## Abstract

We consider a special case of weighted congestion games with player-specific latency functions where each player uses for each particular resource a fixed (non-decreasing) delay function together with a player-specific constant. For each particular resource, the resource-specific delay function and the playerspecific constant (for that resource) are composed by means of a group operation (such as addition or multiplication) into a player-specific latency function. We assume that the underlying group is a totally ordered abelian group. In this way, we obtain the class of weighted congestion games with player-specific constants; we observe that this class is contained in the new intuitive class of dominance weighted congestion games. We obtain the following results: Games on parallel links: Every unweighted congestion game has a generalized ordinal potential. There is a weighted congestion game with 3 players on 3 parallel links that does not have the Finite Best-Improvement Property. There is a particular best-improvement cycle for general weighted congestion games with player-specific latency functions and 3 players whose outlaw implies the existence of a pure Nash equilibrium. This cycle is indeed outlawed for dominance weighted congestion games with 3 players - and hence for weighted congestion games with player-specific constants and 3 players. Network congestion games: For unweighted symmetric network congestion games with player-specific additive constants, it is PLS-complete to find a pure Nash equilibrium. Arbitrary (non-network) congestion games: Every weighted congestion game with linear delay functions and player-specific additive constants has a weighted potential.

Original language | English |
---|---|

Title of host publication | Mathematical Foundations of Computer Science 2007 - 32nd International Symposium, MFCS 2007, Proceedings |

Publisher | Springer Verlag |

Pages | 633-644 |

Number of pages | 12 |

ISBN (Print) | 9783540744559 |

DOIs | |

State | Published - 2007 |

Event | 32nd International Symposium on Mathematical Foundations of Computer Science, MFCS 2007 - Cesky Krumlov, Czech Republic Duration: 26 Aug 2007 → 31 Aug 2007 |

### Publication series

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

Volume | 4708 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 32nd International Symposium on Mathematical Foundations of Computer Science, MFCS 2007 |
---|---|

Country/Territory | Czech Republic |

City | Cesky Krumlov |

Period | 26/08/07 → 31/08/07 |