# Game Theory Introduction

**Topics:**Game theory, Nash equilibrium, Subgame perfect equilibrium

**Pages:**62 (17328 words)

**Published:**December 9, 2012

Strategies and Games

Theory and Practice

prajit k. dutta

The MIT Press Cambridge, Massachusetts

.

London, England

© 1999 Massachusetts Institute of Technology All rights reserved. No part of this book may be reproduced in any form by any electronic or mechanical means (including photocopying, recording, or information storage and retrieval) without permission in writing from the publisher. This book was set in Melior and MetaPlus by Windfall Software using ZzTEX and was printed and bound in the United States of America. Library of Congress Cataloging-in-Publication Data Dutta, Prajit K. Strategies and games : theory and practice / Prajit K. Dutta. p. cm. Includes bibliographical references and index. ISBN 0-262-04169-3 1. Game theory. 2. Equilibrium (Economics). I. Title. HB144.D88 1999 98-42937 330 .01 5193—dc21 CIP

Ma aar Baba ke

Brief Contents

Preface A Reader’s Guide P A R T O N E 1 2 T W O 3 4 5 6 7 8 9 10 T H R E E 11 12 13 14 15 16 Introduction A First Look at the Applications A First Look at the Theory Strategic Form Games: Theory and Practice Strategic Form Games and Dominant Strategies Dominance Solvability Nash Equilibrium An Application: Cournot Duopoly An Application: The Commons Problem Mixed Strategies Two Applications: Natural Monopoly and Bankruptcy Law Zero-Sum Games Extensive Form Games: Theory and Applications Extensive Form Games and Backward Induction An Application: Research and Development Subgame Perfect Equilibrium Finitely Repeated Games Infinitely Repeated Games An Application: Competition and Collusion in the NASDAQ Stock Market An Application: OPEC Dynamic Games with an Application to the Commons Problem Asymmetric Information Games: Theory and Applications Moral Hazard and Incentives Theory Games with Incomplete Information

xxi xxix 1 3 17 33 35 49 63 75 91 103 121 139 155 157 179 193 209 227

C H A P T E R

243 257

17 18

275 291 293 309

F O U R 19 20

viii

Brief Contents

21

An Application: Incomplete Information in a Cournot Duopoly Mechanism Design, the Revelation Principle, and Sales to an Unknown Buyer An Application: Auctions Signaling Games and the Lemons Problem Foundations Calculus and Optimization Probability and Expectation Utility and Expected Utility Existence of Nash Equilibria

331

22

349 367 383 401 403 421 433 451

23 24 F I V E 25 26 27 28

Index

465

Contents

Preface A Reader’s Guide P A R T O N E 1 Introduction A First Look at the Applications 1.1 Games That We Play 1.2 Background 1.3 Examples Summary Exercises C H A P T E R 2 A First Look at the Theory 2.1 Rules of the Game: Background 2.2 Who, What, When: The Extensive Form 2.2.1 Information Sets and Strategies 2.3 Who, What, When: The Normal (or Strategic) Form 2.4 How Much: Von Neumann–Morgenstern Utility Function 2.5 Representation of the Examples Summary Exercises P A R T T W O 3 Strategic Form Games: Theory and Practice Strategic Form Games and Dominant Strategies 3.1 Strategic Form Games 3.1.1 Examples 3.1.2 Equivalence with the Extensive Form 3.2

xxi xxix 1 3 3 7 8 12 12 17 17 18 20 21 23 25 27 28 33 35 35 36 39 40 40 40 41

C H A P T E R

C H A P T E R

case study

The Strategic Form of Art Auctions

3.2.1 Art Auctions: A Description 3.2.2 Art Auctions: The Strategic Form 3.3 Dominant Strategy Solution

x

Contents

3.4

case study again

at the Auction Summary Exercises

A Dominant Strategy 43 44 45 49 49 49 51 51

C H A P T E R

4

Dominance Solvability 4.1 The Idea 4.1.1 Dominated and Undominated Strategies 4.1.2 Iterated Elimination of Dominated Strategies 4.1.3 More Examples 4.2

case study

Secretary General

Electing the United Nations 54 55 57 59 59 63 63 63 64 66 Nash Equilibrium in the 68 69 71 71 75 75 76 77 79 Today’s OPEC 81

4.3 A More Formal Deﬁnition 4.4 A Discussion Summary Exercises C H A P T E R 5 Nash Equilibrium 5.1 The Concept 5.1.1 Intuition and Deﬁnition...

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