### 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 language | English |
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Title of host publication | Approximation and Online Algorithms - 16th International Workshop, WAOA 2018, Revised Selected Papers |

Editors | Leah Epstein, Thomas Erlebach |

Publisher | Springer Verlag |

Pages | 204-217 |

Number of pages | 14 |

ISBN (Print) | 9783030046927 |

DOIs | |

Publication status | Published - Jan 1 2018 |

Event | 16th Workshop on Approximation and Online Algorithms, WAOA 2018 - Helsinki, Finland Duration: Aug 23 2018 → Aug 24 2018 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
---|---|

Volume | 11312 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 16th Workshop on Approximation and Online Algorithms, WAOA 2018 |
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Country | Finland |

City | Helsinki |

Period | 8/23/18 → 8/24/18 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*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.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*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

}

TY - GEN

T1 - Bin packing games with weight decision

T2 - How to get a small value for the price of anarchy

AU - Dosa, Gyorgy

AU - Kellerer, Hans

AU - Tuza, Z.

PY - 2018/1/1

Y1 - 2018/1/1

N2 - 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.

AB - 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.

KW - Algorithmic game theory

KW - Price of anarchy

KW - Selfish bin packing

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U2 - 10.1007/978-3-030-04693-4_13

DO - 10.1007/978-3-030-04693-4_13

M3 - Conference contribution

AN - SCOPUS:85058431813

SN - 9783030046927

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 204

EP - 217

BT - Approximation and Online Algorithms - 16th International Workshop, WAOA 2018, Revised Selected Papers

A2 - Epstein, Leah

A2 - Erlebach, Thomas

PB - Springer Verlag

ER -