Vladislav I Zhukovskiy's Books

The Berge Equilibrium: A Game-Theoretic Framework for the Golden Rule of Ethics

By: Mindia E. Salukvadze,Vladislav I. Zhukovskiy

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The Berge Equilibrium: A Game-Theoretic Framework for the Golden Rule of Ethics

By: Mindia E. Salukvadze,Vladislav I. Zhukovskiy

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? Does the Berge equilibrium exist, and how can it be calculated? The Golden Rule of ethics, which appears in Christianity, Judaism, Islam, Buddhism, Confucianism and other world religions, states the following: “Behave towards others as you would like them to behave towards you." In any game, each party of conflict seeks to maximize some payoff. Therefore, for each player, the Golden Rule is implemented through the maximization of his/her payoff by all other players, which matches well with the concept of the Berge equilibrium. The approach presented here will be of particular interest to researchers (including undergraduates and graduates) and economists focused on decision-making under complex conflict conditions. The peaceful resolution of conflicts is the cornerstone of the approach: as a matter of fact, the Golden Rule precludes military clashes and violence. In turn, the new approach requires new methods; in particular, the existence problems are reduced to saddle point design for the Germeier convolution of payoff functions, with further transition to mixed strategies in accordance with the standard procedure employed by E. Borel, J. von Neumann, J. Nash, and their followers. Moreover, this new approach has proven to be efficient and fruitful with regard to a range of other important problems in mathematical game theory, which are considered in the Appendix.

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Page Count

290

Publisher

Springer Nature

Published Date

ISBN 10

3030255468

ISBN 13

9783030255466

Lyapunov Functions in Differential Games

By: Vladislav I Zhukovskiy

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Lyapunov Functions in Differential Games

By: Vladislav I Zhukovskiy

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 theor

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Page Count

299

Publisher

CRC Press

Published Date

ISBN 10

1482264994

ISBN 13

9781482264999

The Golden Rule of Ethics

A Dynamic Game-Theoretic Framework Based on Berge Equilibrium

By: Vladislav I. Zhukovskiy,Mindia E. Salukvadze

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The Golden Rule of Ethics

A Dynamic Game-Theoretic Framework Based on Berge Equilibrium

By: Vladislav I. Zhukovskiy,Mindia E. Salukvadze

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.

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Page Count

325

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CRC Press

Published Date

ISBN 10

1000370755

ISBN 13

9781000370751

Book's by Vladislav I Zhukovskiy

The Berge Equilibrium: A Game-Theoretic Framework for the Golden Rule of Ethics

The Berge Equilibrium: A Game-Theoretic Framework for the Golden Rule of Ethics

Lyapunov Functions in Differential Games

Lyapunov Functions in Differential Games

The Golden Rule of Ethics

The Golden Rule of Ethics

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