Competitive routing in multiuser communication networks
IEEE/ACM Transactions on Networking (TON)
Journal of the ACM (JACM)
Routing into two parallel links: game-theoretic distributed algorithms
Journal of Parallel and Distributed Computing
Avoiding paradoxes in multi-agent competitive routing
Computer Networks: The International Journal of Computer and Telecommunications Networking
A New Look at the Multiclass Network Equilibrium Problem
Transportation Science
Topological Conditions for Uniqueness of Equilibrium in Networks
Mathematics of Operations Research
Selfish Routing and the Price of Anarchy
Selfish Routing and the Price of Anarchy
A survey on networking games in telecommunications
Computers and Operations Research
Architecting noncooperative networks
IEEE Journal on Selected Areas in Communications
Mixed Nash equilibria in selfish routing problems with dynamic constraints
Theoretical Computer Science
Equilibria of atomic flow games are not unique
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
A survey of uniqueness results for selfish routing
NET-COOP'07 Proceedings of the 1st EuroFGI international conference on Network control and optimization
The equilibrium existence problem in finite network congestion games
WINE'06 Proceedings of the Second international conference on Internet and Network Economics
WINE'05 Proceedings of the First international conference on Internet and Network Economics
On the Existence of Pure Nash Equilibria in Weighted Congestion Games
Mathematics of Operations Research
Coalitions in Nonatomic Network Congestion Games
Mathematics of Operations Research
Hi-index | 0.00 |
We consider the problem of selfish routing in a congested network shared by several users, where each user wishes to minimize the cost of its own flow. Users are atomic, in the sense that each has a nonnegligible amount of flow demand, and flows may be split over different routes. The total cost for each user is the sum of its link costs, which, in turn, may depend on the user's own flow as well as the total flow on that link. Our main interest here is network topologies that ensure uniqueness of the Nash equilibrium for any set of users and link cost functions that satisfy some mild convexity conditions. We characterize the class of two-terminal network topologies for which this uniqueness property holds, and show that it coincides with the class of nearly parallel networks that was recently shown by Milchtaich [Milchtaich, I. 2005. Topological conditions for uniqueness of equilibrium in networks. Math. Oper. Res.30 225--244] to ensure uniqueness in nonatomic (or Wardrop) routing games. We further show that uniqueness of the link flows holds under somewhat weaker convexity conditions, which apply to the mixed Nash-Wardrop equilibrium problem. We finally propose a generalized continuum-game formulation of the routing problem that allows for a unified treatment of atomic and nonatomic users.