Game Theory An Introduction

ISBN-10: 0691129088
ISBN-13: 9780691129082
Edition: 2013
Authors: Steven Tadelis
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Description: This comprehensive textbook introduces readers to the principal ideas and applications of game theory, in a style that combines rigor with accessibility. Steven Tadelis begins with a concise description of rational decision making, and goes on to  More...

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Book details

Copyright year: 2013
Publisher: Princeton University Press
Publication date: 1/6/2013
Binding: Hardcover
Pages: 416
Size: 7.00" wide x 10.00" long x 1.25" tall
Weight: 2.442
Language: English

This comprehensive textbook introduces readers to the principal ideas and applications of game theory, in a style that combines rigor with accessibility. Steven Tadelis begins with a concise description of rational decision making, and goes on to discuss strategic and extensive form games with complete information, Bayesian games, and extensive form games with imperfect information. He covers a host of topics, including multistage and repeated games, bargaining theory, auctions, rent-seeking games, mechanism design, signaling games, reputation building, and information transmission games. Unlike other books on game theory, this one begins with the idea of rationality and explores its implications for multiperson decision problems through concepts like dominated strategies and rationalizability. Only then does it present the subject of Nash equilibrium and its derivatives.Game Theoryis the ideal textbook for advanced undergraduate and beginning graduate students. Throughout, concepts and methods are explained using real-world examples backed by precise analytic material. The book features many important applications to economics and political science, as well as numerous exercises that focus on how to formalize informal situations and then analyze them.Introduces the core ideas and applications of game theoryCovers static and dynamic games, with complete and incomplete informationFeatures a variety of examples, applications, and exercisesTopics include repeated games, bargaining, auctions, signaling, reputation, and information transmissionIdeal for advanced undergraduate and beginning graduate studentsComplete solutions available to teachers and selected solutions available to students

