Computing solutions of the multiclass network equilibrium problem with affine cost functions

  title={Computing solutions of the multiclass network equilibrium problem with affine cost functions},
  author={Fr{\'e}d{\'e}ric Meunier and Thomas Pradeau},
  journal={Annals of Operations Research},
We consider a non-atomic congestion game on a graph, with several classes of players. Each player wants to go from his origin vertex to his destination vertex at the minimum cost and all players of a given class share the same characteristics: cost functions on each arc, and origin–destination pair. Under some mild conditions, it is known that a Nash equilibrium exists, but the computation of such an equilibrium in the multiclass case is an open problem for general functions. We consider the… 

Complexity and Parametric Computation of Equilibria in Atomic Splittable Congestion Games via Weighted Block Laplacians

A homotopy method is developed that traces an equilibrium for varying flow demands of the players that is contained in PPAD and an algorithm is obtained that computes a continuum of equilibria parametrized by the players' flow demand.

Estimating heterogeneous agent preferences by inverse optimization in a randomized nonatomic game

We consider an externality game in which nonatomic agents choose from a finite set of alternatives and disutility is determined only by the number of agents choosing each alternative. The equilibrium



A Lemke-Like Algorithm for the Multiclass Network Equilibrium Problem

This work considers a nonatomic congestion game on a connected graph, with several classes of players, and proposes an extension of Lemke's algorithm able to solve this problem and provides a constructive proof of the existence of an equilibrium in this case.

Computing Economic Equilibria on Affine Networks with Lemke's Algorithm

Lemke's algorithm is used to compute an equilibrium if there is a balance in the shipments, supplies, and demands of goods at each location, if local prices do not exceed the cost of importing, and if shipments are price efficient.

On the solution of affine generalized Nash equilibrium problems with shared constraints by Lemke’s method

This paper treats a large subclass of AGNEPs wherein the coupled constraints are shared by, i.e., common to, the players, and presents and analyzes a modification to Lemke’s method that allows us to compute GNE that are not necessarily VE.

Settling the complexity of computing two-player Nash equilibria

We prove that Bimatrix, the problem of finding a Nash equilibrium in a two-player game, is complete for the complexity class PPAD (Polynomial Parity Argument, Directed version) introduced by

The Traffic Assignment Problem for Multiclass-User Transportation Networks

It is shown that this model is also capable of handling the case of several classes of users in the same transportation network each of which has an individual cost function and, at the same time, contributes to its own and other classes' cost functions in an individual way.

A New Look at the Multiclass Network Equilibrium Problem

This work shows that in spite of the nonmonotonicity of the cost operator, the multiclass network equilibrium problem may actually satisfy a weaker property, induced by the hierarchical nature of the travel cost interactions, that allows a natural decomposition approach that admits provably convergent algorithms.

Traffic Equilibrium and Variational Inequalities

This work uses the techniques of the theory of variational inequalities to establish existence of a traffic equilibrium pattern, to design an algorithm for the construction of this pattern and to derive estimates on the speed of convergence of the algorithm.

Generic Uniqueness of Equilibrium in Large Crowding Games

A crowding game is a noncooperative game in which the payoff of each player depends only on the player's action and the size of the set of players choosing that particular action: The larger the set,

A Pivotal Method for Affine Variational Inequalities

Two classes of matrices are identified which are analogues of the class of copositive-plus and L-matrices in the study of the linear complementarity problem and it is proved that the algorithm processes ACx = a when A is the linear transformation associated with such matrices.

The complexity of pure Nash equilibria

This work focuses on congestion games, and shows that a pure Nash equilibrium can be computed in polynomial time in the symmetric network case, while the problem is PLS-complete in general.