# The Library

### Sensitivity of wardrop equilibria

Tools

Englert, Matthias, Franke, T. and Olbrich, L..
(2010)
*Sensitivity of wardrop equilibria.*
Theory of Computing Systems, Volume 47
(Number 1).
pp. 3-14.
ISSN 1432-4350

PDF
fulltext18.pdf - Published Version Restricted to Repository staff only - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader Download (420Kb) |

Official URL: http://dx.doi.org/10.1007/s00224-009-9196-4

## Abstract

We study the sensitivity of equilibria in the well-known game theoretic traffic model due to Wardrop. We mostly consider single-commodity networks. Suppose, given a unit demand flow at Wardrop equilibrium, one increases the demand by ε or removes an edge carrying only an ε-fraction of flow. We study how the equilibrium responds to such an ε-change.

Our first surprising finding is that, even for linear latency functions, for every ε>0, there are networks in which an ε-change causes every agent to change its path in order to recover equilibrium. Nevertheless, we can prove that, for general latency functions, the flow increase or decrease on every edge is at most ε.

Examining the latency at equilibrium, we concentrate on polynomial latency functions of degree at most p with nonnegative coefficients. We show that, even though the relative increase in the latency of an edge due to an ε-change in the demand can be unbounded, the path latency at equilibrium increases at most by a factor of (1+ε) p . The increase of the price of anarchy is shown to be upper bounded by the same factor. Let us remark that all our bounds are tight.

For the multi-commodity case, we present examples showing that neither the change in edge flows nor the change in the path latency can be bounded.

Item Type: | Journal Article |
---|---|

Subjects: | Q Science > QA Mathematics > QA76 Electronic computers. Computer science. Computer software |

Divisions: | Faculty of Science > Computer Science |

Series Name: | Lecture Notes in Computer Science |

Journal or Publication Title: | Theory of Computing Systems |

Publisher: | Springer New York LLC |

ISSN: | 1432-4350 |

Official Date: | 1 July 2010 |

Volume: | Volume 47 |

Number: | Number 1 |

Page Range: | pp. 3-14 |

Identification Number: | 10.1007/s00224-009-9196-4 |

Status: | Peer Reviewed |

Publication Status: | Published |

Access rights to Published version: | Restricted or Subscription Access |

Funder: | Deutsche Forschungsgemeinschaft (DFG) |

Grant number: | WE 2842/1 (DFG), GK/1298 “AlgoSyn” (DFG) |

Version or Related Resource: | A preliminary version of this paper appeared in Proceedings of the 1st International Symposium on Algorithmic Game Theory (SAGT), 2008. |

URI: | http://wrap.warwick.ac.uk/id/eprint/47511 |

Request changes or add full text files to a record

### Actions (login required)

View Item |