Understanding Game Theory: Introduction to the Analysis of Many Agent Systems with Competition and Cooperation
Game theory is the mathematical discipline aimed to model various interactions of living organisms in quantitative terms. Game theory, as the universal method for the analysis of social interactions has wide applications in economics, in the theory of control and management, financial mathematics, evolutionary biology, sociology, psychology and politics, in modelling different social processes, in particular, the processes of democratic elections, processes of fair distributions of resource, processes of arms control, etc. The book is designed for all wishing to get acquainted with main ideas and methods of game theory.
The first part gives an elementary but systematic exposition of the main ideas of modern game theory without any special prerequisites in mathematics (secondary school level should be quite sufficient). The second part is devoted mostly to the mathematical methods of the theory.
To stimulate mathematical and scientific imagination and to add
charm to the book we illustrate it by carefully selected artistic
graphics of a world renowned mathematician and mathematics imaging
artist A.T. Fomenko (to whom the authors express their deepest
gratitude for allowing to use his works in this text). Though these
works were originally designed to illustrate the geometric structure
of the Universe, they fit nicely in the circle of ideas dealt with here.
For the second edition the book was essentially revised and updated.
When preparing the 1st part of our book we aimed at selecting material
reflecting the most fundamental part of the theory that we did not expected to become outdate soon.
Therefore the first part remained mostly unchanged (with couple of new insightful examples added).
On the other hand, for the second part, apart from correcting typos, lots of new material was prepared.
In particular, Chapter 10 was essentially enlarged by more recent developments on game-theoretic treatment of option pricing and two completely new chapters were written: Chapter 12 on games with many agents analysed via the statistical limit of infinite number of players, and Chapter 13 on quantum games. These two topics represent arguably the most bright new trends in the 21 st century game theory. Due to strong physics input, the theory of quantum games still remains separated from the main stream of game theory, and our exposition is possibly the first appearance of quantum games in a mathematics textbook.