Game Theory An Introduction 2nd Edition by E N Barron ISBN 1118216938 978-1118216934

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Product details: 

ISBN 10:1118216938

ISBN 13:978-1118216934

Author:E.N.Barron

An exciting new edition of the popular introduction to game theory and its applications

The thoroughly expanded Second Edition presents a unique, hands-on approach to game theory. While most books on the subject are too abstract or too basic for mathematicians, Game Theory: An Introduction, Second Edition offers a blend of theory and applications, allowing readers to use theory and software to create and analyze real-world decision-making models.

With a rigorous, yet accessible, treatment of mathematics, the book focuses on results that can be used to determine optimal game strategies. Game Theory: An Introduction, Second Edition demonstrates how to use modern software, such as Maple™, Mathematica®, and Gambit, to create, analyze, and implement effective decision-making models. Coverage includes the main aspects of game theory including the fundamentals of two-person zero-sum games, cooperative games, and population games as well as a large number of examples from various fields, such as economics, transportation, warfare, asset distribution, political science, and biology. The Second Edition features:

• A new chapter on extensive games, which greatly expands the implementation of available models

• New sections on correlated equilibria and exact formulas for three-player cooperative games

• Many updated topics including threats in bargaining games and evolutionary stable strategies

• Solutions and methods used to solve all odd-numbered problems

• A companion website containing the related Maple and Mathematica data sets and code

A trusted and proven guide for students of mathematics and economics, Game Theory: An Introduction, Second Edition is also an excellent resource for researchers and practitioners in economics, finance, engineering, operations research, statistics, and computer science.

Table of contents: 

Matrix Two-Person Games

The Basics
Problems

The von Neumann Minimax Theorem
Proof of von Neumann’s Minimax Theorem (Optional)
Problems

Mixed Strategies
Properties of Optimal Strategies
Dominated Strategies

Solving 2 × 2 Games Graphically
Problems

Graphical Solution of 2 × m and n × 2 Games
Problems

Best Response Strategies
Problems
MapleTM/Mathematica R
Bibliographic Notes

Solution Methods for Matrix Games

Solution of Some Special Games
2 × 2 Games Revisited
Problems

Invertible Matrix Games
Completely Mixed Games
Problems

Symmetric Games
Problems

Matrix Games and Linear Programming
Setting Up the Linear Program: Method 1
A Direct Formulation Without Transforming: Method 2
Problems

Appendix: Linear Programming and the Simplex Method
The Simplex Method Step by Step
Problems

Review Problems
Maple/Mathematica
Invertible Matrices
Linear Programming: Method 1
Linear Programming: Method 2
Bibliographic Notes

Two-Person Nonzero Sum Games

The Basics
Problems

2 × 2 Bimatrix Games, Best Response, Equality of Payoffs
Calculation of the Rational Reaction Sets for 2 × 2 Games
Problems

Interior Mixed Nash Points by Calculus
Calculus Method for Interior Nash
Problems
Proof that There is a Nash Equilibrium for Bimatrix Games (Optional)

Nonlinear Programming Method for Nonzero Sum Two-Person Games
Summary of Methods for Finding Mixed Nash Equilibria
Problems

Correlated Equilibria
LP Problem for a Correlated Equilibrium
Problems

Choosing Among Several Nash Equilibria (Optional)
Problems
Maple/Mathematica
Mathematica for Lemke–Howson Algorithm
Bibliographic Notes

Games in Extensive Form: Sequential Decision Making

Introduction to Game Trees—Gambit
Problems

Backward Induction and Subgame Perfect Equilibrium
Problems
Subgame Perfect Equilibrium
Examples of Extensive Games Using Gambit
Problems
Bibliographic Notes

n-Person Nonzero Sum Games and Games with a Continuum of Strategies

The Basics
Problems

Economics Applications of Nash Equilibria
Cournot Duopoly
A Slight Generalization of Cournot
Cournot Model with Uncertain Costs
The Bertrand Model
The Stackelberg Model
Entry Deterrence
Problems

Duels (Optional)
Silent Duel on [0,1] (Optional)
Problem

Auctions (Optional)
Complete Information
Problems
Incomplete Information
Symmetric Independent Private Value Auctions
Problem
Bibliographic Notes

Cooperative Games

Coalitions and Characteristic Functions
Problems
More on the Core and Least Core
Problems

The Nucleolus
An Exact Nucleolus for Three-Player Games
Problems

The Shapley Value
Problems

Bargaining
The Nash Model with Security Point
Threats
The Kalai–Smorodinsky Bargaining Solution
Sequential Bargaining
Problems

Review Problems
Maple/Mathematica
Finding the Nucleolus One Step at a Time
Mathematica Code for Three-Person Nucleolus
The Shapley Value with Maple
Maple and Bargaining
Bibliographic Notes

Evolutionary Stable Strategies and Population Games

Evolution
Properties of an ESS
Problems

Population Games

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Tags: E N Barron, Game, Theory