## Abstract

Congestion games constitute an important class of games to model resource allocation by different users. As computing an exact [18] or even an approximate [34] pure Nash equilibrium is in general PLS-complete, Caragiannis et al. [9] present a polynomial-time algorithm that computes a (2 + ϵ)-approximate pure Nash equilibria for games with linear cost functions and further results for polynomial cost functions. We show that this factor can be improved to (1.61 + ϵ) and further improved results for polynomial cost functions, by a seemingly simple modification to their algorithm by allowing for the cost functions used during the best response dynamics be different from the overall objective function. Interestingly, our modification to the algorithm also extends to efficiently computing improved approximate pure Nash equilibria in games with arbitrary non-decreasing resource cost functions. Additionally, our analysis exhibits an interesting method to optimally compute universal load dependent taxes and using linear programming duality prove tight bounds on the PoA under universal taxation, e.g., 2.012 for linear congestion games and further results for polynomial cost functions. Although our approach yield weaker results than that in Bilò and Vinci [6], we remark that our cost functions are locally computable and in contrast to [6] are independent of the actual instance of the game.

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

Subtitle of host publication | 16th International Conference, WINE 2020, Proceedings |

Editors | Xujin Chen, Nikolai Gravin, Martin Hoefer, Ruta Mehta |

Publisher | Springer |

Pages | 280-294 |

Number of pages | 15 |

ISBN (Electronic) | 978-3-030-64946-3 |

ISBN (Print) | 978-3-030-64945-6 |

DOIs | |

Publication status | Published - 6 Dec 2020 |

Event | 16th International Conference on Web and Internet Economics, WINE 2020 - Virtual, Beijing, China Duration: 7 Dec 2020 → 11 Dec 2020 Conference number: 16 https://econcs.pku.edu.cn/wine2020/ |

### 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 | 12495 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 16th International Conference on Web and Internet Economics, WINE 2020 |
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Abbreviated title | WINE 2020 |

Country | China |

City | Beijing |

Period | 7/12/20 → 11/12/20 |

Internet address |

## Keywords

- Approximate pure Nash equilibria
- Congestion games
- Price of anarchy
- Universal taxes