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Simplifying the Kohlberg Criterion on the Nucleolus: A Disproof by Oneself

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  • Meinhardt, Holger Ingmar

Abstract

(Nguyen 2016) claimed that he has developed a simplifying set of the Kohlberg criteria that involves checking the balancedness of at most (n-1) sets of coalitions. This claim is not true. Analogous to Nguyen and Thomas (2016), he has incorrectly applied the indirect proof. He established in his purported proofs of the main results that a truth implies a falsehood. This is a wrong statement and such a hypotheses must be rejected (cf. Meinhardt (2015,2016a,2016b)). Executing a logical correct interpretation ought immediately lead him to the conclusion that his proposed algorithms are deficient. In particular, he had to detect that the imposed balancedness requirement on the test condition within his proposed methods cannot be appropriate. As a consequence, either a nucleolus with a weakly balanced set will be dismissed by the implemented algorithms or a solution which is not a nucleolus will be selected as a nucleolus. Hence, one cannot expect that one of these algorithms makes a correct selection. The supposed algorithms are wrongly designed and cannot be set in any relation with Kohlberg.

Suggested Citation

  • Meinhardt, Holger Ingmar, 2017. "Simplifying the Kohlberg Criterion on the Nucleolus: A Disproof by Oneself," MPRA Paper 77143, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:77143
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    File URL: https://mpra.ub.uni-muenchen.de/77143/1/MPRA_paper_77143.pdf
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    References listed on IDEAS

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    1. Nguyen, Tri-Dung & Thomas, Lyn, 2016. "Finding the nucleoli of large cooperative games," European Journal of Operational Research, Elsevier, vol. 248(3), pages 1078-1092.
    2. Meinhardt, Holger Ingmar, 2016. "Finding the Nucleoli of Large Cooperative Games: A Disproof with Counter-Example," MPRA Paper 69789, University Library of Munich, Germany.
    3. Meinhardt, Holger Ingmar, 2015. "The Incorrect Usage of Propositional Logic in Game Theory: The Case of Disproving Oneself," MPRA Paper 66637, University Library of Munich, Germany.
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    Cited by:

    1. 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; Nucleolus; Balancedness; Kohlberg Criteria; Convexity; Affine Hull; Propositional Logic; Circular Reasoning (circulus in probando); Indirect Proof; Proof by Contradiction;
    All these keywords.

    JEL classification:

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

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