Routing without regret: On convergence to nash equilibria of regret-minimizing algorithms in routing games

Avrim Blum*, Eyal Even-Dar, Katrina Ligett

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

91 Scopus citations

Abstract

There has been substantial work developing simple, efficient no-regret algorithms for a wide class of repeated decision-making problems including online routing. These are adaptive strategies an individual can use that give strong guarantees on performance even in adversarially-changhig environments. There has also been substantial work on analyzing properties of Nash equilibria in routing games. In this paper, we consider the question; if each player in a routing game uses a no-regret strategy, will behavior converge to a Nash equilibrium? In general games the answer to this question is known to be no in a strong sense, but routing games have substantially more structure. In this paper we show that in the Wardrop setting of multicommodity flow and infinitesimal agents, behavior will approach Nash, equilibrium (formally, on most days, the cost of the flow will be close to the cost of the cheapest paths possible given that flow) at a rate that depends polynomially on the players' regret bounds and the maximum slope of any latency function. We also show that price-of-anarchy results may be applied to these approximate equilibria, and also consider the finite-size (non-infinitesimal) load-balancing model of Azar [2].

Original languageAmerican English
Title of host publicationProceedings of the 25th Annual ACM Symposium on Principles of Distributed Computing 2006
Pages45-52
Number of pages8
StatePublished - 2006
Externally publishedYes
Event25th Annual ACM Symposium on Principles of Distributed Computing 2006 - Denver, CO, United States
Duration: 23 Jul 200626 Jul 2006

Publication series

NameProceedings of the Annual ACM Symposium on Principles of Distributed Computing
Volume2006

Conference

Conference25th Annual ACM Symposium on Principles of Distributed Computing 2006
Country/TerritoryUnited States
CityDenver, CO
Period23/07/0626/07/06

Keywords

  • Game theory
  • Network games

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