Selfish Bin Packing with Parameterized Punishment

In this paper we consider the problem of selfish bin packing with parameterized punishment. Different from the classical bin packing problem, each item to be packed belongs to a selfish agent, who wants to maximize his utility by selecting an appropriate bin. The utility of the agent is defined as the total size of the items sharing the same bin with its item. If an item moves unilaterally to another bin, it may have to pay the punishment. A parameter is defined such that the items are classified whether or not they are fit for the punishment. We study three versions of punishment-full, expansile and partial punishment, and prove the corresponding bounds of \(PoA^1\) (Price of Anarchy).