Selfish Routing and the Price of Anarchy

by ROUGHGARDEN, TIM

• ISBN13: 9780262182430
• ISBN10: 0262182432
• Format: Hardcover
• Copyright: 2005-05-06
• Publisher: The MIT Press

Summary

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.

Author Biography

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
Introduction	3	(14)
Selfish Routing	3	(1)
Two Motivating Examples	3	(3)
Applications and Caveats	6	(5)
How to Read this Book	11	(1)
Notes	12	(5)
Preliminaries	17	(34)
The Model	17	(3)
Flows at Nash Equilibrium	20	(1)
The Price of Anarchy	21	(1)
A Characterization of Optimal Flows	22	(6)
Examples	28	(6)
Existence and Uniqueness of Nash Flows	34	(3)
Nash Flows in Single-Commodity Networks	37	(4)
Notes	41	(10)
II BOUNDING THE PRICE OF ANARCHY
How Bad Is Selfish Routing?	51	(34)
Overview	51	(2)
The Price of Anarchy with Linear Cost Functions	53	(5)
A General Upper Bound on the Price of Anarchy	58	(4)
Matching Lower Bounds in Simple Networks	62	(7)
Computing the Price of Anarchy	69	(4)
A Bicriteria Bound in General Networks	73	(4)
Notes	77	(8)
Extensions	85	(36)
Nonatomic Congestion Games	85	(3)
Approximate Nash Flows	88	(4)
Edge Capacities	92	(7)
Atomic Selfish Routing	99	(5)
A Quick-and-Dirty Bound on the Price of Anarchy	104	(3)
Better Bounds for Many Traffic Rates	107	(3)
Maximum Cost	110	(4)
Notes	114	(7)
III COPING WITH SELFISHNESS
Bounding and Detecting Braess's Paradox	121	(30)
Overview	121	(1)
Bounding Braess's Paradox	122	(10)
Detecting Braess's Paradox	132	(14)
Notes	146	(5)
Stackelberg Routing	151	(18)
Overview	151	(1)
Stackelberg Strategies and Induced Equilibria	152	(1)
Three Stackelberg Strategies	153	(2)
Upper Bounds for Networks of Parallel Links	155	(4)
Lower Bounds in More General Networks	159	(3)
The Complexity of Computing Optimal Strategies	162	(3)
Notes	165	(4)
References	169	(22)
Index	191