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In the non cooperative version of the classical Minimum Bin Packing problem, an item is charged a cost according to the percentage of the used bin space it requires. We study the game induced by the selfish behavior of the items which are interested in being packed in one of the bins so as to minimize their cost. We prove that such a game always converges to a pure Nash equilibrium starting from any initial packing of the items, estimate the number of steps needed to reach one such equilibrium,doi:10.1109/ipdps.2006.1639283 dblp:conf/ipps/Bilo06 fatcat:mrdn2jeav5bizim2ehnm44rnxa