The Dynamics of Decision Processes, © 2012-2015, Gerald H Thomas, is a series of white papers to Geometry, Language and Strategy, Thomas, 2006, World Scientific (New York), which I refer to as Vol. 1. The white papers have been expanded and form the basis of Vol. 2, published in World Scientific, 2016. Volume 2 details how game theory can be thought of as a DC phenomenon and then extended to a special case of AC behaviors, namely those associated with resonant or harmonic effects where only discrete frequencies appear. These AC behaviors include all steady-state behaviors as well as to possible transient behaviors. Such additional behaviors arise from initial and boundary conditions that act like external forces. Volume 2 is an engineering textbook that applies decision process theory to decision processes. AC type solutions have proved fruitful in electrical engineering and, we hope, will open the possibility for a new discipline of decision engineering.
These white papers consists of 13 chapters, including a summary at the end of each chapter with exercises to solidify understanding and extend the concepts presented. To access a chapter, click on the chapter entries below. New concepts and distinctions are indicated in the text as bold italics. A summary of these concepts and distinctions can be found in the index. The published version, Vol. 2, extends these papers to 20 chapters with significantly updated content, format and organization.
In the first part, chapters 1-4, we lay the theoretical foundations starting with the descriptive basis of game theory, which we also take as our descriptive basis.
- Preface Forward and Introduction, including chapter 1 develops the necessary ideas from physics, differential geometry and game theory on which to create a dynamic theory of decisions.
- chapter 2 inertial behaviors extends the ideas from the previous chapter to include applied forces that move decisions to a new position as distinguished from inertial forces that tend to leave things unchanged.
- chapter 3 Persistent behaviors provides a consistent theory of decisions based on the ideas developed in the first two chapters. Persistency is an important element of the theory, providing a theoretical foundation to describe the agents or players as well as a mechanism for incorporating codes of conduct into the theory,
- chapter 4 Stationary behaviors develops a complete solution of a class of models describing realistic decision processes. This chapter is technical and provides, along with appropriate exercises, sufficient grounding for further investigations of the theory.
In the second part, chapters 5-7, we inquire into the nature of the theory with the scenarios for the prisoner’s dilemma and Robinson Crusoe economics and conclude with a general review of game theory and economic approaches.
- chapter 5 prisoners dilemma is a decision process theory solution to a classic paradox in the theory of games.
- chapter 6 Robinson Crusoe economics: this includes a detailed dynamic account of the economic Robinson Crusoe model
- chapter 7 process formulation puts decision process theory in the context of the game theory and systems dynamics literature.
In the third part, chapters 8-12, we numerically solve games with more than one person, each of which can have one or more strategies. These solutions elucidate the engineering issues that arise when analyzing decision processes based on our deterministic perspective. This third part shows the reader how the theory can be applied in a variety of situations.
- chapter 8 Vorticity with multiple active strategies provides general guide to use decision process theory with quasi-stationary harmonics. It expands the ability to find quantitative dynamic solutions to the case of multiple strategies and multiple players.
- chapter 9 Two-strategy two-person decision processes applies the general techniques to an illustrative example, the attack-defense model
- chapter 10 Interactivity of decision mechanisms examines the interactivity of the various decision mechanisms. We understand each mechanism in isolation but not how they interact with each other.
- chapter 11 Physical distinctions for decision processes summarizes the main distinctions introduced in decision process theory that are physical in the sense they are related more directly to the underlying differential geometry and its equations.
- chapter 12 Social distinctions for decision processes summarizes the main distinctions introduced in decision process theory that are social in the sense that they are intimately related to how the theory is applied in decision processes with human agents that interact; they compete and cooperate.
Afterword Bibliography and Index: the afterword suggests next steps.
I welcome peer review as well as all feedback. When appropriate, I will publish an updated version of this book based on that review and feedback, along with corrections for errors that are bound to creep into a project of this size.