The Berge Equilibrium: A Game-Theoretic Framework for the Golden Rule of Ethics
- 2020
- Buch
- Verfasst von
- Mindia E. Salukvadze
- Vladislav I. Zhukovskiy
- Verlag
- Springer International Publishing
Über dieses Buch
Über dieses Buch
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.
Inhaltsverzeichnis
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Frontmatter
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Chapter 1. What Is the Golden Rule of Ethics?
Mindia E. Salukvadze, Vladislav I. ZhukovskiyAbstractFirst of all, the essence of the Golden Rule is elucidated. Then its connections with philosophy, morality, duty, ethics, and politics are considered. -
Chapter 2. Static Case of the Golden Rule
Mindia E. Salukvadze, Vladislav I. ZhukovskiyAbstractIn this chapter, the concept of Berge equilibrium is introduced as a mathematical model of the Golden Rule. This concept was suggested by the Russian mathematician K. Vaisman in 1994. The Berge–Pareto equilibrium is formalized and sufficient conditions for the existence of such an equilibrium are established. As an application, the existence in the class of mixed strategies is proved. -
Chapter 3. The Golden Rule Under Uncertainty
Mindia E. Salukvadze, Vladislav I. ZhukovskiyAbstractAs an English proverb goes, “Between the cup and lip a morsel may slip.” This chapter is devoted to the Golden Rule under uncertainty, which accompanies every concept of equilibrium (in particular, Berge equilibrium). -
Chapter 4. Applications to Competitive Economic Models
Mindia E. Salukvadze, Vladislav I. ZhukovskiyAbstractThis chapter is devoted to a study of the equilibrium solutions (in the sense of Berge and Nash) of the Cournot and Bertrand oligopoly models. As a special case, the models with import as an uncertain disturbance are also analysed using mathematical theory of noncooperative games. -
Chapter 5. New Approaches to the Solution of Noncooperative Games and Multicriteria Choice Problems
Mindia E. Salukvadze, Vladislav I. ZhukovskiyAbstractThis chapter considers three new approaches to important problems of mathematical game theory and multicriteria choice, which are described in four sections (5.1–5.4). The first approach ensures payoff increase with simultaneous risk reduction in the Savage–Niehans sense in multicriteria choice problems (Sect. 5.1) and noncooperative games (Sect. 5.2). The second approach allows to stabilize coalitional structures in cooperative games without side payments under uncertainty (Sect. 5.3). The third approach serves to integrate the selfish Nash equilibrium with the altruistic Berge equilibrium. Note that the investigations in Sects. 5.2–5.4 involve a special Germeier convolution of criteria and calculation of its saddle point in mixed strategies. -
Chapter 6. Conclusion
Mindia E. Salukvadze, Vladislav I. ZhukovskiyAbstractGame theory is a mathematical framework for strategy analysis and design as well as for optimal decision-making under conflict and behavioral uncertainty. On the one hand, game theory plays a key role for modern economics; on the other, it suggests possible approaches and solutions for complex strategic problems in various fields of human activity. -
Backmatter
- Titel
- The Berge Equilibrium: A Game-Theoretic Framework for the Golden Rule of Ethics
- Verfasst von
-
Mindia E. Salukvadze
Vladislav I. Zhukovskiy
- Copyright-Jahr
- 2020
- Electronic ISBN
- 978-3-030-25546-6
- Print ISBN
- 978-3-030-25545-9
- DOI
- https://doi.org/10.1007/978-3-030-25546-6
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