Competitive routing in multiuser communication networks
IEEE/ACM Transactions on Networking (TON)
Combinatorial algorithms on a class of graphs
Discrete Applied Mathematics - Special issue: efficient algorithms and partial k-trees
Journal of the ACM (JACM)
Stackelberg Scheduling Strategies
SIAM Journal on Computing
Topological Conditions for Uniqueness of Equilibrium in Networks
Mathematics of Operations Research
Selfish routing with atomic players
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Selfish Routing and the Price of Anarchy
Selfish Routing and the Price of Anarchy
The effect of collusion in congestion games
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Topological Uniqueness of the Nash Equilibrium for Selfish Routing with Atomic Users
Mathematics of Operations Research
The effectiveness of Stackelberg strategies and tolls for network congestion games
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Two-terminal routing games with unknown active players
Artificial Intelligence
The Impact of Oligopolistic Competition in Networks
Operations Research
The Worst-Case Efficiency of Cost Sharing Methods in Resource Allocation Games
Operations Research
Local smoothness and the price of anarchy in atomic splittable congestion games
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
The price of collusion in series-parallel networks
IPCO'10 Proceedings of the 14th international conference on Integer Programming and Combinatorial Optimization
The effectiveness of stackelberg strategies and tolls for network congestion games
ACM Transactions on Algorithms (TALG)
On the Existence of Pure Nash Equilibria in Weighted Congestion Games
Mathematics of Operations Research
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In routing games with infinitesimal players, it follows from well-known convexity arguments that equilibria exist and are unique (up to induced delays, and under weak assumptions on delay functions). In routing games with players that control large amounts of flow, uniqueness has been demonstrated only in limited cases: in 2-terminal, nearly-parallel graphs; when all players control exactly the same amount of flow; when latency functions are polynomials of degree at most three. In this work, we answer an open question posed by Cominetti, Correa, and Stier-Moses (ICALP 2006) and show that there may be multiple equilibria in atomic player routing games. We demonstrate this multiplicity via two specific examples. In addition, we show our examples are topologically minimal by giving a complete characterization of the class of network topologies for which unique equilibria exist. Our proofs and examples are based on a novel characterization of these topologies in terms of sets of circulations.