On the packing of selfish items

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, prove the hardness of computing good equilibria and give an upper and a lower bound for the price of anarchy of the game. Then, we consider a multidimensional extension of the problem in which each item can require to be packed in more than just one bin. Unfortunately, we show that in such a case the induced game may not admit a pure Nash equilibrium even under particular restrictions. The study of these games finds applications in the analysis of the bandwidth cost sharing problem in non cooperative networks