Topological Uniqueness of the Nash Equilibrium for Selfish Routing with Atomic Users
Mathematics of Operations Research
Strong equilibrium in cost sharing connection games
Proceedings of the 8th ACM conference on Electronic commerce
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
Equilibrium Results for Dynamic Congestion Games
Transportation Science
The equilibrium existence problem in finite network congestion games
WINE'06 Proceedings of the Second 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
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Equilibrium flow in a physical network with a large number of users (e.g., transportation, communication, and computer networks) need not be unique if the costs of the network elements are not the same for all users. Such differences among users may arise if they are not equally affected by congestion or have different intrinsic preferences. Whether or not, forall assignments of strictly increasing cost functions, each user's equilibrium cost is the same in all Nash equilibria can be determined from the network topology. Specifically, this paper shows that in a two-terminal network, the equilibrium costs are always unique if and only if the network is one of several simple networks or consists of several such networks connected in series. The complementary class of all two-terminal networks with multiple equilibrium costs forsome assignment of (user-specific) strictly increasing cost functions is similarly characterized by an embedded network of a particular simple type.