Martin J. Osborne_An introduction to game theory_1_Frontmatter and Preface

Contents
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6 Extensive Games with Perfect Information: Illustrations 179 6.1 The ultimatum game, the holdup game, and agenda control 179 Experiments on the ultimatum game 181 6.2 Stackelberg’s model of duopoly 185 6.3 Buying votes 190 6.4 A race 195 Notes 201
8 Coalitional Games and the Core 237 8.1 Coalitional games 237 8.2 The core 241 8.3 Illustration: ownership and the distribution of wealth 245 8.4 Illustration: exchanging homogeneous horses 249 8.5 Illustration: exchanging heterogeneous houses 254 8.6 Illustration: voting 258 8.7 Illustration: matching 261 Matching doctors with hospitals 266 8.8 Discussion: other solution concepts 267 Notes 268
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I Games with Perfect Information 9
2 Nash Equilibrium: Theory 11 2.1 Strategic games 11 2.2 Example: the Prisoner’s Dilemma 12 2.3 Example: Bach or Stravinsky? 16 2.4 Example: Matching Pennies 17 2.5 Example: the Stag Hunt 18 2.6 Nash equilibrium 19 John F. Nash, Jr. 21 Studying Nash equilibrium experimentally 22 2.7 Examples of Nash equilibrium 24 Experimental evidence on the Prisoner’s Dilemma 26 Focal points 30 2.8 Best response functions 33 2.9 Dominated actions 43 2.10 Equilibrium in a single population: symmetric games and symmetric equilibria 49 Notes 51
An Introduction to Game Theory
Please send comments to Martin J. Osborne Department of Economics 150 St. George Street University of Toronto Toronto, Canada M5S 3G7 email: martin.osborne@utoronto.ca
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Contents
3 Nash Equilibrium: Illustrations 53 3.1 Cournot’s model of oligopoly 53 3.2 Bertrand’s model of oligopoly 61 Cournot, Bertrand, and Nash: some historical notes 67 3.3 Electoral competition 68 3.4 The War of Attrition 75 3.5 Auctions 78 Auctions from Babylonia to eBay 79 3.6 Accident law 89 Notes 94
5 Extensive Games with Perfect Information: Theory 151 5.1 Extensive games with perfect information 151 5.2 Strategies and outcomes 157 5.3 Nash equilibrium 159 5.4 Subgame perfect equilibrium 162 5.5 Finding subgame perfect equilibria of finite horizon games: backward induction 168 Ticktacktoe, chess, and related games 176 Notes 177
4 Mixed Strategy Equilibrium 97 4.1 Introduction 97 Some evidence on expected payoff functions 102 4.2 Strategic games in which players may randomize 103 4.3 Mixed strategy Nash equilibrium 105 4.4 Dominated actions 117 4.5 Pure equilibria when randomization is allowed 120 4.6 Illustration: expert diagnosis 121 4.7 Equilibrium in a single population 126 4.8 Illustration: reporting a crime 128 Reporting a crime: social psychology and game theory 131 4.9 The formation of players’ beliefs 132 4.10 Extension: Finding all mixed strategy Nash equilibria 135 4.11 Extension: Mixed strategy Nash equilibria of games in which each player has a continuum of actions 140 4.12 Appendix: Representing preferences over lotteries by the expected value of a payoff function 144 Notes 148
This version: 2002/7/25
Note: The categorization of exercises according to the availability of their solutions is tentative. No solutions are currently publicly available. Note: The Index currently covers only Chapters 1 and 2 (and a few other bits and pieces). Note: Bad line breaks and page breaks have not yet been corrected.
7 Extensive Games with Perfect Information: Extensions and Discussion 203 7.1 Allowing for simultaneous moves 203 More experimental evidence on subgame perfect equilibrium 209 7.2 Illustration: entry into a monopolized industry 211 7.3 Illustration: electoral competition with strategic voters 213 7.4 Illustration: committee decision-making 215 7.5 Illustration: exit from a declining industry 219 7.6 Allowing for exogenous uncertainty 224 7.7 Discussion: subgame perfect equilibrium and backward induction 228 Experimental evidence on the centipede game 232 Notes 234
Library of Congress Cataloging-in-Publication Data Osborne, Martin John. An Introduction to Game Theory / Martin J. Osborne p. cm. Includes bibliographical references and index. ISBN ????? 1. Game Theory. 2. Economics, Mathematical. I. II. Title. HB144.O???? 2002