2017;
372 pp;
Hardcover

MSC: Primary 91;

Print ISBN: 978-1-4704-1982-0

Product Code: MBK/101

List Price: $75.00

Individual Member Price: $60.00

**Electronic ISBN: 978-1-4704-3667-4
Product Code: MBK/101.E**

List Price: $75.00

Individual Member Price: $60.00

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#### Supplemental Materials

# Game Theory, Alive

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*Anna R. Karlin; Yuval Peres*

We live in a highly connected world with multiple self-interested
agents interacting and myriad opportunities for conflict and
cooperation. The goal of game theory is to understand these
opportunities.

This book presents a rigorous introduction to the mathematics of
game theory without losing sight of the joy of the subject. This is
done by focusing on theoretical highlights (e.g., at least six Nobel
Prize winning results are developed from scratch) and by presenting
exciting connections of game theory to other fields such as computer
science (algorithmic game theory), economics (auctions and matching
markets), social choice (voting theory), biology (signaling and
evolutionary stability), and learning theory. Both classical topics,
such as zero-sum games, and modern topics, such as sponsored search
auctions, are covered. Along the way, beautiful mathematical tools
used in game theory are introduced, including convexity, fixed-point
theorems, and probabilistic arguments.

The book is appropriate for a first course in game theory at either
the undergraduate or graduate level, whether in mathematics,
economics, computer science, or statistics. The
importance of game-theoretic thinking transcends the academic
setting—for every action we take, we must consider not only its
direct effects, but also how it influences the incentives of
others.

#### Readership

Undergraduate and graduate students and professors interested in game theory and decision making.

#### Reviews & Endorsements

This is an attractive candidate as a text for a mathematically rigorous course in game theory at the upper undergraduate or elementary graduate level. It offers an appealing and versatile selection of topics (including some modern ones), clear and well-motivated exposition, a good selection of examples, and a nicely-chosen selection of exercises (some but not all of which have solutions in the back of the book). People who teach, or simply have an interest in game theory, will certainly find this book worth a look.

-- Mark Hunacek, MAA Reviews

Game theory's influence is felt in a wide range of disciplines, and the authors deliver masterfully on the challenge of presenting both the breadth and coherence of its underlying world-view. The book achieves a remarkable synthesis, introducing the reader to the blend of economic insight, mathematical elegance, scientific impact, and counter-intuitive punch that characterizes game theory as a field.

-- Jon Kleinberg, Cornell University, 2006 Nevanlinna Prize winner

A game theory textbook by people who love … games! It covers many classic as well as recent topics of game theory. Its rigorous treatment, interspersed with illuminating examples, makes it a challenging pleasure to read.

-- Sergiu Hart, The Hebrew University of Jerusalem

This beautifully written book introduces the reader to the rich and flourishing subject of game theory. From an exhaustive account of basics of the classical theory to a wide range of modern themes—including auctions, matching markets, sequential decision making—the book presents a great variety of topics in a rigorous yet entertaining manner. The authors guide the reader through the intricacies of game theory with an exquisite mathematical elegance. For anyone interested in the topic, experts and beginners alike, this book is a must.

-- Gábor Lugosi, Pompeu Fabra University, Barcelona, Spain

It is great to have a comprehensive game theory textbook including so many modern topics.

-- Éva Tardos, Cornell University

# Table of Contents

## Game Theory, Alive

Table of Contents pages: 1 2

- Cover Cover11
- Title page iii4
- Contents v6
- Acknowledgements xi12
- Credits xii13
- Preface xvii18
- Part I: Analyzing games: Strategies and equilibria 128
- Chapter 1. Combinatorial games 229
- Chapter 2. Two-person zero-sum games 2451
- 2.1. Examples 2451
- 2.2. Definitions 2653
- 2.3. The Minimax Theorem and its meaning 2754
- 2.4. Simplifying and solving zero-sum games 2855
- 2.5. Nash equilibria, equalizing payoffs, and optimal strategies 3360
- 2.6. Proof of von Neumann’s Minimax Theorem* 3562
- 2.7. Zero-sum games with infinite action spaces* 3865
- Notes 3865
- Exercises 4067

- Chapter 3. Zero-sum games on graphs 4572
- Chapter 4. General-sum games 6491
- Chapter 5. Existence of Nash equilibria and fixed points 89116
- Chapter 6. Games in extensive form 104131
- Chapter 7. Evolutionary and correlated equilibria 127154
- Chapter 8. The price of anarchy 138165
- Chapter 9. Random-turn games 161188
- Part II: Designing games and mechanisms 169196
- Chapter 10. Stable matching and allocation 170197
- Chapter 11. Fair division 183210
- Chapter 12. Cooperative games 194221
- Chapter 13. Social choice and voting 206233
- 13.1. Voting and ranking mechanisms 206233
- 13.2. Definitions 208235
- 13.3. Arrow’s Impossibility Theorem 209236
- 13.4. The Gibbard-Satterthwaite Theorem 210237
- 13.5. Desirable properties for voting and ranking 210237
- 13.6. Analysis of specific voting rules 211238
- 13.7. Proof of Arrow’s Impossibility Theorem* 214241
- 13.8. Proof of the Gibbard-Satterthwaite Theorem* 216243
- Notes 2249
- Exercises 221248

- Chapter 14. Auctions 223250
- 14.1. Single item auctions 223250
- 14.2. Independent private values 226253
- 14.3. Revenue in single-item auctions 227254
- 14.4. Toward revenue equivalence 228255
- 14.5. Auctions with a reserve price 232259
- 14.6. Characterization of Bayes-Nash equilibrium 236263
- 14.7. Price of anarchy in auctions 239266
- 14.8. The Revelation Principle 240267
- 14.9. Myerson’s optimal auction 242269
- 14.10. Approximately optimal auctions 248275
- 14.11. The plot thickens... 250277
- Notes 252279
- Exercises 253280

- Chapter 15. Truthful auctions in win/lose settings 257284

Table of Contents pages: 1 2