Nash Equilibria and the Price of Anarchy for Flows over Time

We study Nash equilibria and the price of anarchy 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 change over time. This more realistic setting has not been tackled from the viewpoint of algorithmic game theory yet; on the other hand, there is a rich literature on game theoretic aspects of flows over time in the traffic community. In this paper, we present the first known results on the price of anarchy for flows over time. We also present algorithms for computing Nash flows over time. Those algorithms have to iteratively solve certain interesting and new static flow problems. Our results are based on a novel characterization of Nash equilibria for flows over time. The underlying flow over time model is a variant of the so-called deterministic queuing model that is very popul...

• Type: Conference
• Year: 2009
• Where: SAGT
• Authors: Ronald Koch, Martin Skutella
• Keywords: Game Theory, Nash Equilibria, SAGT 2009, Static Routing Games, Time Model