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A Note on the Computation of the Pre-Kernel for Permutation Games

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  • Meinhardt, Holger Ingmar

Abstract

To determine correctly a non-convex pre-kernel for TU games with more than 4 players can be a challenge full of possible pitfalls, even to the experienced researcher. Parts of the pre-kernel can be easily overlooked. In this note we discuss a method to present the full shape of the pre-kernel for a permutation game as discussed by Solymosi (2014). By using the property in which the pre-kernel is located in the least core for permutation games, the least core can be covered by a small collection of payoff equivalence classes as identified by Meinhardt (2013d) to finally establish the correct shape of the pre-kernel.

Suggested Citation

  • Meinhardt, Holger Ingmar, 2014. "A Note on the Computation of the Pre-Kernel for Permutation Games," MPRA Paper 59365, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:59365
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    File URL: https://mpra.ub.uni-muenchen.de/59365/1/MPRA_paper_59365.pdf
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    References listed on IDEAS

    as
    1. Meinhardt, Holger Ingmar, 2014. "On the Single-Valuedness of the Pre-Kernel," MPRA Paper 56074, University Library of Munich, Germany.
    2. 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.
    3. Chih Chang & Chrong-Hsin Lian, 2002. "Some Results On (Pre)Kernel Catchers And The Coincidence Of The Kernel With Prekernel," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 4(03), pages 201-211.
    4. Holger Ingmar Meinhardt, 2014. "The Pre-Kernel as a Tractable Solution for Cooperative Games," Theory and Decision Library C, Springer, edition 127, number 978-3-642-39549-9, December.
    5. repec:spr:thdchp:978-3-642-39549-9_1 is not listed on IDEAS
    6. M. Maschler & B. Peleg & L. S. Shapley, 1979. "Geometric Properties of the Kernel, Nucleolus, and Related Solution Concepts," Mathematics of Operations Research, INFORMS, vol. 4(4), pages 303-338, November.
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    Cited by:

    1. Meinhardt, Holger Ingmar, 2020. "On the Replication of the Pre-Kernel and Related Solutions," MPRA Paper 102676, University Library of Munich, Germany.
    2. Meinhardt, Holger Ingmar, 2021. "Disentangle the Florentine Families Network by the Pre-Kernel," MPRA Paper 106482, University Library of Munich, Germany.

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    More about this item

    Keywords

    Transferable Utility Game: Non-Convex Pre-Kernel: Pre-Kernel Catcher: Convex Analysis: Fenchel-Moreau Conjugation: Indirect Function;

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • D74 - Microeconomics - - Analysis of Collective Decision-Making - - - Conflict; Conflict Resolution; Alliances; Revolutions

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