We consider bin packing games introduced by Faigle and Kern (1993) and we restrict ourselves to the subclass of games for which all bins have unit capacity and all items are larger than 1/3. We adopt the taxation model of Faigle and Kern and we prove that for a tax-rate of ε = 1/7 the ε-core is always non empty. The bound is sharp, since for every ε < 1/7 there exist instances of the bin packing game within our sublass with an empty ε-core.
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