Decision Analysis through Modeling and Game Theory

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 PressMathematical 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.

• Chapter 1: Introduction to Decision Models 1.1 Overview of Decision Making 1.2 Decision Theory 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 1.4 ILLUSTRATE EXAMPLES 1.5 Technology Chapter 2 Decision Theory and Expected Value 2.1 Introduction 2.2 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) Chapter 3 Decisions under certainty: Mathematical Programming Modeling: Linear, Integer, and Mixed Integer Optimization 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) Chapter 4 Multi-Attribute Decision Making using weighting schemes with SAW, AHP and TOPSIS 4.1 Weighting Methods 4.1.1 Rank Order Centroid (ROC) 4.1.2 Ratio Method for Weights 4.1.3 Pairwise Comparison (AHP) 4.1.4 Entropy Method: 4.2 Simple Additive Weights (SAW) Method 4.3 Weighted Product Method 4.4 Analytical Hierarchy Process 4.5 Technique of Order Preference by Similarity to the Ideal Solution Methodology, Normalization, EXERCISES Chapter 4 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: 5.2.2 Saddle Point Method 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 6.2 The Prisoner’s Dilemma 6.3 The Game of Chicken 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 7.6 Summary and Conclusions 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 8.3 Equalizing Strategies 8.4 Prudential Strategies with LP 8.5 Applications EXERCISES Chapter 9 Evolutionary stable Strategies 9.1 Introduction Exercises Chapter 9 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 10.3.2 Issuing a Threat 10.3.3 Issuing a Promise 10.4 Credibility Classical Game Theory and the Missile Crisis (from Brahm ,1994) Theory of Moves and the Missile Crisis Chapter 10 Exercises 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 Introduction Nash Arbitration Scheme 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 Chapter 13 Extensive Form Games 13.1 Introduction Example 1. Kidnapping for ransom Applying TOM