Efficient computation of approximate pure Nash equilibria in congestion games

Ioannis Caragiannis, Angelo Fanelli, Nick Gravin, Alexander Skopalik

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

45 Citations (Scopus)
13 Downloads (Pure)

Abstract

Congestion games constitute an important class of games in which computing an exact or even approximate pure Nash equilibrium is in general {\sf PLS}-complete. We present a surprisingly simple polynomial-time algorithm that computes O(1)-approximate Nash equilibria in these games. In particular, for congestion games with linear latency functions, our algorithm computes $(2+\epsilon)$-approximate pure Nash equilibria in time polynomial in the number of players, the number of resources and $1/\epsilon$. It also applies to games with polynomial latency functions with constant maximum degree $d$; there, the approximation guarantee is $d^{O(d)}$. The algorithm essentially identifies a polynomially long sequence of best-response moves that lead to an approximate equilibrium; the existence of such short sequences is interesting in itself. These are the first positive algorithmic results for approximate equilibria in non-symmetric congestion games. We strengthen them further by proving that, for congestion games that deviate from our mild assumptions, computing $\rho$-approximate equilibria is {\sf PLS}-complete for any polynomial-time computable $\rho$.
Original languageEnglish
Title of host publication2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
PublisherIEEE
Pages532-541
Number of pages10
ISBN (Electronic)978-0-7695-4571-4
ISBN (Print)978-1-4577-1843-4
DOIs
Publication statusPublished - 2011
Externally publishedYes
Event52nd Annual Symposium on Foundations of Computer Science 2011 - Hotel Zoso , Palm Springs, United States
Duration: 22 Oct 201125 Oct 2011
Conference number: 52
http://ieee-focs.org/focs2011/

Publication series

NameIEEE Annual Symposium on Foundations of Computer Science
PublisherIEEE
Number52
Volume2011
ISSN (Print)0272-5428

Conference

Conference52nd Annual Symposium on Foundations of Computer Science 2011
Abbreviated titleFOCS 2011
Country/TerritoryUnited States
CityPalm Springs
Period22/10/1125/10/11
Internet address

Keywords

  • Approximate pure Nash equilibria
  • Computation and complexity
  • Congestion games
  • n/a OA procedure

Fingerprint

Dive into the research topics of 'Efficient computation of approximate pure Nash equilibria in congestion games'. Together they form a unique fingerprint.

Cite this