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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 parts: 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.
Sample Chapter(s)
Chapter 1: Around the prisoner's dilemma (6,732 KB)
Chapter 2: Auctions and networks (2,140 KB)
Chapter 7: At the doors of quantum games (2,570 KB)
Contents:
- Basic Ideas:
- Around the Prisoner's Dilemma
- Auctions and Networks
- Wise Men and Businessmen
- Hawks and Doves, Lions and Lambs
- Coalitions and Distribution
- Presidents and Dictators
- At the Doors of Quantum Games
- It's Party Time!
- Armed with Mathematics:
- A Rapid Course in Mathematical Game Theory
- Examples of Game Models
- Elements of More Advanced Analysis
Readership: Undergraduates and graduate students in applied mathematics, economics, business, finances and systems biology; non-experts interested in the application of mathematical methods and ideas in natural and social sciences, business and life.
