Vladislav I. Zhukovskiy - Böcker

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.

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.

A major step in differential games is determining an explicit form of the strategies of players who follow a certain optimality principle. To do this, the associated modification of Bellman dynamic programming problems has to be solved; for some differential games this could be Lyapunov functions whose "arsenal" has been supplied by stability theory. This approach, which combines dynamic programming and the Lyapunov function method, leads to coefficient criteria, or ratios of the game math model parameters with which optimal strategies of the players not only exist but their analytical form can be specified. In this book coefficient criteria are derived for numerous new and relevant problems in the theory of linear-quadratic multi-player differential games. Those criteria apply when the players formulate their strategies independently (non co-operative games) and use non-Nash equilibria or when the game model recognizes noise, perturbation and other uncertainties of which only their ranges are known (differential games under uncertainty). This text is useful for researchers, engineers and students of applied mathematics, control theory and the engineering sciences.

The goal of this book is to elaborate on the main principles of the theory of the Berge equilibrium by answering the following two questions: What are the basic properties of the Berge equilibrium?