Wu Zijun | Searcharxiv

arXiv2022

$\fracρ{1-ε}$-approximate pure Nash equilibria algorithms for weighted congestion games and their runtimes

This paper concerns computing approximate pure Nash equilibria in weighted congestion games, which has been shown to be PLS-complete. With the help of $\hatΨ$-game and approximate potential functions, we propose two algorithms based on best response dynamics, and prove that they efficiently compute $\fracρ{1-ε}$-approximate pure Nash equilibria for $ρ= d!$ and $ρ=\frac{2\cdot W\cdot(d+1)}{2\cdot W+d+1}\le {d + 1}$, respectively, when the weighted congestion game has polynomial latency functions of degree at most $d \ge 1$ and players' weights are bounded from above by a constant $W \ge 1$. This improves the recent work of Feldotto et al.[2017] and Giannakopoulos et al. [2022] that showed efficient algorithms for computing $d^{d+o(d)}$-approximate pure Nash equilibria.

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arXiv2020

Selfishness need not be bad

We investigate the price of anarchy (PoA) in non-atomic congestion games when the total demand $T$ gets very large. First results in this direction have recently been obtained by \cite{Colini2016On, Colini2017WINE, Colini2017arxiv} for routing games and show that the PoA converges to 1 when the growth of the total demand $T$ satisfies certain regularity conditions. We extend their results by developing a \Wuuu{new} framework for the limit analysis of \Wuuuu{the PoA that offers strong techniques such as the limit of games and applies to arbitrary growth patterns of $T$.} \Wuuu{We} show that the PoA converges to 1 in the limit game regardless of the type of growth of $T$ for a large class of cost functions that contains all polynomials and all regularly varying functions. % For routing games with BPR \Wuu{cost} functions, we show in addition that socially optimal strategy profiles converge to \Wuu{equilibria} in the limit game, and that PoA$=1+o(T^{-β})$, where $β>0$ is the degree of the \Wuu{BPR} functions. However, the precise convergence rate depends crucially on the the growth of $T$, which shows that a conjecture proposed by \cite{O2016Mechanisms} need not hold.

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