Optimal price of anarchy of polynomial and super-polynomial bottleneck congestion games

Rajgopal Kannan, Costas Busch, Athanasios V. Vasilakos

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

2 Scopus citations

Abstract

We introduce (super) polynomial bottleneck games, where the utility costs of the players are (super) polynomial functions of the congestion of the resources that they use, and the social cost is determined by the worst congestion of any resource. In particular, the delay function for any resource r is ofbut the degree is bounded the form CrMr, where Cr is the congestion measured as the number of players that use r, and the degree of the delay function is bounded as 1 ≤ Mr ≤ log Cr. The utility cost of a player is the sum of the individual delays of the resources that it uses. The social cost of the game is the worst bottleneck resource congestion: maxrεR Cr, where R is the set of resources. We show that for super-polynomial bottleneck games with Mr = log Cr, the price of anarchy is o(√|R|), specifically O(2√log|R|). We also consider general polynomial bottleneck games where each resource can have a distinct monomial latency function but the degree is bounded i.e Mr = O(1) with constants α ≤ Mr ≤ β and derive the price of anarchy as min (|R|, max(2β/C*(2|R|)1/α+1 ·,(2β/ C*)α/α+1 · (2β) β-α/α+1)), where C* is the bottleneck congestion in the socially optimal state. We then demonstrate matching lower bounds for both games showing that this price of anarchy is tight.

Original languageEnglish (US)
Title of host publicationGame Theory for Networks - Second International ICST Conference, GAMENETS 2011, Revised Selected Papers
Pages308-320
Number of pages13
DOIs
StatePublished - 2012
Externally publishedYes
Event2nd International ICST Conference on Game Theory in Networks, GAMENETS 2011 - Shanghai, China
Duration: Apr 16 2011Apr 18 2011

Publication series

NameLecture Notes of the Institute for Computer Sciences, Social-Informatics and Telecommunications Engineering
Volume75 LNICST
ISSN (Print)1867-8211

Conference

Conference2nd International ICST Conference on Game Theory in Networks, GAMENETS 2011
CountryChina
CityShanghai
Period4/16/114/18/11

ASJC Scopus subject areas

  • Computer Networks and Communications

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    Kannan, R., Busch, C., & Vasilakos, A. V. (2012). Optimal price of anarchy of polynomial and super-polynomial bottleneck congestion games. In Game Theory for Networks - Second International ICST Conference, GAMENETS 2011, Revised Selected Papers (pp. 308-320). (Lecture Notes of the Institute for Computer Sciences, Social-Informatics and Telecommunications Engineering; Vol. 75 LNICST). https://doi.org/10.1007/978-3-642-30373-9_22