Bottleneck congestion games with logarithmic price of anarchy

Rajgopal Kannan, Costas Busch

Research output: Chapter in Book/Report/Conference proceedingConference contribution

8 Scopus citations

Abstract

We study bottleneck congestion games where the social cost is determined by the worst congestion on any resource. In the literature, bottleneck games assume player utility costs determined by the worst congested resource in their strategy. However, the Nash equilibria of such games are inefficient since the price of anarchy can be very high and proportional to the number of resources. In order to obtain smaller price of anarchy we introduce exponential bottleneck games, where the utility costs of the players are exponential functions of their congestions. In particular, the delay function for any resource r is , where C r denotes the number of players that use r, and is an integer constant. We find that exponential bottleneck games are very efficient and give the following bound on the price of anarchy: O(log|R|), where R is the set of resources. This price of anarchy is tight, since we demonstrate a game with price of anarchy Ω(log|R|). We obtain our tight bounds by using two novel proof techniques: transformation, which we use to convert arbitrary games to simpler games, and expansion, which we use to bound the price of anarchy in a simpler game.

Original languageEnglish (US)
Title of host publicationAlgorithmic Game Theory - Third International Symposium, SAGT 2010, Proceedings
Pages222-233
Number of pages12
EditionM4D
DOIs
StatePublished - 2010
Externally publishedYes
Event3rd International Symposium on Algorithmic Game Theory, SAGT 2010 - Athens, Greece
Duration: Oct 18 2010Oct 20 2010

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
NumberM4D
Volume6386 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference3rd International Symposium on Algorithmic Game Theory, SAGT 2010
CountryGreece
CityAthens
Period10/18/1010/20/10

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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  • Cite this

    Kannan, R., & Busch, C. (2010). Bottleneck congestion games with logarithmic price of anarchy. In Algorithmic Game Theory - Third International Symposium, SAGT 2010, Proceedings (M4D ed., pp. 222-233). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6386 LNCS, No. M4D). https://doi.org/10.1007/978-3-642-16170-4_20