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Game Theory An Introduction.pdf

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    Cover
    GAME THEORY
    Title
    Copyright
    Contents
    Preface
    PART I Rational Decision Making
    Chapter 1 The Single-Person Decision Problem
    1.1 Actions, Outcomes, and Preferences
    1.1.1 Preference Relations
    1.1.2 Payoff Functions
    1.2 The Rational Choice Paradigm
    1.4 Exercises
    1.3 Summary
    Chapter 2 Introducing Uncertainty and Time
    2.1 Risk, Nature, and Random Outcomes
    2.1.1 Finite Outcomes and Simple Lotteries
    2.1.2 Simple versus Compound Lotteries
    2.1.3 Lotteries over Continuous Outcomes
    2.2 Evaluating Random Outcomes
    2.2.1 Expected Payoff: The Finite Case
    2.2.2 Expected Payoff: The Continuous Case
    2.2.3 Caveat: It’s Not Just the Order Anymore
    2.2.4 Risk Attitudes
    2.2.5 The St. Petersburg Paradox
    2.3 Rational Decision Making with Uncertainty
    2.3.1 Rationality Revisited
    2.3.2 Maximizing Expected Payoffs
    2.4 Decisions over Time
    2.4.1 Backward Induction
    2.4.2 Discounting Future Payoffs
    2.5 Applications
    2.5.1 The Value of Information
    2.5.2 Discounted Future Consumption
    2.6 Theory versus Practice
    2.7 Summary
    2.8 Exercises
    PART II Static Games of Complete Information
    Chapter 3 Preliminaries
    3.1 Normal-Form Games with Pure Strategies
    3.1.1 Example: The Prisoner’s Dilemma
    3.1.2 Example: Cournot Duopoly
    3.1.3 Example: Voting on a New Agenda
    3.2 Matrix Representation: Two-Player Finite Game
    3.2.1 Example: The Prisoner’s Dilemma
    3.2.2 Example: Rock-Paper-Scissors
    3.3 Solution Concepts
    3.3.1 Assumptions and Setup
    3.3.2 Evaluating Solution Concepts
    3.3.3 Evaluating Outcomes
    3.4 Summary
    3.5 Exercises
    Chapter 4 Rationality and Common Knowledge
    4.1 Dominance in Pure Strategies
    4.1.1 Dominated Strategies
    4.1.2 Dominant Strategy Equilibrium
    4.1.3 Evaluating Dominant Strategy Equilibrium
    4.2 Iterated Elimination of Strictly Dominated Pure Strategies
    4.2.1 Iterated Elimination and Common Knowledge of Rationality
    4.2.2 Example: Cournot Duopoly
    4.2.3 Evaluating IESDS
    4.3 Beliefs, Best Response, and Rationalizability
    4.3.1 The Best Response
    4.3.2 Beliefs and Best-Response Correspondences
    4.3.3 Rationalizability
    4.3.4 The Cournot Duopoly Revisited
    4.3.5 The “p-Beauty Contest”
    4.3.6 Evaluating Rationalizability
    4.4 Summary
    4.5 Exercises
    Chapter 5 Pinning Down Beliefs: Nash Equilibrium
    5.1 Nash Equilibrium in Pure Strategies
    5.1.1 Pure-Strategy Nash Equilibrium in a Matrix
    5.1.2 Evaluating the Nash Equilibria Solution
    5.2 Nash Equilibrium: Some Classic Applications
    5.2.1 Two Kinds of Societies
    5.2.2 The Tragedy of the Commons
    5.2.3 Cournot Duopoly
    5.2.4 Bertrand Duopoly
    5.2.5 Political Ideology and Electoral Competition
    5.3 Summary
    5.4 Exercises
    Chapter 6 Mixed Strategies
    6.1 Strategies, Beliefs, and Expected Payoffs
    6.1.1 Finite Strategy Sets
    6.1.2 Continuous Strategy Sets
    6.1.3 Beliefs and Mixed Strategies
    6.1.4 Expected Payoffs
    6.2 Mixed-Strategy Nash Equilibrium
    6.2.1 Example: Matching Pennies
    6.2.2 Example: Rock-Paper-Scissors
    6.2.3 Multiple Equilibria: Pure and Mixed
    6.3 IESDS and Rationalizability Revisited
    6.4 Nash’s Existence Theorem
