Matroids Are Immune to Braess' Paradox

Satoru Fujishige, Michel X. Goemans, Tobias Harks, Britta Peis, Rico Zenklusen
2017 Mathematics of Operations Research  
The famous Braess paradox describes the counter-intuitive phenomenon in which, in certain settings, the increase of resources, like building a new road 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
more » ... ve this characterization by two novel sensitivity results for convex separable optimization problems over polymatroid base polyhedra which may be of independent interest.
doi:10.1287/moor.2016.0825 fatcat:qqmsftbd5revtjmtdvmut2u274