## Abstract

We study the multidimensional vector packing problem with selfish items. An item is d-dimensional non-zero vector, whose rational components are in [0, 1], and a set of items can be packed into a bin if for any 1 ≤ i ≤ d, the sum of the i^{th} components of all items of this set does not exceed 1. Items share costs of bins proportionally to their ℓ_{1}- norms, and each item corresponds to a selfish player in the sense that it prefers to be packed into a bin minimizing its resulting cost. This defines a class of games called vector packing games. We show that any game in this class has a packing that is a strong equilibrium, and that the strong price of anarchy (and the strong price of stability) is logarithmic in d, and provide an algorithm that constructs such a packing. We also show improved and nearly tight lower and upper bounds of d + 0.657067 and d+0.657143 respectively, on the price of anarchy, exhibiting a difference between the multidimensional problem and the one dimensional problem, for which that price of anarchy is at most 1.6428.

Original language | English |
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Title of host publication | Algorithms – ESA 2015 - 23rd Annual European Symposium, Proceedings |

Editors | Nikhil Bansal, Irene Finocchi |

Publisher | Springer Verlag |

Pages | 471-482 |

Number of pages | 12 |

ISBN (Print) | 9783662483497 |

DOIs | |

State | Published - 2015 |

Event | 23rd European Symposium on Algorithms, ESA 2015 - Patras, Greece Duration: 14 Sep 2015 → 16 Sep 2015 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 9294 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 23rd European Symposium on Algorithms, ESA 2015 |
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Country/Territory | Greece |

City | Patras |

Period | 14/09/15 → 16/09/15 |

### Bibliographical note

Publisher Copyright:© Springer-Verlag Berlin Heidelberg 2015.

## ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science (all)