A Gentle Introduction to Game Theory VOLUME 13 1st edition by Saul Stahl ISBN 0821813390 9780821813393

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ISBN 10:       0821813390
ISBN 13: 978-0821813393
Author:         Saul Stahl

The mathematical theory of games was first developed as a model for situations of conflict, whether actual or recreational. It gained widespread recognition when it was applied to the theoretical study of economics by von Neumann and Morgenstern in Theory of Games and Economic Behavior in the 1940s. The later bestowal in 1994 of the Nobel Prize in economics on Nash underscores the important role this theory has played in the intellectual life of the twentieth century.

This volume is based on courses given by the author at the University of Kansas. The exposition is “gentle” because it requires only some knowledge of coordinate geometry; linear programming is not used. It is “mathematical” because it is more concerned with the mathematical solution of games than with their applications.

Existing textbooks on the topic tend to focus either on the applications or on the mathematics at a level that makes the works inaccessible to most non-mathematicians. This book nicely fits in between these two alternatives. It discusses examples and completely solves them with tools that require no more than high school algebra.

In this text, proofs are provided for both von Neumann’s Minimax Theorem and the existence of the Nash Equilibrium in the $2 times 2$ case. Readers will gain both a sense of the range of applications and a better understanding of the theoretical framework of these two deep mathematical concepts.

A Gentle Introduction to Game Theory VOLUME 13 1st Table of contents:

1. Introduction to Game Theory
   1.1 What is Game Theory?
   1.2 Brief History and Applications
   1.3 Key Concepts and Assumptions

2. Basic Concepts and Terminology
   2.1 Players, Strategies, and Payoffs
   2.2 Games in Normal Form
   2.3 Dominant and Dominated Strategies

3. Strategic Games
   3.1 Pure Strategy Nash Equilibrium
   3.2 Mixed Strategies
   3.3 Examples of Strategic Games

4. Extensive Form Games
   4.1 Game Trees and Representation
   4.2 Subgame Perfect Equilibrium
   4.3 Backward Induction

5. Cooperative Games
   5.1 The Core
   5.2 Shapley Value
   5.3 Applications of Cooperative Games

6. Repeated Games
   6.1 Finite and Infinite Repetition
   6.2 Folk Theorem
   6.3 Applications of Repeated Games

7. Bayesian Games and Incomplete Information
   7.1 Games with Incomplete Information
   7.2 Bayesian Nash Equilibrium
   7.3 Applications to Auctions

8. Evolutionary Game Theory
   8.1 Replicator Dynamics
   8.2 Evolutionarily Stable Strategies
   8.3 Biological and Social Applications

9. Applications of Game Theory
   9.1 Economics and Markets
   9.2 Political Science and Voting
   9.3 Military and Security
   9.4 Artificial Intelligence

10. Advanced Topics
    10.1 Mechanism Design
    10.2 Auctions and Bidding Strategies
    10.3 Behavioral Game Theory

11. Mathematical Foundations
    11.1 Probability and Utility Theory
    11.2 Linear Algebra in Game Theory
    11.3 Optimization Techniques

12. Case Studies and Real-World Examples
    12.1 Classic Game Theory Problems (Prisoner’s Dilemma, etc.)
    12.2 Case Studies in Economics and Business
    12.3 Case Studies in Biology and Evolution

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