Twenty Lectures on Algorithmic Game Theory

334 Pages·2016·4.47 MB·English

by  Tim Roughgarden

Twenty Lectures on Algorithmic
Game Theory
Computer science and economics have engaged in a lively interaction over the
past 15 years, resulting in the new field of algorithmic game theory. Many
problems central to modern computer science, ranging from resource allocation in
large networks to online advertising, involve interactions between multiple self-
interested parties. Economics and game theory offer a host of useful models and
definitions to reason about such problems. The flow of ideas also travels in the
other direction, and concepts from computer science are increasingly important in
economics.
This book grew out of the author’s Stanford course on algorithmic game
theory, and aims to give students and other newcomers a quick and accessible
introduction to many of the most important concepts in the field. The book also
includes case studies on online advertising, wireless spectrum auctions, kidney
exchange, and network management.
Tim Roughgarden is an Associate Professor of Computer Science at Stanford
University. For his research in algorithmic game theory, he has been awarded the
ACM Grace Murray Hopper A ward, the Presidential Early Career Award for
Scientists and Engineers (PECASE), the Kalai Prize in Game Theory and
Computer Science, the Social Choice and Welfare Prize, the Mathematical
Programming Society’s Tucker Prize, and the EATCS-SIGACT Gödel Prize. He
wrote the book Selfish Routing and the Price of Anarchy (2005) and coedited
the book Algorithmic Game Theory (2007).
Twenty Lectures
on Algorithmic Game Theory
Tim Roughgarden
Stanford University, California
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Information on this title: www.cambridge.org/9781107172661
10.1017/9781316779309
© Tim Roughgarden 2016
This publication is in copyright. Subject to statutory exception and to the
provisions of relevant collective licensing agreements, no reproduction of any part
may take place without the written permission of Cambridge University Press.
First published 2016
Printed in the United States of America
A catalogue record for this publication is available from the British Library.
Library of Congress Cataloging in Publication Data
Names: Roughgarden, Tim.
Title: Twenty lectures on algorithmic game theory / Tim Roughgarden,
Stanford University, California.
Description: Cambridge: Cambridge University Press, 2016. | Includes
bibliographical references and index.
Identifiers: LCCN 2016028351 | ISBN 9781107172661 (hardback: alk. paper)
Subjects: LCSH: Game theory. | Algorithms.
Classification: LCC QA269. R68 2016 | DDC 519.3-dc23
LC record available at https://lccn.loc.gov/2016028351
ISBN 978-1-107-17266-1 Hardback
ISBN 978-1-316-62479-1 Paperback
Cambridge University Press has no responsibility for the persistence or accuracy
of URLs for external or third-party Internet Web sites referred to in this
publication and does not guarantee that any content on such Web sites is, or will
remain, accurate or appropriate.
To Emma
Contents
Preface
1 Introduction and Examples
1.1 The Science of Rule-Making
1.2 When Is Selfish Behavior Near-Optimal?
1.3 Can Strategic Players Learn an Equilibrium?
Notes
Exercises
Problems
2 Mechanism Design Basics
2.1 Single-Item Auctions
2.2 Sealed-Bid Auctions
2.3 First-Price Auctions
2.4 Second-Price Auctions and Dominant Strategies
2.5 Ideal Auctions
2.6 Case Study: Sponsored Search Auctions
Notes
Exercises
Problems
3 Myerson’s Lemma
3.1 Single-Parameter Environments
