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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Partially supported by “the Fundamental Research Funds for the Central Universities” and NSFC (11101065, 11171086, 11071215), No. CXB201005250021A and HK RGC grant HKU-7171/08E.
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Ma, R., Dósa, G., Han, X. et al. A note on a selfish bin packing problem. J Glob Optim 56, 1457–1462 (2013). https://doi.org/10.1007/s10898-012-9856-9
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DOI: https://doi.org/10.1007/s10898-012-9856-9