org/10.1007/s00186-017-0597-x
Publication status	Published - 2017

Funding

Acknowledgements The authors would like to thank an associate editor and two referees for their helpful suggestions to improve this article. Moreover, we would also like to thank the financial support of Ministerio de Ciencia e Innovación through Grant MTM2011-27731-C03 and Ministerio de Economía y Competitividad through Grant MTM2014-53395-C3-3-P.

Funders	Funder number
Ministerio de Economía y Competitividad	MTM2014-53395-C3-3-P
Ministerio de Ciencia e Innovación	MTM2011-27731-C03

Keywords

1-nucleolus
Aumann–Maschler rule
Compromise stable games
Nucleolus

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AU - Fiestras-Janeiro, M.G.

AU - Mosquera, M.A.

AU - Sánchez-Rodríguez, E.

PY - 2017

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On the 1-nucleolus

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On the 1-Nucleolus for Classes of Cooperative Games

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