This unique book presents decision analysis in the context of mathematical modeling and game theory. The author emphasizes and focuses on the model formulation and modeling building skills required for decision analysis, as well as the technology to support the analysis.
The primary objective of this book is illustrative in nature. It sets the tone through the introduction to mathematical modeling. The text provides a process for formally thinking about the problem and illustrates many scenarios and illustrative examples.
These techniques and this approach center on the fact (a) decision makers at all levels must be exposed to the tools and techniques available to help them in the decision process (b) decision makers as well as analysts need to have and use technology to assist in the entire analysis process, (c) the interpretation and explanation of the results are crucial to understanding the strengths and limitations of modeling, and (d) the interpretation and use of sensitivity analysis is essential.
The book begins with a look at decision making methods, including probability and statistics methods under risk of uncertainty. It moves to linear programming and multi-attribute decision making methods as a discussion of weighting methods. Game theory is introduced through conflict games and zero-sum or constant sum games. Nash equilibriums are next, followed by utility theory. Evolutionary stable strategies lead to Nash arbitration and cooperation methods and N-person methods presented for both total and partial conflict games.
Several real-life examples and case studies using game theory, are used throughout. This book would be best used for a senior-level course in mathematics, operations research, or graduate-level courses or decision modeling courses offered in business schools. The book will be interest to departments offering mathematical modeling courses with any emphasis on modeling for decision making.
Chapter 1: Introduction to Decision Models
1.1 Overview of Decision Making
1.3 Game Theory: Total Conflict
Example 1.5: A Total Conflict Game with Pure Strategies
1.4 Game Theory: Partial Conflict
1.5 Mathematical Modeling of Decisions
Chapter 2 Decision Theory and Expected Value
2.3 Decisions Under Risk: Probabilities are known or estimated in advance
2.4 Decisions under Uncertainty: Probabilities are not known nor can they be estimated
2.5 Decision Trees
2.6 Sequential Decisions and Conditional Probability (from Fox, Mathematical Modeling for Business Analytics, Taylor and Francis, 2018)
3.1 Introduction
3.2 Formulating Linear Programming Problems
3.3 Graphical Linear Programming
3.4 Linear Programming with Technology
3.5 Case Studies in Linear Programming
Projects
3.5.1 Modeling of Ranking Units using Data Envelopment Analysis (DEA) as a LP
3.5.2 Recruiting Raleigh Office (modified from McGrath, 2007)
References and Suggested Further Readings
Chapter 4 Multi-Attribute Decision Making using weighting schemes with SAW, AHP and TOPSIS
4.1.1 Rank Order Centroid (ROC)
4.1.2 Ratio Method for Weights
4.1.3 Pairwise Comparison (AHP)
4.2 Simple Additive Weights (SAW) Method
4.4 Analytical Hierarchy Process
4.5 Technique of Order Preference by Similarity to the Ideal Solution
Additional Reading and References
CHAPTER 5 Game Theory: Total Conflict
5.1 Introduction to Total Conflict Games
5.2 Models with Pure Strategy Solutions
5.2.1 Movement Arrows with two players and a payoff matrix:
5.3 Dominance and Dominated strategies
Exercises Section 5.1 Pure Strategy Games
5.3 Mixed Strategy in two player 2 strategy games
5.3 Linear Programming and Total Conflict Games
Chapter 6 Partial Conflict Games: The Classical Two-Player Games. Error! Bookmark not defined.
6.1 Partial Conflict Simultaneous Games Introduction
Reference and Further Readings
Chapter 7 Utility Theory
7.1 Introduction
7.2 Ordinal Numbers
7.3 Cardinal numbers
7.4 Utility
7.4 Von Neumann-Morgenstern Utilities Applied to Game Theory.
7.5 An alternative approach to the lottery method in utility theory for game theory
7.5.1 Lottery Method Illustrated
7.5.2 AHP Method
7.5.3 AHP Example in Game Theory
Chapter 8. Nash Equilibrium and Non-Cooperative Solutions in Partial Conflict Games
8.1 Introduction
8.2 Pure Strategies and Dominance review in symmetric games
8.4 Prudential Strategies with LP
8.5 Applications
Chapter 9 Evolutionary stable Strategies
Summary
Exercises Chapter 9
Reference
Chapter 10 Communications
10.1 Introduction
10.2 The Game of Chicken Without Communication
10.3 The Game of Chicken With Communication
10.3.1 Moving First or Committing to Move First
Classical Game Theory and the Missile Crisis (from Brahm ,1994)
Theory of Moves and the Missile Crisis
References and Further Reading
Chapter 11 Nash Arbitration Method
11.1 Introduction to Nash Arbitration
11.2 Methods without calculus
11.3 More than two strategies
11.4 Writer’s Guild Strike example with cardinal numbers
Chapter 12 Three Person Games
12.1 Three Person Zero-Sum games
12.2 Three-Person Partial Conflict Game ( Non-Zero Sum Game).
12.4 NON-ZERO Sum (non-constant sum) with no pure strategies.
12.5 3-Person game with Technology
Exercises
Chapter 13 Extensive Form Games
Example 1. Kidnapping for ransom
Applying TOM
Exercises Chapter 13
Biography
Dr. William P. Fox is currently a visiting professor of Computational Operations Research at the College of William and Mary. He is an emeritus professor in the Department of Defense Analysis at the Naval Postgraduate School and teaches a three-course sequence in mathematical modeling for decision making. He received his Ph.D. in Industrial Engineering from Clemson University. He has taught at the United States Military Academy for twelve years until retiring and at Francis Marion University where he was the chair of mathematics for eight years. He has many publications and scholarly activities including twenty plus books and one hundred and fifty journal articles.
Books by William P. Fox from CRC Press:
Probability and Statistics for Engineering and the Sciences with Modeling using R
(w/Rodney X. Sturdivant, 2023, CRC Press
Mathematical Modeling in the Age of the Pandemic, 2021, CRC Press.
Advanced Problem Solving Using Maple: Applied Mathematics, Operations Research, Business Analytics, and Decision Analysis (w/William Bauldry), 2020, CRC Press.
Mathematical Modeling with Excel (w/Brian Albright), 2020, CRC Press.
Nonlinear Optimization: Models and Applications, 2020, CRC Press.
Advanced Problem Solving with Maple: A First Course (w/William Bauldry), 2019. CRC Press.
Mathematical Modeling for Business Analytics, 2018, CRC Press.
