Book contents
- Frontmatter
- Contents
- Preface
- 1 Overview
- Part I Graph Theory and Social Networks
- Part II Game Theory
- 6 Games
- 7 Evolutionary Game Theory
- 8 Modeling Network Traffic Using Game Theory
- 9 Auctions
- Part III Markets and Strategic Interaction in Networks
- Part IV Information Networks and the World Wide Web
- Part V Network Dynamics: Population Models
- Part VI Network Dynamics: Structural Models
- Part VII Institutions and Aggregate Behavior
- Bibliography
- Index
8 - Modeling Network Traffic Using Game Theory
from Part II - Game Theory
Published online by Cambridge University Press: 05 June 2012
- Frontmatter
- Contents
- Preface
- 1 Overview
- Part I Graph Theory and Social Networks
- Part II Game Theory
- 6 Games
- 7 Evolutionary Game Theory
- 8 Modeling Network Traffic Using Game Theory
- 9 Auctions
- Part III Markets and Strategic Interaction in Networks
- Part IV Information Networks and the World Wide Web
- Part V Network Dynamics: Population Models
- Part VI Network Dynamics: Structural Models
- Part VII Institutions and Aggregate Behavior
- Bibliography
- Index
Summary
Among the initial examples in our discussion of game theory in Chapter 6, we noted that traveling through a transportation network, or sending packets through the Internet, involves fundamentally game-theoretic reasoning: rather than simply choosing a route in isolation, individuals must evaluate routes in the presence of the congestion resulting from the decisions made by themselves and everyone else. In this chapter, we develop models for network traffic using the game-theoretic ideas developed thus far. In the process, we will discover a rather unexpected result – known as Braess's Paradox [76] – which shows that adding capacity to a network can sometimes actually slow down the traffic.
Traffic at Equilibrium
Let's begin by developing a model of a transportation network and how it responds to traffic congestion; with this model in place, we can then introduce the game-theoretic aspects of the problem.
We represent a transportation network by a directed graph: we consider the edges to be highways, and the nodes to be exits where you can get on or off a particular highway. There are two particular nodes, which we call A and B, and we assume everyone wants to drive from A to B. For example, we can imagine that A is an exit in the suburbs, B is an exit downtown, and we're looking at a large collection of morning commuters. Finally, each edge has a designated travel time that depends on the amount of traffic it contains.
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- Networks, Crowds, and MarketsReasoning about a Highly Connected World, pp. 207 - 224Publisher: Cambridge University PressPrint publication year: 2010
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