The Golden Rule of Ethics

A Dynamic Game-Theoretic Framework Based on Berge Equilibrium

Vladislav I. Zhukovskiy, Mindia E. Salukvadze

• Publisher: CRC Press
• Year: 2021
• Print ISBN: 9780367681814
• eBook ISBN: 9781000370775
• Edition: 1
• Topic: Mathematics
• Subtopic: Game Theory
• Index: Mathematics

This book synthesizes the game-theoretic modeling of decision-making processes and an ancient moral requirement called the Golden Rule of ethics (GR). This rule states "Behave to others as you would like them to behave to you." The GR is one of the oldest, most widespread, and specific moral requirements that appear in Christianity, Islam, Judaism, Buddhism, and Confucianism.

This book constructs and justifies mathematical models of dynamic socio-economic processes and phenomena that reveal the mechanism of the GR and are based on the concept of Berge equilibrium. The GR can be naturally used for resolving or balancing conflicts, and its "altruistic character" obviously excludes wars, blood-letting, and armed clashes.

The previous book by the authors, The Berge Equilibrium: A Game-Theoretic Framework for the Golden Rule of Ethics, covers the static case of the GR. In this book, the dynamic case of the GR is investigated using the altruistic concept of Berge equilibrium and three factors as follows: 1) a modification of N.N. Krasovskii's mathematical formalization of differential positional games (DPGs), in view of the counterexamples given by A.I. Subbotin and A.F. Kononenko; 2) the method of guiding control, proposed by N.N. Krasovskii; and 3) the Germier convolution of the payoff functions of different players. Additionally, this book features exercises, problems, and solution tips collected together in Appendix 1, as well as new approaches to conflict resolution as presented in Appendices 2 to 4.

This book will be of use to undergraduate and graduate students and experts in the field of decision-making in complex control and management systems, as well as anyone interested in game theory and applications.

Chapter 1

Compendium

Start from inferiority in order to reach superiority; in other words, scratch your heels rather than the back of your head.

—Kozma Prutkov¹

Following this aphorism of K. Prutkov, let us start with preliminaries. Along this way, we will however try to forget his 40th aphorism, which says, “Explanatory sentences clarify obscure thoughts.” [232, p. 83]. In Section 1.1 of this chapter, the meaning of the Golden Rule of ethics and its connection to philosophy are briefly considered. For a detailed discussion, the interested reader is referred to Chapter 1 of the previous book [417]. In Section 1.2, the key sources and components of the static case of the Golden Rule for “frozen” conflicts [417], including the fundamental concept of Berge equilibrium, are outlined. In Section 1.3, the elementary statement of “struggle with nature” (single-criterion choice under uncertainty) is introduced, and our hierarchical approach to constructing a guaranteed (maximin) solution for this statement, in the static and dynamic cases, is presented. As an example, a discrete-time model of optimal advertising is considered. In Section 1.4, the principle of minimax regret and the concept of guaranteed solution in risks are described.

1.1 What is the Meaning of the Golden Rule of Ethics?

Quod tibi fieri non vis, alteri ne feceris.²

In this section, The Golden Rule of ethics in different religions as well as its connection with philosophy, ethics, and moral behavior are discussed in detail.

1.1.1 The Golden Rule as a basis of world religions

The Golden Rule of ethics is a general moral rule that can be formulated in the following way: “Behave to others as you would like them to behave to you.” The negative statement of this rule is: “Do not do unto others what you don’t want others to do unto you.”

¹ An English tran...

Table of contents

• Cover
• Half Title
• Series Page
• Title Page
• Copyright Page
• Dedication
• Table of Contents
• Editorial board
• Abstract
• Biography of Mindia E. Salukvadze
• Introduction
• 1 Compendium
• 2 Mathematical model of the Golden Rule of ethics in form of differential positional game
• 3 Berge equilibria in multistage games
• Appendix 1: Exercises, problems, and solution tips
• Appendix 2: Pareto equilibrium in threats and counter-threats for a differential three-player game
• Appendix 3: Guaranteed solution for risk-neutral decision-maker: an analog of maximin in single-criterion choice problems
• Appendix 4: The concept of strong coalitional equilibrium
• Bibliography
• Subject Index
• Author Index