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 Decision Analysis through Modeling and Game Theory 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 with 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 of interest to departments offering mathematical modeling courses with any emphasis on modeling for decision making.

Table of Contents:
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 Summary 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) Exercises References and Suggested Further Readings 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 Additional Reading and References 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 Summary 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 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 7.6 Summary and Conclusions References 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 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 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 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 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 Exercises Chapter 13 Extensive Form Games 13.1 Introduction Example 1. Kidnapping for ransom Applying TOM Exercises Chapter 13