On Best Response Dynamics in Weighted Congestion Games with Polynomial Delays

We investigate the speed of convergence of best response dynamics to approximately optimal solutions in weighted congestion games with polynomial delay functions. In [1] it has been shown that the convergence cane of such dynamics to Nash equilibrium may be exponential in the number of players n even for unweighted players and linear delay functions. Nevertheless, extending the work of [11] we show that Theta(n log log W) (where W is the sum of all the players' weights) best responses are necessary and sufficient to achieve states that approximate the optimal solution by a constant factor, under the assumption that every O(n) steps each player performs a constant (and non-mill) number of best responses.