Matroids are Immune to Braess Paradox

TL;DR

This paper characterizes the conditions under which the Braess paradox does not occur in nonatomic congestion games, revealing that matroid bases are the maximal structure immune to this paradox.

Contribution

It provides a novel characterization showing that matroid bases are exactly the maximal strategy spaces avoiding the Braess paradox in congestion games.

Findings

Matroid bases are the maximal strategy spaces immune to Braess paradox.

Two new sensitivity results for convex optimization over polymatroid base polyhedra.

Theoretical framework linking matroid theory with congestion game stability.

Abstract

The famous Braess paradox describes the following phenomenon: It might happen that the improvement of resources, like building a new street 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 maximal combinatorial property of strategy spaces for which Braess paradox does not occur. In a nutshell, bases of matroids are exactly this maximal structure. We prove our characterization by two novel sensitivity results for convex separable optimization problems over polymatroid base polyhedra which may be of independent interest.