Selfish Routing and the Price of Anarchy

by Tim Roughgarden

Overview

An analysis of the loss in performance caused by selfish, uncoordinated behavior in networks.

Most of us prefer to commute by the shortest route available, without taking into account the traffic congestion that we cause for others. Many networks, including computer networks, suffer from some type of this "selfish routing." In Selfish Routing and the Price of Anarchy, Tim Roughgarden studies the loss of social welfare caused by selfish, uncoordinated behavior in networks. He quantifies the price of anarchy—the worst-possible loss of social welfare from selfish routing—and also discusses several methods for improving the price of anarchy with centralized control.

Roughgarden begins with a relatively nontechnical introduction to selfish routing, describing two important examples that motivate the problems that follow. The first, Pigou's Example, demonstrates that selfish behavior need not generate a socially optimal outcome. The second, the counterintiuitve Braess's Paradox, shows that network improvements can degrade network performance. He then develops techniques for quantifying the price of anarchy (with Pigou's Example playing a central role). Next, he analyzes Braess's Paradox and the computational complexity of detecting it algorithmically, and he describes Stackelberg routing, which improves the price of anarchy using a modest degree of central control. Finally, he defines several open problems that may inspire further research. Roughgarden's work will be of interest not only to researchers and graduate students in theoretical computer science and optimization but also to other computer scientists, as well as to economists, electrical engineers, and mathematicians.

Product Details

ISBN-13:	9780262182430
Publisher:	MIT Press
Publication date:	05/06/2005
Series:	The MIT Press
Edition description:	New Edition
Pages:	240
Product dimensions:	7.31(w) x 9.25(h) x 0.74(d)
Age Range:	18 Years

About the Author

Tim Roughgarden is Assistant Professor of Computer Science at Stanford University and recipient of the ACM's Grace Hopper Award.

Table of Contents

Preface vii
I INTRODUCTION AND PRELIMINARIES 1 Introduction 3
1.1 Selfish Routing 3
1.2 Two Motivating Examples 3
1.3 Applications and Caveats 6
1.4 How to Read this Book 11
1.5 Notes 12
2 Preliminaries 17
2.1 The Model 17
2.2 Flows at Nash Equilibrium 20
2.3 The Price of Anarchy 21
2.4 A Characterization of Optimal Flows 22
2.5 Examples 28
2.6 Existence and Uniqueness of Nash Flows 34
2.7 Nash Flows in Single-Commodity Networks 37
2.8 Notes 41
II BOUNDING THE PRICE OF ANARCHY
3 How Bad Is Selfish Routing? 51
3.1 Overview 51
3.2 The Price of Anarchy with Linear Cost Functions 53
3.3 A General Upper Bound on the Price of Anarchy 58
3.4 Matching Lower Bounds in Simple Networks 62
3.5 Computing the Price of Anarchy 69
3.6 A Bicriteria Bound in General Networks 73
3.7 Notes 77
4 Extensions 85
4.1 Nonatomic Congestion Games 85
4.2 Approximate Nash Flows 88
4.3 Edge Capacities 92
4.4 Atomic Selfish Routing 99
4.5 A Quick-and-Dirty Bound on the Price of Anarchy 104
4.6 Better Bounds for Many Traffic Rates 107
4.7 Maximum Cost 110
4.8 Notes 114
III COPING WITH SELFISHNESS
5 Bounding and Detecting Braess's Paradox 121
5.1 Overview 121
5.2 Bounding Braess's Paradox 122
5.3 Detecting Braess's Paradox 132
5.4 Notes 146
6 Stackelberg Routing 151
6.1 Overview 151
6.2 Stackelberg Strategies and Induced Equilibria 152
6.3 Three Stackelberg Strategies 153
6.4 Upper Bounds for Networks of Parallel Links 155
6.5 Lower Bounds in More General Networks 159
6.6 The Complexity of Computing Optimal Strategies 162
6.7 Notes 165
References 169
Index 191

What People are Saying About This

Noam Nisan

Recent trends in the analysis and design of computer networks take into account rationally selfish behavior by the network's different components. This book introduces this exciting interdisciplinary type of analysis and presents some of its clearest and most influential applications.

Vijay V. Vazirani

Distributed competitive decision making, as opposed to centralized planning, is emerging as the norm in modern systems such as the Internet. The exciting area of algorithmic game theory, which combines methodology from two rich fields, attempts to identify and understand new issues arising as a consequence of this fact. This book provides a vivid glimpse into this area by dealing comprehensively with one of its well-studied problems.

