Considerations on the aggregate monotonicity of the nucleolus and the core-center

Miguel Ángel Mirás Calvo (), Carmen Quinteiro Sandomingo and Estela Sánchez-Rodríguez
Additional contact information
Miguel Ángel Mirás Calvo: Universidade de Vigo
Carmen Quinteiro Sandomingo: Universidade de Vigo
Estela Sánchez-Rodríguez: Universidade de Vigo

Mathematical Methods of Operations Research, 2021, vol. 93, issue 2, No 4, 325 pages

Abstract: Abstract Even though aggregate monotonicity appears to be a reasonable requirement for solutions on the domain of convex games, there are well known allocations, the nucleolus for instance, that violate it. It is known that the nucleolus is aggregate monotonic on the domain of essential games with just three players. We provide a simple direct proof of this fact, obtaining an analytic formula for the nucleolus of a three-player essential game. We also show that the core-center, the center of gravity of the core, satisfies aggregate monotonicity for three-player balanced games. The core is aggregate monotonic as a set-valued solution, but this is a weak property. In fact, we show that the core-center is not aggregate monotonic on the domain of convex games with at least four players. Our analysis allows us to identify a subclass of bankruptcy games for which we can obtain analytic formulae for the nucleolus and the core-center. Moreover, on this particular subclass, aggregate monotonicity has a clear interpretation in terms of the associated bankruptcy problem and both the nucleolus and the core-center satisfy it.

Keywords: Aggregate monotonicity; Balanced games; Convex games; Bankruptcy games; Nucleolus; Core-center (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1007/s00186-020-00733-7 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:mathme:v:93:y:2021:i:2:d:10.1007_s00186-020-00733-7

Ordering information: This journal article can be ordered from
http://www.springer.com/economics/journal/00186

DOI: 10.1007/s00186-020-00733-7

Access Statistics for this article

Mathematical Methods of Operations Research is currently edited by Oliver Stein

More articles in Mathematical Methods of Operations Research from Springer, Gesellschaft für Operations Research (GOR), Nederlands Genootschap voor Besliskunde (NGB)
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().