Individual weighted excess and least square values

Xia Zhang*, René van den Brink, Arantza Estévez-Fernández, Hao Sun

*Corresponding author for this work

Research output: Contribution to JournalArticleAcademicpeer-review

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Abstract

This work deals with the weighted excesses of players in cooperative games which are obtained by summing up all the weighted excesses of all coalitions to which they belong. We first show that the resulting payoff vector is the corresponding least square value by lexicographically minimizing the individual weighted excesses of players over the preimputation set, and thus give an alternative characterization of the least square values. Second, we show that these results give rise to lower and upper bounds for the core payoff vectors and, using these bounds, we show that the least square values can be seen as the center of a polyhedron defined by these bounds. This provides a second new characterization of the least square values. Third, we show that the individually rational least square value is the solution that lexicographically minimizes the individual weighted excesses of players over the imputation set.

Original languageEnglish
Pages (from-to)281-296
Number of pages16
JournalMathematical Methods of Operations Research
Volume95
Issue number2
Early online date16 Apr 2022
DOIs
Publication statusPublished - Apr 2022

Bibliographical note

Funding Information:
The research has been supported by the National Natural Science Foundation of China (Grant Nos. 72071158) and the China Scholarship Council (Grant No. 201906290164). We thank two anonymous reviewers for comments on an earlier draft of this paper.

Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.

Keywords

  • Individual weighted excess
  • Least square value
  • Nucleolus
  • Prenucleolus

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