UNDERSTANDING GAME THEORY: INTRODUCTION TO THE ANALYSIS OF MANY AGENT SYSTEMS WITH COMPETITION AND COOPERATION

by Vasily N Kolokoltsov, Oleg A. Malafeyev

Steadily growing applications of game theory in modern science (including psychology, biology and economics) require sources to provide rapid access in both classical tools and recent developments to readers with diverse backgrounds. This book on game theory, its applications and mathematical methods, is written with this objective in mind.The book gives a concise but wide-ranging introduction to games including older (pre-game theory) party games and more recent topics like elections and evolutionary games and is generously spiced with excursions into philosophy, history, literature and politics. A distinguished feature is the clear separation of the text into two elementary and advanced, which makes the book ideal for study at various levels.Part I displays basic ideas using no more than four arithmetic operations and requiring from the reader only some inclination to logical thinking. It can be used in a university degree course without any (or minimal) prerequisite in mathematics (say, in economics, business, systems biology), as well as for self-study by school teachers, social and natural scientists, businessmen or laymen.Part II is a rapid introduction to the mathematical methods of game theory, suitable for a mathematics degree course of various levels. It includes an advanced material not yet reflected in standard textbooks, providing links with the exciting modern developments in financial mathematics (rainbow option pricing), tropical mathematics, statistical physics (interacting particles) and discusses structural stability, multi-criteria differential games and turnpikes.To stimulate the mathematical and scientific imagination, graphics by a world-renowned mathematician and mathematics imaging artist, A T Fomenko, are used. The carefully selected works of this artist fit remarkably into the many ideas expressed in the book.

300 pages, Hardcover

First published March 31, 2010

Reviews

[Erickson · Rating 5 out of 5]

The book is divided into two parts, the first part being the general ideas of game theory and some implications of it in many analyses such as Pascal's wager, volunteer's dilemma and many more. Has minimal mathematics unless insight necessitates the mathematics, and both the mathematics and the prose are very clear in explaining the implications of game theoretic reasoning. The part on Kant's Categorical Imperative was quite insightful.

The other part, which covers all the mathematical formalism sufficiently in-depth to be used for post-graduate studies, are included as well. I skipped this part for the time being since I have no background necessary to understand it, but even the first half alone is rich.

[Adeesh · Rating 5 out of 5]

Very lucid in language. Few grammatical errors, but nothing distracting. Excellent examples and was well satisfied with the mathematical approach. An excellent introduction to game theoretic analysis. Helped me tremendously.