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.
