A note on a selfish bin packing problem

A note on a selfish bin packing problem

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Article ID: iaor20134064
Volume: 56
Issue: 4
Start Page Number: 1457
End Page Number: 1462
Publication Date: Aug 2013
Journal: Journal of Global Optimization
Authors: , , , , ,
Keywords: bin packing, Nash equilibrium
Abstract:

In this paper, we consider a selfish bin packing problem, where each item is a selfish player and wants to minimize its cost. In our new model, if there are k items packed in the same bin, then each item pays a cost 1/k, where k ≥ 1. First we find a Nash Equilibrium (NE) in time O(n log n) within a social cost at most 1.69103OPT + 3, where OPT is the social cost of an optimal packing; where n is the number of items or players; then we give tight bounds for the worst NE on the social cost; finally we show that any feasible packing can be converged to a Nash Equilibrium in O(n 2) steps without increasing the social cost.

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