### Abstract

We devise the first polynomial time algorithm computing a pure nash equilibrium for atomic splittable congestion games with singleton strategies and player-specific affine cost functions. Our algorithm is purely combinatorial and computes the exact equilibrium assuming rational input. The idea is to compute a pure nash equilibrium for an associated integrally-splittable singleton congestion game in which the players can only split their demands in integral multiples of a common packet size. While integral games have been considered in the literature before, no polynomial time algorithm computing an equilibrium was known. Also for this class, we devise the first polynomial time algorithm and use it as a building block for our main algorithm.

Original language | English |
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Title of host publication | Integer Programming and Combinatorial Optimization. IPCO 2017. |

Subtitle of host publication | 19th International Conference, IPCO 2017, Waterloo, ON, Canada, June 26-28, 2017, Proceedings |

Publisher | Springer |

Pages | 442-454 |

Volume | 10328 |

ISBN (Electronic) | 978-3-319-59250-3 |

ISBN (Print) | 978-3-319-59249-7 |

DOIs | |

Publication status | Published - 2017 |

Event | IPCO 2017: Integer Programming and Combinatorial Optimization: 19th International Conference - Waterloo, ON, Waterloo, Canada Duration: 26 Jun 2017 → 28 Jun 2017 |

### Publication series

Series | Lecture Notes in Computer Science |
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Number | 10328 |

### Conference

Conference | IPCO 2017 |
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Country | Canada |

City | Waterloo |

Period | 26/06/17 → 28/06/17 |

## Cite this

Timmermans, V., & Harks, T. (2017). Equilibrium Computation in Atomic Splittable Singleton Congestion Games. In

*Integer Programming and Combinatorial Optimization. IPCO 2017. : 19th International Conference, IPCO 2017, Waterloo, ON, Canada, June 26-28, 2017, Proceedings*(Vol. 10328, pp. 442-454). Springer. Lecture Notes in Computer Science, No. 10328 https://doi.org/10.1007/978-3-319-59250-3_36