The Equilibrium Existence Problem in Finite Network Congestion Games
An open problem is presented regarding the existence of pure strategy Nash equilibrium (PNE) in network congestion games with a finite number of non-identical players, in which the strategy set of each player is the collection of all paths in a given network that link the player’s origin and destination vertices, and congestion increases the costs of edges. A network congestion game in which the players differ only in their origin–destination pairs is a potential game, which implies that, regardless of the exact functional form of the cost functions, it has a PNE. A PNE does not necessarily exist if (i) the dependence of the cost of each edge on the number of users is player- as well as edge-specific or (ii) the (possibly, edge-specific) cost is the same for all players but it is a function (not of the number but) of the total weight of the players using the edge, with each player i having a different weight w i . In a parallel two-terminal network, in which the origin and the destination are the only vertices different edges have in common, a PNE always exists even if the players differ in either their cost functions or weights, but not in both. However, for general two-terminal networks this is not so. The problem is to characterize the class of all two-terminal network topologies for which the existence of a PNE is guaranteed even with player-specific costs, and the corresponding class for player-specific weights. Some progress in solving this problem is reported.
KeywordsCongestion games network topology heterogeneous users existence of equilibrium
Unable to display preview. Download preview PDF.
- 1.Anantharam, V.: On the Nash Dynamics of Congestion Games With Player-Specific Utility. In: Proceedings of the 43rd IEEE Conference on Decision and Control, pp. 4673–4678 (2004)Google Scholar
- 2.Awerbuch, B., Azar, Y., Epstein, A.: The Price of Routing Unsplittable Flow. In: Proceedings of the 37th Annual ACM Symposium on Theory of Computing, pp. 57–66 (2005)Google Scholar
- 3.Beckmann, M., McGuire, C.B., Winsten, C.B.: Studies in the Economics of Transportation. Yale University Press, New Haven (1956)Google Scholar
- 4.Christodoulou, G., Koutsoupias, E.: The Price of Anarchy of Finite Congestion Games. In: Proceedings of the 37th Annual ACM Symposium on Theory of Computing, pp. 67–73 (2005)Google Scholar
- 7.Fabrikant, A., Papadimitriou, C., Talwar, K.: The Complexity of Pure Nash Equilibria. In: Proceedings of the 36th Annual ACM Symposium on Theory of Computing, pp. 604–612 (2004)Google Scholar
- 22.Papadimitriou, C.H.: Algorithms, Games, and the Internet. In: Proceedings of the 33rd Annual ACM Symposium on Theory of Computing, pp. 749–753 (2001)Google Scholar
- 23.Richman, O., Shimkin, N.: Topological Uniqueness of the Nash Equilibrium for Atomic Selfish Routing. Math. Oper. Res. (forthcoming)Google Scholar
- 26.Roughgarden, T.: Selfish Routing With Atomic Players. In: Proceedings of the 6th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 1184–1185 (2005)Google Scholar
- 30.Wardrop, J.G.: Some Theoretical Aspects of Road Traffic Research. In: Proceedings of the Institute of Civil Engineers, Part II, vol. 1, pp. 325–378 (1952)Google Scholar