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Nguyen and Thomas (2016) claimed that they have found a method to compute thenucleoli of games with more than $50$ players using nested linear programs(LP). Unfortunately, this claim is false. They incorrectly applied the indirectproof by "$A \land \neg B$ implies $A \land \neg A$" to conclude that "if $A$then $B$" is valid. In fact, they prove that a truth implies a falsehood. Asestablished by Meinhardt (2015a), this is a wrong statement. Therefore, insteadof giving a proof of their main Theorem 4b, they give a disproof. It comes asno surprise to us that the flow game example presented by these authors tosupport their arguments is obviously a counter-example of their algorithm. Weshow that the computed solution by this algorithm is neither the nucleolus nora core element of the flow game. Moreover, the stopping criterion of allproposed methods is wrong, since it does not satisfy one of Kohlberg'sproperties (cf. Kohlberg (1971)). As a consequence, none of these algorithms isrobust.

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