A survey of dynamic network flows
Annals of Operations Research
A new class of instantaneous dynamic user-optimal traffic assignment models
Operations Research
Advances in the Continuous Dynamic Network Loading Problem
Transportation Science
An Efficient Algorithm for Dynamic Traffic Equilibrium Assignment with Queues
Transportation Science
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Detecting Dynamic Traffic Assignment Capacity Paradoxes in Saturated Networks
Transportation Science
Selfish Routing and the Price of Anarchy
Selfish Routing and the Price of Anarchy
Algorithmic Game Theory
Convergence to Equilibrium in Dynamic Traffic Networks when Route Cost Is Decay Monotone
Transportation Science
Equilibria in Dynamic Selfish Routing
SAGT '09 Proceedings of the 2nd International Symposium on Algorithmic Game Theory
Efficient continuous-time dynamic network flow algorithms
Operations Research Letters
WINE '09 Proceedings of the 5th International Workshop on Internet and Network Economics
Braess's paradox for flows over time
SAGT'10 Proceedings of the Third international conference on Algorithmic game theory
A competitive strategy for routing flow over time
ACM SIGecom Exchanges
A Stackelberg strategy for routing flow over time
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Contention issues in congestion games
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part II
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We study Nash equilibria in the context of flows over time. Many results on static routing games have been obtained over the last ten years. In flows over time (also called dynamic flows), flow travels through a network over time and, as a consequence, flow values on edges are time-dependent. This more realistic setting has not been tackled from the viewpoint of algorithmic game theory yet; but there is a rich literature on game theoretic aspects of flows over time in the traffic community. We present a novel characterization of Nash equilibria for flows over time. It turns out that Nash flows over time can be seen as a concatenation of special static flows. The underlying flow over time model is the so-called deterministic queuing model that is very popular in road traffic simulation and related fields. Based upon this, we prove the first known results on the price of anarchy for flows over time.