### Abstract

Original language | Undefined |
---|---|

Place of Publication | Enschede |

Publisher | Centre for Telematics and Information Technology (CTIT) |

Number of pages | 16 |

Publication status | Published - 22 Feb 2016 |

### Publication series

Name | CTIT Technical Report Series |
---|---|

Publisher | University of Twente, Centre for Telematics and Information Technology (CTIT) |

No. | TR-CTIT-16-04 |

ISSN (Print) | 1381-3625 |

### Keywords

- MSC-90C27
- Matroid strategy spaces
- IR-100255
- Price of Anarchy
- Affine cost functions
- EWI-26855
- METIS-316842
- Atomic congestion games

### Cite this

*Efficiency of equilibria in uniform matroid congestion games*. (CTIT Technical Report Series; No. TR-CTIT-16-04). Enschede: Centre for Telematics and Information Technology (CTIT).

}

*Efficiency of equilibria in uniform matroid congestion games*. CTIT Technical Report Series, no. TR-CTIT-16-04, Centre for Telematics and Information Technology (CTIT), Enschede.

**Efficiency of equilibria in uniform matroid congestion games.** / de Jong, Jasper; Klimm, Max; Uetz, Marc Jochen.

Research output: Book/Report › Report › Other research output

TY - BOOK

T1 - Efficiency of equilibria in uniform matroid congestion games

AU - de Jong, Jasper

AU - Klimm, Max

AU - Uetz, Marc Jochen

N1 - eemcs-eprint-26855

PY - 2016/2/22

Y1 - 2016/2/22

N2 - Network routing games, and more generally congestion games play a central role in algorithmic game theory, comparable to the role of the traveling salesman problem in combinatorial optimization. It is known that the price of anarchy is independent of the network topology for non-atomic congestion games. In other words, it is independent of the structure of the strategy spaces of the players, and for affine cost functions it equals 4/3. In this paper, we show that the dependence of the price of anarchy on the network topology is considerably more intricate for atomic congestion games. More specifically, we consider congestion games with affine cost functions where the strategy spaces of players are symmetric and equal to the set of bases of a k-uniform matroid. In this setting, we show that the price of anarchy is strictly larger than the price of anarchy for singleton strategy spaces where the latter is 4/3. As our main result we show that the price of anarchy can be bounded from above by 28/13. This constitutes a substantial improvement over the price of anarchy bound 5/2, which is known to be tight for arbitrary network routing games with affine cost functions.

AB - Network routing games, and more generally congestion games play a central role in algorithmic game theory, comparable to the role of the traveling salesman problem in combinatorial optimization. It is known that the price of anarchy is independent of the network topology for non-atomic congestion games. In other words, it is independent of the structure of the strategy spaces of the players, and for affine cost functions it equals 4/3. In this paper, we show that the dependence of the price of anarchy on the network topology is considerably more intricate for atomic congestion games. More specifically, we consider congestion games with affine cost functions where the strategy spaces of players are symmetric and equal to the set of bases of a k-uniform matroid. In this setting, we show that the price of anarchy is strictly larger than the price of anarchy for singleton strategy spaces where the latter is 4/3. As our main result we show that the price of anarchy can be bounded from above by 28/13. This constitutes a substantial improvement over the price of anarchy bound 5/2, which is known to be tight for arbitrary network routing games with affine cost functions.

KW - MSC-90C27

KW - Matroid strategy spaces

KW - IR-100255

KW - Price of Anarchy

KW - Affine cost functions

KW - EWI-26855

KW - METIS-316842

KW - Atomic congestion games

M3 - Report

T3 - CTIT Technical Report Series

BT - Efficiency of equilibria in uniform matroid congestion games

PB - Centre for Telematics and Information Technology (CTIT)

CY - Enschede

ER -