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DETERMINING THE NUCLEOLUS OF COMPROMISE STABLE GAMES

Part of: Game theory

Published online by Cambridge University Press:  09 September 2015

DONGSHUANG HOU  and
THEO DRIESSEN
DONGSHUANG HOU*
Affiliation:
Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an, Shaanxi, PR China email dshhou@126.com
THEO DRIESSEN
Affiliation:
Faculty of Electrical Engineering, Mathematics and Computer Science, Department of Applied Mathematics, University of Twente, PO Box 217, 7500 AE Enschede, The Netherlands email t.s.h.driessen@ewi.utwente.nl
*
✉dshhou@126.com
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Abstract

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The main goal is to illustrate that the so-called indirect function of a cooperative game in characteristic function form is applicable to determine the nucleolus for a subclass of coalitional games called compromise stable transferable utility (TU) games. In accordance with the Fenchel–Moreau theory on conjugate functions, the indirect function is known as the dual representation of the characteristic function of the coalitional game. The key feature of a compromise stable TU game is the coincidence of its core with a box prescribed by certain upper and lower core bounds. For the purpose of the determination of the nucleolus, we benefit from the interrelationship between the indirect function and the prekernel of coalitional TU games. The class of compromise stable TU games contains the subclasses of clan games, big boss games and $1$- and $2$-convex $n$-person TU games. As an adjunct, this paper reports the indirect function of clan games for the purpose of determining their nucleolus.

Keywords

cooperative gamedual representationindirect functioncompromise stable TU gameclan gamecoreprekernel

MSC classification

Primary: 91A12: Cooperative games
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 92 , Issue 3 , December 2015 , pp. 488 - 495
Copyright
© 2015 Australian Mathematical Publishing Association Inc. 

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