Upper and lower bounds of the kernel and nucleolus

Y. Funaki

doi:10.1007/BF01770980

Upper and lower bounds of the kernel and nucleolus

Y. Funaki^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

6 Citations (Scopus)

Abstract

This paper examines relationships between the smallest contribution of a player and a lower bound of the kernel, and also an upper bound of the nucleolus. We show that the smallest contribution is a lower bound of the kernel outside the core. Moreover we present a necessary and sufficient condition for the smallest contribution to be an upper bound of the nucleolus. In this case, the equivalence of the nucleolus and SCRB solution is also obtained.

Original language	English
Pages (from-to)	121-129
Number of pages	9
Journal	International Journal of Game Theory
Volume	15
Issue number	2
DOIs	https://doi.org/10.1007/BF01770980
Publication status	Published - 1986 Jun 1
Externally published	Yes

ASJC Scopus subject areas

Statistics and Probability
Mathematics (miscellaneous)
Social Sciences (miscellaneous)
Economics and Econometrics
Statistics, Probability and Uncertainty

Access to Document

10.1007/BF01770980

Cite this

@article{5a192e3a609f425e86061b7e7595574d,

title = "Upper and lower bounds of the kernel and nucleolus",

abstract = "This paper examines relationships between the smallest contribution of a player and a lower bound of the kernel, and also an upper bound of the nucleolus. We show that the smallest contribution is a lower bound of the kernel outside the core. Moreover we present a necessary and sufficient condition for the smallest contribution to be an upper bound of the nucleolus. In this case, the equivalence of the nucleolus and SCRB solution is also obtained.",

author = "Y. Funaki",

year = "1986",

month = jun,

day = "1",

doi = "10.1007/BF01770980",

language = "English",

volume = "15",

pages = "121--129",

journal = "International Journal of Game Theory",

issn = "0020-7276",

publisher = "Springer Verlag",

number = "2",

}

TY - JOUR

T1 - Upper and lower bounds of the kernel and nucleolus

AU - Funaki, Y.

PY - 1986/6/1

Y1 - 1986/6/1

N2 - This paper examines relationships between the smallest contribution of a player and a lower bound of the kernel, and also an upper bound of the nucleolus. We show that the smallest contribution is a lower bound of the kernel outside the core. Moreover we present a necessary and sufficient condition for the smallest contribution to be an upper bound of the nucleolus. In this case, the equivalence of the nucleolus and SCRB solution is also obtained.

AB - This paper examines relationships between the smallest contribution of a player and a lower bound of the kernel, and also an upper bound of the nucleolus. We show that the smallest contribution is a lower bound of the kernel outside the core. Moreover we present a necessary and sufficient condition for the smallest contribution to be an upper bound of the nucleolus. In this case, the equivalence of the nucleolus and SCRB solution is also obtained.

UR - http://www.scopus.com/inward/record.url?scp=34250127228&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34250127228&partnerID=8YFLogxK

U2 - 10.1007/BF01770980

DO - 10.1007/BF01770980

M3 - Article

AN - SCOPUS:34250127228

SN - 0020-7276

VL - 15

SP - 121

EP - 129

JO - International Journal of Game Theory

JF - International Journal of Game Theory

IS - 2

ER -

Upper and lower bounds of the kernel and nucleolus

Abstract

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this