3.2 Allocation and Payment Rules
3.3 Statement of Myerson’s Lemma
*3.4 Proof of Myerson’s Lemma
3.5 Applying the Payment Formula
Notes
Exercises
Problems
4 Algorithmic Mechanism Design
4.1 Knapsack Auctions
4.2 Algorithmic Mechanism Design
4.3 The Revelation Principle
Notes
Exercises
Problems
5 Revenue-Maximizing Auctions
5.1 The Challenge of Revenue Maximization
5.2 Characterization of Optimal DSIC Mechanisms
5.3 Case Study: Reserve Prices in Sponsored Search
*5.4 Proof of Lemma 5.1
Notes
Exercises
Problems
6 Simple Near-Optimal Auctions
6.1 Optimal Auctions Can Be Complex
6.2 The Prophet Inequality
6.3 Simple Single-Item Auctions
6.4 Prior-Independent Mechanisms
Notes
Exercises
Problems
7 Multi-Parameter Mechanism Design
7.1 General Mechanism Design Environments
7.2 The VCG Mechanism
7.3 Practical Considerations
Notes
Exercises
Problems
8 Spectrum Auctions
8.1 Indirect Mechanisms
8.2 Selling Items Separately
8.3 Case Study: Simultaneous Ascending Auctions
8.4 Package Bidding
8.5 Case Study: The 2016 FCC Incentive Auction
Notes
Exercises
Problems
9 Mechanism Design with Payment Constraints
9.1 Budget Constraints
9.2 The Uniform-Price Multi-Unit Auction
*9.3 The Clinching Auction
9.4 Mechanism Design without Money
Notes
Exercises
Problems
10 Kidney Exchange and Stable Matching
10.1 Case Study: Kidney Exchange
10.2 Stable Matching
*10.3 Further Properties
Notes
Exercises
Problems
11 Selfish Routing and the Price of Anarchy
11.1 Selfish Routing: Examples
11.2 Main Result: Informal Statement
11.3 Main Result: Formal Statement
11.4 Technical Preliminaries
*11.5 Proof of Theorem 11.2
Notes
Exercises
Problems
12 Over-Provisioning and Atomic Selfish Routing
12.1 Case Study: Network Over-Provisioning
12.2 A Resource Augmentation Bound
*12.3 Proof of Theorem 12.1
12.4 Atomic Selfish Routing
*12.5 Proof of Theorem 12.3
Notes
Exercises
Problems
13 Equilibria: Definitions, Examples, and Existence
13.1 A Hierarchy of Equilibrium Concepts
13.2 Existence of Pure Nash Equilibria
13.3 Potential Games
Notes
Exercises
Problems
14 Robust Price-of-Anarchy Bounds in Smooth Games
*14.1 A Recipe for POA Bounds
*14.2 A Location Game
*14.3 Smooth Games
*14.4 Robust POA Bounds in Smooth Games
Notes
Exercises
Problems
15 Best-Case and Strong Nash Equilibria
15.1 Network Cost-Sharing Games
15.2 The Price of Stability
15.3 The POA of Strong Nash Equilibria
*15.4 Proof of Theorem 15.3
Notes
Exercises
Problems
16 Best-Response Dynamics
16.1 Best-Response Dynamics in Potential Games
16.2 Approximate PNE in Selfish Routing Games
*16.3 Proof of Theorem 16.3
*16.4 Low-Cost Outcomes in Smooth Potential Games
Notes
Exercises
Problems
17 No-Regret Dynamics
17.1 Online Decision Making
17.2 The Multiplicative Weights Algorithm
17.3 Proof of Theorem 17.6
*17.4 No Regret and Coarse Correlated Equilibria
Notes
Exercises
Problems
18 Swap Regret and the Minimax Theorem
18.1 Swap Regret and Correlated Equilibria
*18.2 Proof of Theorem 18.5
18.3 The Minimax Theorem for Zero-Sum Games
*18.4 Proof of Theorem 18.7
Notes
Exercises
Problems
19 Pure Nash Equilibria and -Completeness
19.1 When Are Equilibrium Concepts Tractable?
19.2 Local Search Problems
19.3 Computing a PNE of a Congestion Game
Notes
Exercises
Problems
20 Mixed Nash Equilibria and -Completeness
20.1 Computing a MNE of a Bimatrix Game
20.2 Total Search Problems ( )
*20.3 : A Syntactic Subclass of
*20.4 A Canonical Problem: Sperner’s Lemma
*20.5 MNE and
20.6 Discussion
Notes
Exercises
Problems
The Top 10 List
Hints to Selected Exercises and Problems
Bibliography
Index