Crowding games are sequentially solvable
International Journal of Game Theory
Algorithms, games, and the internet
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Journal of the ACM (JACM)
The price of anarchy is independent of the network topology
Journal of Computer and System Sciences - STOC 2002
The complexity of pure Nash equilibria
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Uniqueness of User Equilibrium in Transportation Networks with Heterogeneous Commuters
Transportation Science
Topological Conditions for Uniqueness of Equilibrium in Networks
Mathematics of Operations Research
The Price of Routing Unsplittable Flow
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
The price of anarchy of finite congestion games
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Selfish routing with atomic players
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Topological Uniqueness of the Nash Equilibrium for Selfish Routing with Atomic Users
Mathematics of Operations Research
Convergence time to Nash equilibria
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
Symmetry in network congestion games: pure equilibria and anarchy cost
WAOA'05 Proceedings of the Third international conference on Approximation and Online Algorithms
Congestion Games with Linearly Independent Paths: Convergence Time and Price of Anarchy
SAGT '08 Proceedings of the 1st International Symposium on Algorithmic Game Theory
Pure Nash equilibria in player-specific and weighted congestion games
Theoretical Computer Science
On the complexity of pure Nash equilibria in player-specific network congestion games
WINE'07 Proceedings of the 3rd international conference on Internet and network economics
Local search: simple, successful, but sometimes sluggish
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
On the existence of pure nash equilibria inweighted congestion games
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Congestion games with variable demands
Proceedings of the 13th Conference on Theoretical Aspects of Rationality and Knowledge
Demand allocation games: integrating discrete and continuous strategy spaces
WINE'11 Proceedings of the 7th international conference on Internet and Network Economics
On the Existence of Pure Nash Equilibria in Weighted Congestion Games
Mathematics of Operations Research
Capacitated network design games
SAGT'12 Proceedings of the 5th international conference on Algorithmic Game Theory
Optimal Cost Sharing for Resource Selection Games
Mathematics of Operations Research
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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 wi. 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.