Endorsement

Recent trends in the analysis and design of computer networks take into account rationally selfish behavior by the network's different components. This book introduces this exciting interdisciplinary type of analysis and presents some of its clearest and most influential applications.

—Noam Nisan, School of Computer Science and Engineering, Hebrew University of Jerusalem

From the Publisher

Distributed competitive decision making, as opposed to centralized planning, is emerging as the norm in modern systems such as the Internet. The exciting area of algorithmic game theory, which combines methodology from two rich fields, attempts to identify and understand new issues arising as a consequence of this fact. This book provides a vivid glimpse into this area by dealing comprehensively with one of its well-studied problems.

—Vijay V. Vazirani, College of Computing, Georgia Institute of Technology

Recent trends in the analysis and design of computer networks take into account rationally selfish behavior by the network's different components. This book introduces this exciting interdisciplinary type of analysis and presents some of its clearest and most influential applications.

—Noam Nisan, School of Computer Science and Engineering, Hebrew University of Jerusalem

Editorial Reviews

"Distributed competitive decision making, as opposed to centralized planning, is emerging as the norm in modern systems such as the Internet. The exciting area of algorithmic game theory, which combines methodology from two rich fields, attempts to identify and understand new issues arising as a consequence of this fact. This book provides a vivid glimpse into this area by dealing comprehensively with one of its well-studied problems."--Vijay V. Vazirani, College of Computing, Georgia Institute of Technology

"In recent years we have seen a fascinating confluence of ideas from algorithmic computer science and game theory, chiefly in the service of advancing our understanding of the technological and sociological mystery that is the Internet. Nowhere is the excitement, novelty, power, and elegance of these new ideas exemplified better than in Tim Roughgarden's doctoral dissertation, which is the basis for this important book."--Christos Papadimitriou, C. Lester Hogan Professor of Computer Science, University of California, Berkeley

"Recent trends in the analysis and design of computer networks take into account rationally selfish behavior by the network's different components. This book introduces this exciting interdisciplinary type of analysis and presents some of its clearest and most influential applications."--Noam Nisan, School of Computer Science and Engineering, Hebrew University of Jerusalem

& quot; Distributed competitive decision making, as opposed to centralized planning, is emerging as the norm in modern systems such as the Internet. The exciting area of algorithmic game theory, which combines methodology from two rich fields, attempts to identify and understand new issues arising as a consequence of this fact. This book provides a vivid glimpse into this area by dealing comprehensively with one of its well-studied problems.& quot; --Vijay V. Vazirani, College of Computing, Georgia Institute of Technology

& quot; In recent years we have seen a fascinating confluence of ideas from algorithmic computer science and game theory, chiefly in the service of advancing our understanding of the technological and sociological mystery that is the Internet. Nowhere is the excitement, novelty, power, and elegance of these new ideas exemplified better than in Tim Roughgarden's doctoral dissertation, which is the basis for this important book.& quot; --Christos Papadimitriou, C. Lester Hogan Professor of Computer Science, University of California, Berkeley

& quot; Recent trends in the analysis and design of computer networks take into account rationally selfish behavior by the network's different components. This book introduces this exciting interdisciplinary type of analysis and presents some of its clearest and most influential applications.& quot; --Noam Nisan, School of Computer Science and Engineering, Hebrew University of Jerusalem

" Distributed competitive decision making, as opposed to centralized planning, is emerging as the norm in modern systems such as the Internet. The exciting area of algorithmic game theory, which combines methodology from two rich fields, attempts to identify and understand new issues arising as a consequence of this fact. This book provides a vivid glimpse into this area by dealing comprehensively with one of its well-studied problems." --Vijay V. Vazirani, College of Computing, Georgia Institute of Technology

" In recent years we have seen a fascinating confluence of ideas from algorithmic computer science and game theory, chiefly in the service of advancing our understanding of the technological and sociological mystery that is the Internet. Nowhere is the excitement, novelty, power, and elegance of these new ideas exemplified better than in Tim Roughgarden's doctoral dissertation, which is the basis for this important book." --Christos Papadimitriou, C. Lester Hogan Professor of Computer Science, University of California, Berkeley

" Recent trends in the analysis and design of computer networks take into account rationally selfish behavior by the network's different components. This book introduces this exciting interdisciplinary type of analysis and presents some of its clearest and most influential applications." --Noam Nisan, School of Computer Science and Engineering, Hebrew University of Jerusalem

--Christos Papadimitriou, C. Lester Hogan Professor of Computer Science, University of California, Berkeley

--Noam Nisan, School of Computer Science and Engineering, Hebrew University of Jerusalem

--Vijay V. Vazirani, College of Computing, Georgia Institute of Technology

From the Publisher