Matroids Are Immune to Braess' Paradox

The famous Braess paradox describes the counterintuitive phenomenon in which, in certain settings, an increase of resources, such as a new road built within a congested network, may in fact lead to larger costs for the players in an equilibrium. In this paper, we consider general nonatomic congestion games and give a characterization of the combinatorial property of strategy spaces for which the Braess paradox does not occur. In short, matroid bases are precisely the required structure. We prove this characterization by two novel sensitivity results for convex separable optimization problems over polymatroid base polyhedra, which may be of independent interest.