Journal of Combinatorial Optimization

, Volume 35, Issue 2, pp 632–640 | Cite as

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

  • Q. Q. Nong
  • T. Sun
  • T. C. E. Cheng
  • Q. Z. Fang


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 \(\frac{3}{2}\) and prove that any feasible packing can converge to a Nash equilibrium in \(n^2-n\) steps without increasing the social cost.


Game Nash equilibrium Price of anarchy Bin packing 



This research was supported in part by the National Natural Science Foundation of China under Grant Numbers 11201439 and 11271341. This work was also supported in part by the Shandong Provincial Natural Science Foundation under Grant Number ZR2012AQ12 and by the Doctoral Fund of the Ministry of Education of China (20120132120001).


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© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.School of Mathematical ScienceOcean University of ChinaQingdaoPeople’s Republic of China
  2. 2.Department of Logistics and Maritime StudiesThe Hong Kong Polytechnic UniversityKowloonHong Kong

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