Competitive routing over time

Hoefer, Martin; Mirrokni, Vahab; Röglin, Heiko; Teng, Shang‐Hua

doi:10.1016/j.tcs.2011.05.055

Cited by 46 publications

(56 citation statements)

References 48 publications

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“…Hoefer et. al [22] also consider a discrete routing game. They study existence and complexity properties of pure Nash equilibria and best-response strategies.…”

Section: Introductionmentioning

confidence: 99%

Nash Equilibria and the Price of Anarchy for Flows over Time

Koch

Skutella

2009

Algorithmic Game Theory

142

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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. Keywords Flow over time • Nash equilibrium • Routing game • Deterministic queuing model Supported by DFG Research Center Matheon "Mathematics for key technologies" in Berlin. An extended abstract of this work has been presented at the 2nd International Symposium on Algorithmic Game Theory, see [25].

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“…Hoefer et. al [22] also consider a discrete routing game. They study existence and complexity properties of pure Nash equilibria and best-response strategies.…”

Section: Introductionmentioning

confidence: 99%

Nash Equilibria and the Price of Anarchy for Flows over Time

Koch

Skutella

2009

Algorithmic Game Theory

142

View full text Add to dashboard Cite

show abstract

“…Each job has a weight and the time needed to traverse an edge is given by the product of speed and weight. In contrast to our model, traversal times in [11] might be rational, but zero travel times are not allowed. Furthermore, the type of capacity constraints is different: While [11] capacitates the total weight of players using an edge at the same point in time, our model capacitates the number of players that may enter an edge simultaneously.…”

Section: Competitive Routing Over Timementioning

confidence: 89%

“…In contrast to our model, traversal times in [11] might be rational, but zero travel times are not allowed. Furthermore, the type of capacity constraints is different: While [11] capacitates the total weight of players using an edge at the same point in time, our model capacitates the number of players that may enter an edge simultaneously. Hoefer et al analyzed four different scheduling policies: FIFO, non-preemptive global ranking, preemptive global ranking and fair Time-Sharing.…”

Section: Competitive Routing Over Timementioning

confidence: 89%

“…Moreover, it is NP-hard to compute a best response in symmetric games with local priority lists. These results are obtained by adapting the reduction described in Hoefer et al [11] used to prove hardness in a more general setting. For global priority lists, we get an efficient Dijkstra-type algorithm for computing a best response and thus a pure Nash equilibrium.…”

Section: Computational Complexitymentioning

confidence: 99%

“…Hoefer et al [11] considered weighted network congestion games in the continuous-time setting. In their model, the edges represent machines with predefined speed.…”

Section: Competitive Routing Over Timementioning

confidence: 99%

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Competitive Packet Routing with Priority Lists

Harks

Peis

Schmand

et al. 2018

ACM Trans. Econ. Comput.

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In competitive packet routing games, packets are routed selfishly through a network and scheduling policies at edges determine which packages are forwarded first if there is not enough capacity on an edge to forward all packages at once. We analyze the impact of priority lists on the worst-case quality of pure Nash equilibria. A priority list is an ordered list of players that may or may not depend on the edge. Whenever the number of packets entering an edge exceeds the inflow capacity, packets are processed in list order. We derive several new bounds on the price of anarchy and stability for global and local priority policies. We also consider the question of the complexity of computing an optimal priority list. It turns out that even for very restricted cases, i.e., for routing on a tree, the computation of an optimal priority list is APX-hard.

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Equilibria in Routing Games with Edge Priorities

Schleicher

Strehler

Koch

2018

Web and Internet Economics

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In this paper we present a new competitive packet routing model with edge priorities. We consider players that route selfishly through a network over time and try to reach their destinations as fast as possible. If the number of players who want to enter an edge at the same time exceeds the inflow capacity of this edge, edge priorities with respect to the preceding edge solve these conflicts. Our edge priorities are well-motivated by applications in traffic. For this class of games, we show the existence of equilibrium solutions for single-source-single-sink games and we analyze structural properties of these solutions. We present an algorithm that computes Nash equilibria and we prove bounds both on the Price of Stability and on the Price of Anarchy. Moreover, we introduce the new concept of a Price of Mistrust. Finally, we also study the relations to earliest arrival flows. MotivationRouting games over time are widely studied [8,15,16] due to various applications, e.g., road and air traffic control, logistic in production systems, communication networks like the internet, and financial flows. Depending on applications, there is a huge range of models. There are games with non-atomic [16] as well as atomic players [15], further there are games with continuous time [15] as well as games with discrete time steps [14].Usually, players are allowed to enter an edge directly at their arrival time. An essential ingredient of these models is the priority rule for tie-breaking. If two or more players arrive at a node at the same time, one needs to decide which player may enter the subsequent link first. Some models maintain the overall arrival order with a first-in firstout rule [8,15,16], i.e., only players with the exact same arrival time are re-arranged. Other models allow overtaking by higher prioritized players with global priority lists [14,15] or local priority lists [14] of players, that is, priority is a player inherent property and players are linearly ordered.

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Competitive routing over time

Cited by 46 publications

References 48 publications

Nash Equilibria and the Price of Anarchy for Flows over Time

Nash Equilibria and the Price of Anarchy for Flows over Time

Competitive Packet Routing with Priority Lists

Equilibria in Routing Games with Edge Priorities

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