An Introduction to Game Theory
Selected chapters from draft of
An Introduction to Game Theory by Martin J. Osborne
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
This version:
2000/11/6
Copyright c 1995–2000 by Martin J. Osborne All rights reserved. No part of this book may be reproduced by any electronic or mechanical means (including photocopying, recording, or information storage and retrieval) without permission in writing from Oxford University Press.
Contents
Preface 1
xiii
Introduction 1 1.1 What is game theory? 1 An outline of the history of game theory John von Neumann 3 1.2 The theory of rational choice 4 1.3 Coming attractions 7 Notes 8
3
I
2
Games with Perfect Information
9
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. 20 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
v
vi
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 3.3 Electoral competition 68 3.4 The War of Attrition 75 3.5 Auctions 79 Auctions from Babylonia to eBay 79 3.6 Accident law 89 Notes 94
67
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 119 4.6 Illustration: expert
An Introduction to Game Theory by Martin J. Osborne
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
This version:
2000/11/6
Copyright c 1995–2000 by Martin J. Osborne All rights reserved. No part of this book may be reproduced by any electronic or mechanical means (including photocopying, recording, or information storage and retrieval) without permission in writing from Oxford University Press.
Contents
Preface 1
xiii
Introduction 1 1.1 What is game theory? 1 An outline of the history of game theory John von Neumann 3 1.2 The theory of rational choice 4 1.3 Coming attractions 7 Notes 8
3
I
2
Games with Perfect Information
9
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. 20 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
v
vi
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 3.3 Electoral competition 68 3.4 The War of Attrition 75 3.5 Auctions 79 Auctions from Babylonia to eBay 79 3.6 Accident law 89 Notes 94
67
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 119 4.6 Illustration: expert