    6.5 Summary
    6.6 Exercises
    PART III Dynamic Games of Complete Information
    Chapter 7 Preliminaries
    7.1 The Extensive-Form Game
    7.1.1 Game Trees
    7.1.2 Imperfect versus Perfect Information
    7.2 Strategies and Nash Equilibrium
    7.2.1 Pure Strategies
    7.2.2 Mixed versus Behavioral Strategies
    7.2.3 Normal-Form Representation of Extensive-Form Games
    7.3 Nash Equilibrium and Paths of Play
    7.4 Summary
    7.5 Exercises
    Chapter 8 Credibility and Sequential Rationality
    8.1 Sequential Rationality and Backward Induction
    8.2 Subgame-Perfect Nash Equilibrium: Concept
    8.3 Subgame-Perfect Nash Equilibrium: Examples
    8.3.1 The Centipede Game
    8.3.2 Stackelberg Competition
    8.3.3 Mutually Assured Destruction
    8.3.4 Time-Inconsistent Preferences
    8.4 Summary
    8.5 Exercises
    Chapter 9 Multistage Games
    9.1 Preliminaries
    9.2 Payoffs
    9.3 Strategies and Conditional Play
    9.4 Subgame-Perfect Equilibria
    9.5 The One-Stage Deviation Principle
    9.6 Summary
    9.7 Exercises
    Chapter 10 Repeated Games
    10.1 Finitely Repeated Games
    10.2 Infinitely Repeated Games
    10.2.1 Payoffs
    10.2.2 Strategies
    10.3 Subgame-Perfect Equilibria
    10.4 Application: Tacit Collusion
    10.5 Sequential Interaction and Reputation
    10.5.1 Cooperation as Reputation
    10.5.2 Third-Party Institutions as Reputation Mechanisms
    10.5.3 Reputation Transfers without Third Parties
    10.6 The Folk Theorem: Almost Anything Goes
    10.7 Summary
    10.8 Exercises
    Chapter 11 Strategic Bargaining
    11.1 One Round of Bargaining: The Ultimatum Game
    11.2 Finitely Many Rounds of Bargaining
    11.3 The Infinite-Horizon Game
    11.4 Application: Legislative Bargaining
    11.4.1 Closed-Rule Bargaining
    11.4.2 Open-Rule Bargaining
    11.5 Summary
    11.6 Exercises
    PART IV Static Games of Incomplete Information
    Chapter 12 Bayesian Games
    12.1 Strategic Representation of Bayesian Games
    12.1.1 Players, Actions, Information, and Preferences
    12.1.2 Deriving Posteriors from a Common Prior: A Player’s Beliefs
    12.1.3 Strategies and Bayesian Nash Equilibrium
    12.2 Examples
    12.2.1 Teenagers and the Game of Chicken
    12.2.2 Study Groups
    12.3 Inefficient Trade and Adverse Selection
    12.4 Committee Voting
    12.5 Mixed Strategies Revisited: Harsanyi’s Interpretation
    12.6 Summary
    12.7 Exercises
    Chapter 13 Auctions and Competitive Bidding
    13.1 Independent Private Values
    13.1.1 Second-Price Sealed-Bid Auctions
    13.1.2 English Auctions
    13.1.3 First-Price Sealed-Bid and Dutch Auctions
    13.1.4 Revenue Equivalence
    13.2 Common Values and the Winner’s Curse
    13.3 Summary
    13.4 Exercises
    Chapter 14 Mechanism Design
    14.1 Setup: Mechanisms as Bayesian Games
    14.1.1 The Players
    14.1.2 The Mechanism Designer
    14.1.3 The Mechanism Game
    14.2 The Revelation Principle
    14.3 Dominant Strategies and Vickrey-Clarke-Groves Mechanisms
    14.3.1 Dominant Strategy Implementation
    14.3.2 Vickrey-Clarke-Groves Mechanisms
    14.4 Summary
    14.5 Exercises
    PART V Dynamic Games of Incomplete Information
    Chapter 15 Sequential Rationality with Incomplete Information
    15.1 The Problem with Subgame Perfection
    15.2 Perfect Bayesian Equilibrium
    15.3 Sequential Equilibrium
    15.4 Summary
    15.5 Exercises
    Chapter 16 Signaling Games
