1-ε-approximate pure Nash equilibria algorithms for weighted congestion games and their runtimes
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This paper concerns computing approximate pure Nash equilibria in weighted congestion games, which has been shown to be PLS-complete. With the help of Ψ̂-game and approximate potential functions, we propose two algorithms based on best response dynamics, and prove that they efficiently compute ρ/1-ϵ-approximate pure Nash equilibria for ρ= d! and ρ =2· W·(d+1)/2· W+d+1≤d + 1, respectively, when the weighted congestion game has polynomial latency functions of degree at most d ≥ 1 and players' weights are bounded from above by a constant W ≥ 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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