Summary: Equilibria in Dynamic Selfish Routing
In both transportation and communication networks we are faced with "selfish flows", where
every agent sending flow over the network desires to get it to its destination as soon as possible. Such
flows have been well studied in time-invariant networks in the last few years. A key observation that
must be taken into account in defining and studying selfish flow, however, is that a flow can take a
non-negligible amount of time to travel across the network from the source to destination, and that
network states like traffic load and congestion can vary during this period. Such flows are called
dynamic flows (a.k.a. flows over time). This variation in network state as the flow progresses through
the network results in the fundamentally different and significantly more complex nature of dynamic
flow equilibria, as compared to those defined in static network settings.
In this paper, we study equilibria in dynamic flows, and prove various bounds about their quality,
as well as give algorithms on how to compute them. In general, we show that unlike in static flows,
Nash equilibria may not exist, and the price of anarchy can be extremely high. If the system obeys
FIFO (first-in first-out), however, we show the existence and how to compute an equilibrium for all
single-source single-sink networks. In addition, we prove a set of much stronger results about price
of anarchy and stability in the case where the delay on an edge is flow-independent.