The kernel is in the least core for permutation games

Permutation games are totally balanced transferable utility cooperative games arising from certain sequencing and re-assignment optimization problems. It is known that for permutation games the bargaining set and the core coincide, consequently, the kernel is a subset of the core. We prove that for...

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Bibliographic Details
Published inCentral European journal of operations research Vol. 23; no. 4; pp. 795 - 809
Main Author Solymosi, Tamás
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.12.2015
Springer
Springer Nature B.V
Subjects
Balancing
Bargaining
Business and Management
Game theory
Games
Kernel functions
Kernels
Mathematical models
Mathematical research
Operations research
Operations Research/Decision Theory
Optimization
Original Paper
Payoffs
Permutations
Sequencing
Studies
Utilities
Hungary
Least core
Kernel
Permutation game
Primary 91A12
Secondary 91A40
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Summary:Permutation games are totally balanced transferable utility cooperative games arising from certain sequencing and re-assignment optimization problems. It is known that for permutation games the bargaining set and the core coincide, consequently, the kernel is a subset of the core. We prove that for permutation games the kernel is contained in the least core, even if the latter is a lower dimensional subset of the core. By means of a 5-player permutation game we demonstrate that, in sense of the lexicographic center procedure leading to the nucleolus, this inclusion result can not be strengthened. Our 5-player permutation game is also an example (of minimum size) for a game with a non-convex kernel.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 23
ISSN:1435-246X
1613-9178
DOI:10.1007/s10100-014-0342-y