Individual weighted excess and least square values

Xia Zhang (), René van den Brink (), Arantza Estévez-Fernández () and Hao Sun ()
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Xia Zhang: NingboTech University
René van den Brink: VU University
Arantza Estévez-Fernández: VU University
Hao Sun: Northwestern Polytechnical University

Mathematical Methods of Operations Research, 2022, vol. 95, issue 2, No 5, 296 pages

Abstract: 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.

Keywords: Individual weighted excess; Prenucleolus; Nucleolus; Least square value (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s00186-022-00781-1

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