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Lyapunov Functions in Differential Games
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.
Multiple Criteria Decision Making
The organizers of the 12th International Conference on Multiple Cri teria Decision Making (MCDM) held June 19-23, 1995 in Hagen received the second time the opportunity to prepare an international conference on MCDM in Germany; the first opportunity has been the 3rd International Conference on MCDM in Konigswinter, 1979. Quite a time ellapsed since then and therefore it might be interesting to compare some indicators of the development of the International Society on MCDM, which has been founded in Konigswinter. Stanley Zionts has been elected first president and all 44 participants of that Conference became founding members. Today our Society has over 1200 members and its own Journal (MCDM ...
The Berge Equilibrium: A Game-Theoretic Framework for the Golden Rule of Ethics
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 c...
The Golden Rule of Ethics
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-...
Mathematical Reviews
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Wonderful Solutions and Habitual Domains for Challenging Problems in Changeable Spaces
This book introduces a new paradigm called ‘Optimization in Changeable Spaces’ (OCS) as a useful tool for decision making and problem solving. It illustrates how OCS incorporates, searches, and constructively restructures the parameters, tangible and intangible, involved in the process of decision making. The book elaborates on OCS problems that can be modeled and solved effectively by using the concepts of competence set analysis, Habitual Domain (HD) and the mental operators called the 7-8-9 principles of deep knowledge of HD. In addition, new concepts of covering and discovering processes are proposed and formulated as mathematical tools to solve OCS problems. The book also includes r...
Multicriteria Optimization
Multi-criteria optimization problems naturally arise in practice when there is no single criterion for measuring the quality of a feasible solution. Since different criteria are contradictory, it is difficult and often impossible to find a single feasible solution that is good for all the criteria. Hence, some compromise is needed. As such, this book examines the commonly accepted compromise of the traditional Pareto-optimality approach. It also proposes one new alternative approach for generating feasible solutions to multi-criteria optimization problems. Finally, the book presents two chapters on the existing solution methods for two real-life, multi-criteria optimization problems.
The Golden Rule of Ethics
This book synthesizes the game-theoretic modeling of decision-making processes and an ancient moral requirement, called the Golden Rule of ethics. Of interest to undergraduate and graduate students and experts in the field of decision-making in complex control and management systems, or anyone interested in game theory and applications.
