Computing optimal taxes in atomic congestion games

When the performance of a system is dictated by the behaviour of its users, self-interested choices can result in sub-optimal system operation, as is the case in road traffic networks. The inefficiency resulting from such selfish behaviour is commonly measured by the ratio between the emergent worst-case system cost and the minimum system cost, termed price-of-anarchy. As the degree of inefficiency can be significant even for relatively simple systems (e.g., affine congestion games), researchers have proposed a variety of approaches to align the emergent selfish behaviour with the desired system objective. A well-studied and promising method is that of altering users' perceived costs by means of taxes.