Abstract
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.
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Research supported by OTKA grant K-101224 and by the Hungarian Academy of Sciences under its Momentum Programme (LD-004/2010). The author is grateful to Holger Meinhardt and to two anonymous referees for their comments and suggestions on how to improve the presentation.
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Solymosi, T. The kernel is in the least core for permutation games. Cent Eur J Oper Res 23, 795–809 (2015). https://doi.org/10.1007/s10100-014-0342-y
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DOI: https://doi.org/10.1007/s10100-014-0342-y