Analysis of price of anarchy in heterogeneous price-sensitive populations

In this paper, we investigate the effect of scaled marginal-cost road pricing on the price of anarchy (POA) for noncooperative congestion games in which players are divided into several groups according to their price sensitivities. The POA is defined as the worst possible ratio between the total latency of Nash flows and that of the socially optimal flow. First, the existence and uniqueness of Nash flow is considered. For a probability distribution of price sensitivities satisfying given conditions, a road pricing scheme is designed such that POA = 1. If those given conditions are not satisfied, then it holds that POA > 1. Finally, we apply the results to a traffic routing problem via simulations. The numerical results show that the scaled marginal-cost road pricing reduces the total latency of the network, and the optimal POA depends on the probability distribution of price sensitivities.