Stretch in bottleneck games

Costas Busch, Rajgopal Kannan

Research output: Contribution to journalConference articlepeer-review

1 Scopus citations


In bottleneck congestion games the social cost is the worst congestion (bottleneck) on any resource, and each player selfishly minimizes the worst resource congestion in its strategy. We examine the price of anarchy with respect to the stretch which is a measure of variation in the resource utilization in the strategy sets of the players. The stretch is particularly important in routing problems since it compares the chosen path lengths with the respective shortest path lengths. We show that the price of anarchy in general bottleneck games is bounded by O(sm), where s is the stretch and m is the total number of resources. In linear bottleneck games, where the resource latencies are linearly proportional to the players' workloads, the price of anarchy is improved to O√sm). These bounds are asymptotically tight. For constant stretch linear games we obtain a Θ(√m) improvement over the previously best known bound.

Original languageEnglish (US)
Pages (from-to)592-603
Number of pages12
JournalLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume7434 LNCS
StatePublished - 2012
Externally publishedYes
Event18th Annual International Computing and Combinatorics Conference, COCOON 2012 - Sydney, NSW, Australia
Duration: Aug 20 2012Aug 22 2012


  • algorithmic game theory
  • bottleneck games
  • congestion games
  • price of anarchy

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)


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