Finding the Nucleoli of Large Cooperative Games: A Disproof with Counter-Example

Holger Meinhardt

MPRA Paper from University Library of Munich, Germany

Abstract: Nguyen and Thomas (2016) claimed that they have found a method to compute the nucleoli of games with more than 50 players using nested linear programs (LP). Unfortunately, this claim is false. They incorrectly applied the indirect proof by ``A and not B implies A and not A'' to conclude that ``if A then B''is valid. In fact, they prove that a truth implies a falsehood. As established by Meinhardt (2015a), this is a wrong statement. Therefore, instead of giving a proof of their main Theorem 4b, they give a disproof. It comes as no surprise to us that the flow game example presented by these authors to support their arguments is obviously a counter-example of their algorithm. We show that the computed solution by this algorithm is neither the nucleolus nor a core element of the flow game. Moreover, the stopping criterion of all proposed methods is wrong, since it does not satisfy one of Kohlberg's properties (cf. Kohlberg (1971)). As a consequence, none of these algorithms is robust.

Keywords: Transferable Utility Game, Nucleolus, Flow Problem, Propositional Logic; Circular Reasoning (circulus in probando); Indirect Proof; Proof by Contradiction; Proof by Contraposition. (search for similar items in EconPapers)
JEL-codes: C71 (search for similar items in EconPapers)
Date: 2016-03-01
New Economics Papers: this item is included in nep-gth, nep-ore and nep-upt
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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