Models of Conflict and Cooperation
Rick Gillman, David Housman
Price
1670.00
ISBN
9780821891834
Language
English
Pages
432
Format
Paperback
Dimensions
180 x 240 mm
Year of Publishing
2012
Territorial Rights
Restricted
Imprint
American Mathematical Society
Catalogues

Models of Conflict and Cooperation is a comprehensive, introductory, game theory text for general undergraduate students. As a textbook, it provides a new and distinctive experience for students working to become quantitatively literate. Each chapter begins with a "dialogue" that models quantitative discourse while previewing the topics presented in the rest of the chapter. Subsequent sections develop the key ideas starting with basic models and ending with deep concepts and results. Throughout all of the sections, attention is given to promoting student engagement with the material through relevant models, recommended activities, and exercises. The general game models that are discussed include deterministic, strategic, sequential, bargaining, coalition, and fair division games. A separate, essential chapter discusses player preferences. All of the chapters are designed to strengthen the fundamental mathematical skills of quantitative literacy: logical reasoning, basic algebra and probability skills, geometric reasoning, and problem solving. A distinctive feature of this book is its emphasis on the process of mathematical modeling.

Rick Gillman, Valparaiso University, IN, and David Housman, Goshen College, IN

Preface

Chapter 1. Deterministic Games

A Very Simple Game
Rules of the Game
Heuristics and Strategies
Game Trees
A Solution for Nim
Theorems of Zermelo and Nash

Chapter 2. Player Preferences

Measurement
Ordinal Preferences
Cardinal Preferences
Ratio Scale Preferences

Chapter 3. Strategic Games

Tosca
Fingers and Matches
Four Solution Concepts
Once Again, Game Trees
Trees and Matrices

Chapter 4. Probabilistic Strategies

It’s Child’s Play
Mixed Strategy Solutions
Finding Solutions in 2 × 2 Games
Nash Equilibria in m × 2 Games
Zero-Sum Games

Chapter 5. Strategic Game Cooperation

Experiments
The Prisoners’ Dilemma
Resolving the Prisoners’ Dilemma

Chapter 6. Negotiation and Arbitration

A Simple Negotiation
Bargaining Games
The Egalitarian Method
The Raiffa Method
The Nash Method

Chapter 7. Coalition Games

A Savings Allocation Problem
Two Properties and Five Methods
The Shapley Method
The Nucleolus Method
You Can’t Always Get What You Want

Chapter 8. Fair Division

An Inheritance Problem
Fair Division Games and Methods
Fairness Properties
Choosing a Fair Method
Epilogue
Answers to Selected Exercises
Deterministic Games
Player Preferences
Strategic Games
Probabilistic Strategies
Strategic Game Cooperation
Negotiation and Arbitration
Coalition Games
Fair Division
Bibliography
Index

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