# 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

39 Citations (Scopus)

## 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 language English 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science 532-541 10 978-0-7695-4571-4 https://doi.org/10.1109/FOCS.2011.50 Published - 2011 52nd Annual Symposium on Foundations of Computer Science 2011 - Hotel Zoso , Palm Springs, United StatesDuration: 22 Oct 2011 → 25 Oct 2011Conference number: 52http://ieee-focs.org/focs2011/

### Conference

Conference 52nd Annual Symposium on Foundations of Computer Science 2011 FOCS 2011 United States Palm Springs 22/10/11 → 25/10/11 http://ieee-focs.org/focs2011/

## Keywords

• approximate pure Nash equilibria
• computation and complexity
• congestion games

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