Central European Journal of Operations Research

, Volume 23, Issue 4, pp 795–809 | Cite as

The kernel is in the least core for permutation games

  • Tamás Solymosi
Original Paper


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.


Permutation game Least core Kernel 

Mathematics Subject Classification (2010)

Primary 91A12 Secondary 91A40 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Department of Operations Research and Actuarial SciencesCorvinus University of BudapestBudapestHungary
  2. 2.‘Momentum’ Game Theory Research Group, Institute of Economics, Research Center for Economic and Regional StudiesHungarian Academy of SciencesBudapestHungary

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