Selfish bin packing with punishment

In this paper we study the problem of selfish bin packing with punishment. Different from the selfish bin packing problem proposed by Bila in 2006, where the items are astute to minimize their shared proportional cost in a bin, we consider the case that items are into the utility defined as the load of bin it is packed in and, a unilateral moving may incur punishment. We define and consider several kinds of punishment, which can be roughly classified into two types: the punishment according to the behavior and the punishment based on the result. For both types we present the tight bound for Price of Anarchy (PoA) under the objective of minimizing the number of bins used. The results proved show that punishment does not always work, a punishment based on the result can be viewed as a delicate designed threat in advance which could perform much better, with an approximate 1.48 upper bound comparing to the optimal solution.