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The kernel is in the least core for permutation games

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  • Tamás Solymosi

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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. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Tamás Solymosi, 2015. "The kernel is in the least core for permutation games," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 23(4), pages 795-809, December.
  • Handle: RePEc:spr:cejnor:v:23:y:2015:i:4:p:795-809
    DOI: 10.1007/s10100-014-0342-y
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    File URL: http://hdl.handle.net/10.1007/s10100-014-0342-y
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    References listed on IDEAS

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    1. Curiel, I. & Tijs, S.H., 1986. "Assignment games and permutation games," Other publications TiSEM c9a47c3b-28d3-4874-b0a2-f, Tilburg University, School of Economics and Management.
    2. Tamás Solymosi, 2002. "The bargaining set of four-person balanced games," International Journal of Game Theory, Springer;Game Theory Society, vol. 31(1), pages 1-11.
    3. repec:spr:thdlic:978-3-642-39549-9 is not listed on IDEAS
    4. Solymosi, T. & Raghavan, T.E.S. & Tijs, S.H., 2003. "Bargaining sets and the core in permutation games," Other publications TiSEM a14f6955-62c4-4bf0-8a54-f, Tilburg University, School of Economics and Management.
    5. Solymosi, Tamas & Raghavan, T. E. S. & Tijs, Stef, 2005. "Computing the nucleolus of cyclic permutation games," European Journal of Operational Research, Elsevier, vol. 162(1), pages 270-280, April.
    6. Quint, Thomas, 1996. "On One-Sided versus Two-Sided Matching Games," Games and Economic Behavior, Elsevier, vol. 16(1), pages 124-134, September.
    7. Daniel Granot, 2010. "The reactive bargaining set for cooperative games," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(1), pages 163-170, March.
    8. Tijs, S.H. & Parthasarathy, T. & Potters, J.A.M. & Rajendra Prasad, V., 1984. "Permutation games : Another class of totally balanced games," Other publications TiSEM a7edfa18-6224-4be3-b677-5, Tilburg University, School of Economics and Management.
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    Cited by:

    1. Meinhardt, Holger Ingmar, 2014. "A Note on the Computation of the Pre-Kernel for Permutation Games," MPRA Paper 59365, University Library of Munich, Germany.
    2. Ferenc Forgó & László Kóczy & Miklós Pintér, 2015. "Editorial," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 23(4), pages 723-725, December.

    More about this item

    Keywords

    Permutation game; Least core; Kernel; Primary 91A12; Secondary 91A40;

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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