Games of strateGy Fourth Edition

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G a m e s o f s t r a t e G y

F o u r t h E d i t i o n

Av i n a s h D i x i t Princeton University Su s a n Sk e a t h Wellesley College D a v i d Re i l e y Google

B

W. W. Norton & Company New York • London

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Library of Congress Cataloging-in-Publication Data

Dixit, Avinash K.

Games of strategy / Avinash Dixit, Susan Skeath, David Reiley.—Fourth edition.

pages cm

Includes bibliographical references and index.

ISBN 978-0-393-91968-4 (hardcover)

1. Game theory. 2. Policy sciences. 3. Decision making. I. Skeath, Susan.

II. Reiley, David. III. Title.

HB144.D59 2015

519.3—dc23

2014037581

W. W. Norton & Company, Inc., 500 Fifth Avenue, New York, N.Y. 10110

www.wwnorton.com

W. W. Norton & Company Ltd., Castle House, 75/76 Wells Street, London W1T 3QT

1 2 3 4 5 6 7 8 9 0

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To the memory of my father, Kamalakar Ramachandra Dixit

— Avinash Dixit

To the memory of my father, James Edward Skeath

— Susan Skeath

To my mother, Ronie Reiley

— David Reiley

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Contents

Preface

xx

Part one Introduction and General Principles

1Basic Ideas and Examples 3
1what iS a gamE oF StratEgy? 4
2SomE ExamPlES and StoriES oF StratEgic gamES6
A. Which Passing Shot?6
B. The GPA Rat Race7
C. “We Can’t Take the Exam Because We Had a Flat Tire”9
D. Why Are Professors So Mean?10
E. Roommates and Families on the Brink11
F. The Dating Game13
3our StratEgy For Studying gamES oF StratEgy14

vii

viii CON TE N TS

2 How to Think about Strategic Games 17 1 dEciSionS vErSuS gamES 18 2 claSSiFying gamES 20 A. Are the Moves in the Game Sequential or Simultaneous? 20 B. Are the Players’ Interests in Total Conflict or Is There Some Commonality? 21 C. Is the Game Played Once or Repeatedly, and with the Same or Changing Opponents? 22 D. Do the Players Have Full or Equal Information? 23 E. Are the Rules of the Game Fixed or Manipulable? 25 F. Are Agreements to Cooperate Enforceable? 26 3 SomE tErminology and background aSSumPtionS 27 A. Strategies 27 B. Payoffs 28 C. Rationality 29 D. Common Knowledge of Rules 31 E. Equilibrium 32 F. Dynamics and Evolutionary Games 34 G. Observation and Experiment 35 4 thE uSES oF gamE thEory 36 5 thE StructurE oF thE chaPtErS to Follow 38 Summary 41 kEy tErmS 41 ExErciSES 42

Part two

Concepts and Techniques

3 Games with Sequential Moves

47

1 gamE trEES 48

• A. Nodes, Branches, and Paths of Play 48 B. Uncertainty and “Nature’s Moves” 48

• C. Outcomes and Payoffs 50

• D. Strategies 50

• E. Tree Construction 51

CON T E N TS i x

2Solving gamES by uSing trEES52
3adding morE PlayErS57
4ordEr advantagES62
5adding morE movES63
A. Tic-Tac-Toe 63
B. Chess65
C. Checkers 69
6EvidEncE concErning rollback71
7StratEgiES in _survivor_75
Summary80
kEy tErmS81
ExErciSES81
4Simultaneous-Move Games: Discrete Strategies
1dEPicting SimultanEouS-movE gamES with diScrEtE StratEgiES92 2naSh Equilibrium94
A. Some Further Explanation of the Concept of Nash Equilibrium 95
B. Nash Equilibrium as a System of Beliefs and Choices 97
3dominancE99
A. Both Players Have Dominant Strategies 100
B. One Player Has a Dominant Strategy 101
C. Successive Elimination of Dominated Strategies 104
4bESt-rESPonSE analySiS106
5thrEE PlayErS108
6multiPlE Equilibria in PurE StratEgiES111
A. Will Harry Meet Sally? Pure Coordination 111
B. Will Harry Meet Sally? And Where? Assurance 113
C. Will Harry Meet Sally? And Where? Battle of the Sexes 114
D. Will James Meet Dean? Chicken 116
7no Equilibrium in PurE StratEgiES118
Summary120
kEy tErmS120
ExErciSES121

91