Using weight decision for decreasing the price of anarchy in selfish bin packing games

Abstract

Abstract A selfish bin packing game is a variant of the classical bin packing problem in a game theoretic setting. In our model the items have not only a size but also a nonnegative weight. Each item plays the role of a selfish agent, and any agent/item pays some cost for being in a bin. The cost of a bin is 1, and this cost is shared among the items being in the bin, proportionally to their weight. A packing of the items into bins is called a Nash equilibrium if no item can decrease its cost by moving to another bin. In this paper we present two different settings for the weights which provide better values for the price of anarchy (PoA) than previous settings investigated so far. The improved PoA is not bigger than 16/11 ≈ 1.4545. Moreover, we give a general lower bound for the price of anarchy which holds for all possible choices of the weights.