Computing Approximate Equilibria in Weighted Congestion Games via Best-Responses

We present a deterministic polynomial-time algorithm for computing [Formula: see text]-approximate (pure) Nash equilibria in (proportional sharing) weighted congestion games with polynomial cost functions of degree at most text]. This is an exponential improvement the approximation factor respect to previously best algorithm. An appealing additional feature that it only uses best-improvement steps actual game, as opposed algorithms, first had transform game itself. Our adaptation seminal by Caragiannis al. [Caragiannis I, Fanelli A, Gravin N, Skopalik A (2011) Efficient computation approximate pure games. Ostrovsky R, ed. Proc. 52nd Annual Symp. Foundations Comput. Sci. (FOCS) (IEEE Computer Society, Los Alamitos, CA), 532–541; (2015) Approximate games: Existence, efficient computation, and structure. ACM Trans. Econom. 3(1):2:1–2:32.], but we utilize potential function directly on original instead exact one modified game. critical component our analysis, which independent interest, derivation novel bound text] price anarchy (PoA) games, where Lambert-W function. More specifically, show this PoA exactly equal text], unique positive solution equation upper derived via smoothness-like argument, thus holds even mixed correlated equilibria, whereas lower simple enough apply singleton