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$\frac{\rho}{1-\epsilon}$-approximate pure Nash equilibria algorithms for weighted congestion games and their runtimes
- Publication Year :
- 2022
-
Abstract
- This paper concerns computing approximate pure Nash equilibria in weighted congestion games, which has been shown to be PLS-complete. With the help of $\hat{\Psi}$-game and approximate potential functions, we propose two algorithms based on best response dynamics, and prove that they efficiently compute $\frac{\rho}{1-\epsilon}$-approximate pure Nash equilibria for $\rho= d!$ and $\rho =\frac{2\cdot W\cdot(d+1)}{2\cdot W+d+1}\le {d + 1}$, 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.<br />Comment: 31 pages
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2208.11309
- Document Type :
- Working Paper