### Abstract

We study bottleneck congestion games where the social cost is determined by the worst congestion on any resource. In the literature, bottleneck games assume player utility costs determined by the worst congested resource in their strategy. However, the Nash equilibria of such games are inefficient since the price of anarchy can be very high and proportional to the number of resources. In order to obtain smaller price of anarchy we introduce exponential bottleneck games, where the utility costs of the players are exponential functions of their congestions. In particular, the delay function for any resource r is , where C _{r} denotes the number of players that use r, and is an integer constant. We find that exponential bottleneck games are very efficient and give the following bound on the price of anarchy: O(log|R|), where R is the set of resources. This price of anarchy is tight, since we demonstrate a game with price of anarchy Ω(log|R|). We obtain our tight bounds by using two novel proof techniques: transformation, which we use to convert arbitrary games to simpler games, and expansion, which we use to bound the price of anarchy in a simpler game.

Original language | English (US) |
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Title of host publication | Algorithmic Game Theory - Third International Symposium, SAGT 2010, Proceedings |

Pages | 222-233 |

Number of pages | 12 |

Edition | M4D |

DOIs | |

State | Published - 2010 |

Externally published | Yes |

Event | 3rd International Symposium on Algorithmic Game Theory, SAGT 2010 - Athens, Greece Duration: Oct 18 2010 → Oct 20 2010 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Number | M4D |

Volume | 6386 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 3rd International Symposium on Algorithmic Game Theory, SAGT 2010 |
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Country | Greece |

City | Athens |

Period | 10/18/10 → 10/20/10 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Algorithmic Game Theory - Third International Symposium, SAGT 2010, Proceedings*(M4D ed., pp. 222-233). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6386 LNCS, No. M4D). https://doi.org/10.1007/978-3-642-16170-4_20