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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.
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.
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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