Equilibrium Results for Dynamic Congestion Games

Meunier, Frédéric; Wagner, Nicolas

doi:10.1287/trsc.1100.0329

Cited by 27 publications

(23 citation statements)

References 28 publications

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“…A general existence result for dynamic network equilibrium beyond strict FIFO was recently presented by Meunier and Wagner [15]. Their model considers both route choice and departure time choice, and is based on a weak form of strict FIFO: the travel time T e (·) strictly increases on any interval on which there is some inflow into the link.…”

Section: Discussionmentioning

confidence: 99%

“…This network loading process typically requires additional conditions to be well defined, such as an acyclic network structure or when link travel times are bounded away from zero which is a natural and mild assumption (see e.g. [15,21,22]). Since we will not require network loading until §5, we defer its discussion to that section.…”

Section: Example Consider the Simple Network Inmentioning

confidence: 99%

“…Under suitable assumptions, an existence result was eventually obtained by Zhu and Marcotte [22]. Also, Meunier and Wagner [15] establish the existence of dynamic equilibria using an alternative specification of the model and exploiting general results for games with a continuum of players. Recently Koch and Skutella [10] studied a more specific model, which can be traced back to Vickrey [20], in which there is an inflow stream at a single source that travels across the network towards a sink through edges that are characterized by a travel time or latency and a pertime-unit capacity.…”

Section: Introductionmentioning

confidence: 99%

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Dynamic Equilibria in Fluid Queueing Networks

Cominetti

Correa

Larré

2015

Operations Research

127

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Artículo de publicación ISIFlows over time provide a natural and convenient description for the dynamics of a continuous stream of particles traveling from a source to a sink in a network, allowing to track the progress of each infinitesimal particle along time. A basic model for the propagation of flow is the so-called fluid queue model in which the time to traverse an edge is composed of a flow-dependent waiting time in a queue at the entrance of the edge plus a constant travel time after leaving the queue. In a dynamic network routing game each infinitesimal particle is interpreted as a player that seeks to complete its journey in the least possible time. Players are forward looking and anticipate the congestion and queuing delays induced by others upon arrival to any edge in the network. Equilibrium occurs when each particle travels along a shortest path. This paper is concerned with the study of equilibria in the fluid queue model and provides a constructive proof of existence and uniqueness of equilibria in single origin-destination networks with piecewise constant inflow rate. This is done through a detailed analysis of the underlying static flows obtained as derivatives of a dynamic equilibrium. Furthermore, for multicommodity networks, we give a general nonconstructive proof of existence of equilibria when the inflow rates belong to Lp.Nucleo Milenio Informacion y Coordinacion en Rede

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Section: Discussionmentioning

confidence: 99%

Section: Example Consider the Simple Network Inmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Dynamic Equilibria in Fluid Queueing Networks

Cominetti

Correa

Larré

2015

Operations Research

127

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“…Variational inequality formulations [11] turn out to be the most successful in investigating Nash equilibria of the simultaneous departure-time route-choice models, where each player has to make a decision on his departure time as well. Unfortunately, little is known about the existence, uniqueness and characterizations of equilibria under the general formulation [22].…”

Section: Related Literaturementioning

confidence: 99%

A Network Game of Dynamic Traffic

Cao

Chen

et al. 2017

Proceedings of the 2017 ACM Conference on Economics and Computation

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We study a network congestion game of discrete-time dynamic traffic of atomic agents with a single origin-destination pair. Any agent freely makes a dynamic decision at each vertex (e.g., road crossing) and traffic is regulated with given priorities on edges (e.g., road segments). We first constructively prove that there always exists a subgame perfect equilibrium (SPE) in this game. We then study the relationship between this model and a simplified model, in which agents select and fix an origin-destination path simultaneously. We show that the set of Nash equilibrium (NE) flows of the simplified model is a proper subset of the set of SPE flows of our main model. We prove that each NE is also a strong NE and hence weakly Pareto optimal. We establish several other nice properties of NE flows, including global First-In-First-Out. Then for two classes of networks, including series-parallel ones, we show that the queue lengths at equilibrium are bounded at any given instance, which means the price of anarchy of any given game instance is bounded, provided that the inflow size never exceeds the network capacity.

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“…Although dynamic equilibria have been around for almost fifty years (see, e.g., [2][3][4]6,7,[9][10][11][12]), their existence has only been proved recently by Zhu and Marcotte [13] though in a somewhat different setting, and by Meunier and Wagner [8] who gave the first existence result for a model that covers the case of fluid queuing networks. These proofs, however, rely heavily on functional analysis techniques and provide little intuition on the combinatorial structure of dynamic equilibria, their characterization, or feasible approaches to compute them.…”

Section: Introductionmentioning

confidence: 99%

Long Term Behavior of Dynamic Equilibria in Fluid Queuing Networks

Cominetti

Correa

Olver

2017

Integer Programming and Combinatorial Optimization

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Abstract.A fluid queuing network constitutes one of the simplest models in which to study flow dynamics over a network. In this model we have a single source-sink pair and each link has a per-time-unit capacity and a transit time. A dynamic equilibrium (or equilibrium flow over time) is a flow pattern over time such that no flow particle has incentives to unilaterally change its path. Although the model has been around for almost fifty years, only recently results regarding existence and characterization of equilibria have been obtained. In particular the long term behavior remains poorly understood. Our main result in this paper is to show that, under a natural (and obviously necessary) condition on the queuing capacity, a dynamic equilibrium reaches a steady state (after which queue lengths remain constant) in finite time. Previously, it was not even known that queue lengths would remain bounded. The proof is based on the analysis of a rather non-obvious potential function that turns out to be monotone along the evolution of the equilibrium. Furthermore, we show that the steady state is characterized as an optimal solution of a certain linear program. When this program has a unique solution, which occurs generically, the long term behavior is completely predictable. On the contrary, if the linear program has multiple solutions the steady state is more difficult to identify as it depends on the whole temporal evolution of the equilibrium.

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Equilibrium Results for Dynamic Congestion Games

Cited by 27 publications

References 28 publications

Dynamic Equilibria in Fluid Queueing Networks

Dynamic Equilibria in Fluid Queueing Networks

A Network Game of Dynamic Traffic

Long Term Behavior of Dynamic Equilibria in Fluid Queuing Networks

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