Preface
Rational Decision Making
The Single-Person Decision Problem
Actions, Outcomes, and Preferences
Preference Relations
Payoff Functions
The Rational Choice Paradigm
Summary
Exercises
Introducing Uncertainty and Time
Risk, Nature, and Random Outcomes
Finite Outcomes and Simple Lotteries
Simple versus Compound Lotteries
Lotteries over Continuous Outcomes
Evaluating Random Outcomes
Expected Payoff: The Finite Case
Expected Payoff: The Continuous Case
Caveat: It's Not Just the Order Anymore
Risk Attitudes
The St. Petersburg Paradox
Rational Decision Making with Uncertainty
Rationality Revisited
Maximizing Expected Payoffs
Decisions over Time
Backward Induction
Discounting Future Payoffs
Applications
The Value of Information
Discounted Future Consumption
Theory versus Practice
Summary
Exercises
Static Games of Complete Information
Preliminaries
Normal-Form Games with Pure Strategies
Example: The Prisoner's Dilemma
Example: Cournot Duopoly
Example: Voting on a New Agenda
Matrix Representation: Two-Player Finite Game
Example: The Prisoner's Dilemma
Example: Rock-Paper-Scissors
Solution Concepts
Assumptions and Setup
Evaluating Solution Concepts
Evaluating Outcomes
Summary
Exercises
Rationality and Common Knowledge
Dominance in Pure Strategies
Dominated Strategies
Dominant Strategy Equilibrium
Evaluating Dominant Strategy Equilibrium
Iterated Elimination of Strictly Dominated Pure Strategies
Iterated Elimination and Common Knowledge of Rationality
Example: Cournot Duopoly
Evaluating IESDS
Beliefs, Best Response, and Rationalizability
The Best Response
Beliefs and Best-Response Correspondences
Rationalizability
The Cournot Duopoly Revisited
The "p-Beauty Contest"
Evaluating Rationalizability
Summary
Exercises
Pinning Down Beliefs: Nash Equilibrium
Nash Equilibrium in Pure Strategies
Pure-Strategy Nash Equilibrium in a Matrix
Evaluating the Nash Equilibria Solution
Nash Equilibrium: Some Classic Applications
Two Kinds of Societies
The Tragedy of the Commons
Coumot Duopoly
Bertrand Duopoly
Political Ideology and Electoral Competition
Summary
Exercises
Mixed Strategies
Strategies, Beliefs, and Expected Payoffs
Finite Strategy Sets
Continuous Strategy Sets
Beliefs and Mixed Strategies
Expected Payoffs
Mixed-Strategy Nash Equilibrium
Example: Matching Pennies
Example: Rock-Paper-Scissors
Multiple Equilibria: Pure and Mixed
IESDS and Rationalizability Revisited
Nash's Existence Theorem
Summary
Exercises
Dynamic Games of Complete Information
Preliminaries
The Extensive-Form Game
Game Trees
Imperfect versus Perfect Information
Strategies and Nash Equilibrium
Pure Strategies
Mixed versus Behavioral Strategies
Normal-Form Representation of Extensive-Form Games
Nash Equilibrium and Paths of Play
Summary
Exercises
Credibility and Sequential Rationality
Sequential Rationality and Backward Induction
Subgame-Perfect Nash Equilibrium: Concept
Subgame-Perfect Nash Equilibrium: Examples
The Centipede Game
Stackelberg Competition
Mutually Assured Destruction
Time-Inconsistent Preferences
Summary
Exercises
Multistage Games
Preliminaries
Payoffs
Strategies and Conditional Play
Subgame-Perfect Equilibria
The One-Stage Deviation Principle
Summary
Exercises
Repeated Games
Finitely Repeated Games
Infinitely Repeated Games
Payoffs
Strategies
Subgame-Perfect Equilibria
Application: Tacit Collusion
Sequential Interaction and Reputation
Cooperation as Reputation
Third-Party Institutions as Reputation Mechanisms
Reputation Transfers without Third Parties
The Folk Theorem: Almost Anything Goes
Summary
Exercises
Strategic Bargaining
One Round of Bargaining: The Ultimatum Game
Finitely Many Rounds of Bargaining
The Infinite-Horizon Game
Application: Legislative Bargaining
Closed-Rule Bargaining
Open-Rule Bargaining
Summary
Exercises
Static Games of Incomplete Information
Bayesian Games
Strategic Representation of Bayesian Games
Players, Actions, Information, and Preferences
Deriving Posteriors from a Common Prior: A Player's Beliefs
Strategies and Bayesian Nash Equilibrium
Examples
Teenagers and the Game of Chicken
Study Groups
Inefficient Trade and Adverse Selection
Committee Voting
Mixed Strategies Revisited: Harsanyi's Interpretation
Summary
Exercises
Auctions and Competitive Bidding
Independent Private Values
Second-Price Sealed-Bid Auctions
English Auctions
First-Price Sealed-Bid and Dutch Auctions
Revenue Equivalence
Common Values and the Winner's Curse
Summary
Exercises
Mechanism Design
Setup: Mechanisms as Bayesian Games
The Players
The Mechanism Designer
The Mechanism Game
The Revelation Principle
Dominant Strategies and Vickrey-Clarke-Groves Mechanisms
Dominant Strategy Implementation
Vickrey-Clarke-Groves Mechanisms
Summary
Exercises
Dynamic Games of Incomplete Information
Sequential Rationality with Incomplete Information
The Problem with Subgame Perfection
Perfect Bayesian Equilibrium
Sequential Equilibrium
Summary
Exercises
Signaling Games
Education Signaling: The MBA Game
Limit Pricing and Entry Deterrence
Separating Equilibria
Pooling Equilibria
Refinements of Perfect Bayesian Equilibrium in Signaling Games
Summary
Exercises
Building a Reputation
Cooperation in a Finitely Repeated Prisoner's Dilemma
Driving a Tough Bargain
A Reputation for Being "Nice"
Summary
Exercises
Information Transmission and Cheap Talk
Information Transmission: A Finite Example
Information Transmission: The Continuous Case
Application: Information and Legislative Organization
Summary
Exercises
Mathematical Appendix
Sets and Sequences
Basic Definitions
Basic Set Operations
Functions
Basic Definitions
Continuity
Calculus and Optimization
Basic Definitions
Differentiation and Optimization
Integration
Probability and Random Variables
Basic Definitions
Cumulative Distribution and Density Functions
Independence, Conditional Probability, and Bayes' Rule
Expected Values
References
Index

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