Bin packing game with a price of anarchy of $$\frac{3}{2}$$ 3 2

Q. Q. Nong (), T. Sun, T. C. E. Cheng and Q. Z. Fang
Additional contact information
Q. Q. Nong: Ocean University of China
T. Sun: Ocean University of China
T. C. E. Cheng: The Hong Kong Polytechnic University
Q. Z. Fang: Ocean University of China

Journal of Combinatorial Optimization, 2018, vol. 35, issue 2, No 21, 632-640

Abstract: Abstract We consider the bin packing problem in the non-cooperative game setting. In the game there are a set of items with sizes between 0 and 1 and a number of bins each with a capacity of 1. Each item seeks to be packed in one of the bins so as to minimize its cost (payoff). The social cost is the number of bins used in the packing. Existing research has focused on three bin packing games with selfish items, namely the Unit game, the Proportional game, and the General Weight game, each of which uses a unique payoff rule. In this paper we propose a new bin packing game in which the payoff of an item is a function of its own size and the size of the maximum item in the same bin. We find that the new payoff rule induces the items to reach a better Nash equilibrium. We show that the price of anarchy of the new bin packing game is $$\frac{3}{2}$$ 3 2 and prove that any feasible packing can converge to a Nash equilibrium in $$n^2-n$$ n 2 - n steps without increasing the social cost.

Keywords: Game; Nash equilibrium; Price of anarchy; Bin packing (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s10878-017-0201-6

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