## Abstract

In bottleneck congestion games the social cost is the worst congestion (bottleneck) on any resource, and each player selfishly minimizes the worst resource congestion in its strategy. We examine the price of anarchy with respect to the stretch which is a measure of variation in the resource utilization in the strategy sets of the players. The stretch is particularly important in routing problems since it compares the chosen path lengths with the respective shortest path lengths. We show that the price of anarchy in general bottleneck games is bounded by O(sm), where s is the stretch and m is the total number of resources. In linear bottleneck games, where the resource latencies are linearly proportional to the players' workloads, the price of anarchy is improved to O√sm). These bounds are asymptotically tight. For constant stretch linear games we obtain a Θ(√m) improvement over the previously best known bound.

Original language | English (US) |
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Pages (from-to) | 592-603 |

Number of pages | 12 |

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

Volume | 7434 LNCS |

DOIs | |

State | Published - 2012 |

Externally published | Yes |

Event | 18th Annual International Computing and Combinatorics Conference, COCOON 2012 - Sydney, NSW, Australia Duration: Aug 20 2012 → Aug 22 2012 |

## Keywords

- algorithmic game theory
- bottleneck games
- congestion games
- price of anarchy

## ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)