Bin packing games with weight decision: How to get a small value for the price of anarchy

Gyorgy Dosa, Hans Kellerer, Z. Tuza

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

Abstract

A selfish bin packing game is a variant of the classical bin packing problem in a game theoretic setting. In our model the items have not only a size but also a positive weight. The cost of a bin is 1, and this cost is shared among the items being in the bin, proportionally to their weights. A packing is a Nash equilibrium (NE) if no item can decrease its cost by moving to another bin, and OPT means a packing where the items are packed optimally (into minimum number of bins). Without any misunderstanding we denote by NE both the packing and the number of bins in the packing, and the same holds for the OPT packing. We are interested in the Price of Anarchy (PoA), which is the limsup of NE/OPT ratios. Recently there is a growing interest for games where the PoA is low. We give a setting for the weights where the PoA is between 1.4646 and 1.5. The lower bound is valid also for the special case of the game where the weight of any item is the same as its size, and any item has size at most one half. The previous bound was about 1.46457. Next we give another setting where the PoA is at most 16/11 ≈ 1.4545. This value is better than any previous, that was got for such games.

Original languageEnglish
Title of host publicationApproximation and Online Algorithms - 16th International Workshop, WAOA 2018, Revised Selected Papers
EditorsLeah Epstein, Thomas Erlebach
PublisherSpringer Verlag
Pages204-217
Number of pages14
ISBN (Print)9783030046927
DOIs
Publication statusPublished - Jan 1 2018
Event16th Workshop on Approximation and Online Algorithms, WAOA 2018 - Helsinki, Finland
Duration: Aug 23 2018Aug 24 2018

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume11312 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other16th Workshop on Approximation and Online Algorithms, WAOA 2018
CountryFinland
CityHelsinki
Period8/23/188/24/18

Fingerprint

Price of Anarchy
Bin Packing
Bins
Packing
Game
Nash Equilibrium
Costs
Bin Packing Problem
Valid
Lower bound
Denote
Decrease

Keywords

  • Algorithmic game theory
  • Price of anarchy
  • Selfish bin packing

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Dosa, G., Kellerer, H., & Tuza, Z. (2018). Bin packing games with weight decision: How to get a small value for the price of anarchy. In L. Epstein, & T. Erlebach (Eds.), Approximation and Online Algorithms - 16th International Workshop, WAOA 2018, Revised Selected Papers (pp. 204-217). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11312 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-030-04693-4_13

Bin packing games with weight decision : How to get a small value for the price of anarchy. / Dosa, Gyorgy; Kellerer, Hans; Tuza, Z.

Approximation and Online Algorithms - 16th International Workshop, WAOA 2018, Revised Selected Papers. ed. / Leah Epstein; Thomas Erlebach. Springer Verlag, 2018. p. 204-217 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11312 LNCS).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Dosa, G, Kellerer, H & Tuza, Z 2018, Bin packing games with weight decision: How to get a small value for the price of anarchy. in L Epstein & T Erlebach (eds), Approximation and Online Algorithms - 16th International Workshop, WAOA 2018, Revised Selected Papers. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 11312 LNCS, Springer Verlag, pp. 204-217, 16th Workshop on Approximation and Online Algorithms, WAOA 2018, Helsinki, Finland, 8/23/18. https://doi.org/10.1007/978-3-030-04693-4_13
Dosa G, Kellerer H, Tuza Z. Bin packing games with weight decision: How to get a small value for the price of anarchy. In Epstein L, Erlebach T, editors, Approximation and Online Algorithms - 16th International Workshop, WAOA 2018, Revised Selected Papers. Springer Verlag. 2018. p. 204-217. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-030-04693-4_13
Dosa, Gyorgy ; Kellerer, Hans ; Tuza, Z. / Bin packing games with weight decision : How to get a small value for the price of anarchy. Approximation and Online Algorithms - 16th International Workshop, WAOA 2018, Revised Selected Papers. editor / Leah Epstein ; Thomas Erlebach. Springer Verlag, 2018. pp. 204-217 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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