Bin packing game with a price of anarchy of 3/2

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

Research output: Journal article publicationJournal articleAcademic researchpeer-review

6 Citations (Scopus)

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 3/2 and prove that any feasible packing can converge to a Nash equilibrium in n2 − n steps without increasing the social cost.

Original languageEnglish
Pages (from-to)632-640
Number of pages9
JournalJournal of Combinatorial Optimization
Volume35
Issue number2
DOIs
Publication statusPublished - 1 Jan 2018

Keywords

  • Bin packing
  • Game
  • Nash equilibrium
  • Price of anarchy

ASJC Scopus subject areas

  • Computer Science Applications
  • Discrete Mathematics and Combinatorics
  • Control and Optimization
  • Computational Theory and Mathematics
  • Applied Mathematics

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