Computing solutions of the multiclass network equilibrium problem with affine cost functions
Abstract
We consider a nonatomic congestion game on a graph, with several classes of players. Each player wants to go from its origin vertex to its destination vertex at the minimum cost and all players of a given class share the same characteristics: cost functions on each arc, and origindestination pair. Under some mild conditions, it is known that a Nash equilibrium exists, but the computation of an equilibrium in the multiclass case is an open problem for general functions. We consider the specific case where the cost functions are affine. We show that this problem is polynomially solvable when the number of vertices and the number of classes are fixed. In particular, it shows that the parallellink case with a fixed number of classes is polynomially solvable. On a more practical side, we propose an extension of Lemke's algorithm able to solve this problem.
 Publication:

arXiv eprints
 Pub Date:
 December 2014
 arXiv:
 arXiv:1412.6496
 Bibcode:
 2014arXiv1412.6496M
 Keywords:

 Computer Science  Computer Science and Game Theory;
 Mathematics  Optimization and Control