### Abstract

Network congestion games with player-specific delay functions do not necessarily possess pure Nash equilibria. We therefore address the computational complexity of the corresponding decision problem, and show that it is NP-complete to decide whether such games possess pure Nash equilibria. This negative result still holds in the case of games with two players only. In contrast, we show that one can decide in polynomial time whether an equilibrium exists if the number of resources is constant. In addition, we introduce a family of player-specific network congestion games which are guaranteed to possess equilibria. In these games players have identical delay functions, however, each player may only use a certain subset of the edges. For this class of games we prove that finding a pure Nash equilibrium is PLS-complete even in the case of three players. Again, in the case of a constant number of edges an equilibrium can be computed in polynomial time. We conclude that the number of resources has a bigger impact on the computation complexity of certain problems related to network congestion games than the number of players.

Original language | English |
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Title of host publication | Internet and Network Economics |

Subtitle of host publication | Third International Workshop, WINE 2007, Proceedings |

Editors | Xiaotie Deng, Fan Chung Graham |

Pages | 419-430 |

Number of pages | 12 |

ISBN (Electronic) | 978-3-540-77105-0 |

DOIs | |

Publication status | Published - 1 Dec 2007 |

Externally published | Yes |

Event | 3rd International Workshop on Internet and Network Economics, WINE 2007 - San Diego, United States Duration: 12 Dec 2007 → 14 Dec 2007 Conference number: 3 |

### 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 | 4858 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 3rd International Workshop on Internet and Network Economics, WINE 2007 |
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Abbreviated title | WINE 2007 |

Country | United States |

City | San Diego |

Period | 12/12/07 → 14/12/07 |

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### Cite this

*Internet and Network Economics : Third International Workshop, WINE 2007, Proceedings*(pp. 419-430). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4858 LNCS). https://doi.org/10.1007/978-3-540-77105-0_47