## Abstract

In standard bin packing, the goal is to partition or pack items with positive sizes of at most 1 into a minimum number of subsets, called bins, each of a total size no larger than 1. We study bin packing games. In these games, given a valid partition of the items, each item has a cost associated with it, based on the partition and on its size. Specifically, the cost of an item is the ratio between its size and the total size of items packed into its bin, that is, the cost sharing is in proportion to item sizes. We study pure Nash equilibria, which exist for all such games, and prove a new lower bound on the price of anarchy, which is the asymptotic worst-case ratio between the cost of the worst Nash equilibrium and a socially optimal packing.

Original language | English |
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Pages (from-to) | 6-12 |

Number of pages | 7 |

Journal | Information Processing Letters |

Volume | 150 |

DOIs | |

State | Published - Oct 2019 |

### Bibliographical note

Funding Information:Supported by EFOP-3.6.1-16-2016-00015 and grant SNN 129364 “National Research, Development and Innovation Office - NKFIH”.Partially supported by a grant from GIF - the German-Israeli Foundation for Scientific Research and Development (grant number I-1366-407.6/2016).

Publisher Copyright:

© 2019 Elsevier B.V.

## Keywords

- Bin packing
- Combinatorial problems
- Price of anarchy

## ASJC Scopus subject areas

- Theoretical Computer Science
- Signal Processing
- Information Systems
- Computer Science Applications