    16.1 Education Signaling: The MBA Game
    16.2 Limit Pricing and Entry Deterrence
    16.2.1 Separating Equilibria
    16.2.2 Pooling Equilibria
    16.3 Refinements of Perfect Bayesian Equilibrium in Signaling Games
    16.4 Summary
    16.5 Exercises
    Chapter 17 Building a Reputation
    17.1 Cooperation in a Finitely Repeated Prisoner’s Dilemma
    17.2 Driving a Tough Bargain
    17.3 A Reputation for Being “Nice”
    17.4 Summary
    17.5 Exercises
    Chapter 18 Information Transmission and Cheap Talk
    18.1 Information Transmission: A Finite Example
    18.2 Information Transmission: The Continuous Case
    18.3 Application: Information and Legislative Organization
    18.4 Summary
    18.5 Exercises
    Chapter 19 Mathematical Appendix
    19.1 Sets and Sequences
    19.1.1 Basic Definitions
    19.1.2 Basic Set Operations
    19.2 Functions
    19.2.1 Basic Definitions
    19.2.2 Continuity
    19.3 Calculus and Optimization
    19.3.1 Basic Definitions
    19.3.2 Differentiation and Optimization
    19.3.3 Integration
    19.4 Probability and Random Variables
    19.4.1 Basic Definitions
    19.4.2 Cumulative Distribution and Density Functions
    19.4.3 Independence, Conditional Probability, and Bayes’ Rule
    19.4.4 Expected Values
    References
    Index
    A PRINCETON UNIVERSITY PRESS E-BOOKGame TheoryAn IntroductionSteven Tadelis
    GAME THEORY
    GAME THEORY AN INTRODUCTION Steven Tadelis PRINCETON UNIVERSITY PRESS Princeton and Oxford
    Copyright © 2013 by Princeton University Press Published by Princeton University Press, 41 William Street, Princeton, New Jersey 08540 In the United Kingdom: Princeton University Press, 6 Oxford Street, Woodstock, Oxfordshire OX20 1TW press.princeton.edu All Rights Reserved Library of Congress Cataloging-in-Publication Data Tadelis, Steve. Game theory : an introduction / Steven Tadelis. p. cm. Includes bibliographical references and index. ISBN 978-0-691-12908-2 (hbk. : alk. paper) 1. Game theory. HB144.T33 2013 519.3—dc23 I. Title. 2012025166 British Library Cataloging-in-Publication Data is available This book has been composed in Times Roman and Myriad using ZzTEX by Princeton Editorial Associates Inc., Scottsdale, Arizona Printed on acid-free paper. Printed in the United States of America 10 9 8 7 6 5 4 3 2 1
    Contents Preface PART I Rational Decision Making Chapter 1 The Single-Person Decision Problem 1.1 Actions, Outcomes, and Preferences 1.1.1 Preference Relations 1.1.2 Payoff Functions The Rational Choice Paradigm Summary Exercises 1.2 1.3 1.4 Chapter 2 Introducing Uncertainty and Time 2.1 2.2 2.3 Simple versus Compound Lotteries Risk, Nature, and Random Outcomes 2.1.1 Finite Outcomes and Simple Lotteries 2.1.2 2.1.3 Lotteries over Continuous Outcomes Evaluating Random Outcomes 2.2.1 Expected Payoff: The Finite Case 2.2.2 Expected Payoff: The Continuous Case 2.2.3 Caveat: It’s Not Just the Order Anymore 2.2.4 Risk Attitudes 2.2.5 The St. Petersburg Paradox Rational Decision Making with Uncertainty 2.3.1 Rationality Revisited 2.3.2 Maximizing Expected Payoffs 2.4 Decisions over Time 2.4.1 Backward Induction 2.4.2 Discounting Future Payoffs 2.5 Applications 2.5.1 The Value of Information 2.5.2 Discounted Future Consumption Theory versus Practice Summary Exercises 2.6 2.7 2.8 xi 3 4 5 7 9 11 11 14 14 15 16 17 18 19 20 21 22 23 24 24 24 26 26 28 29 29 31 32 33 33 v
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