Non-atomic one-round walks in congestion games

In this paper we study the approximation ratio of the solutions achieved after an epsilon-approximate one-round walk in non-atomic congestion games. Prior to this work, the solution concept of one-round walks had been studied for atomic congestion games with linear latency functions only (Christodoulou et al. [1], Bilo et al. [2]). We give an explicit formula to determine the approximation ratio for non-atomic congestion games having general latency functions. In particular, we focus on polynomial latency functions, and, we prove that the approximation ratio is exactly ((1 + epsilon)(p + 1))(p+1) for every polynomial of degree p. Then, we show that, by resorting to static (resp. dynamic) resource taxation, the approximation ratio can be lowered to (1 + epsilon)(p+1)(p + 1)(p) (resp. (1 + epsilon)(p+1) (p + 1)!). (C) 2018 Elsevier B.V. All rights reserved.