Understanding Game Theory: Introduction to the Analysis of Many Agent Systems with Competition and Cooperation

UNDERSTANDING GAME THEORY

Posted: 27 Apr 2010

See all articles by Vassili N. Kolokoltsov

Vassili N. Kolokoltsov

University of Warwick - Department of Statistics

Oleg Malafeyev

Saint Petersburg State University - Faculty of Applied Mathematics and Control Processes

Date Written: January 20, 2010

Abstract

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.

Keywords: Game Theory, Mathematical Modeling, Evolutionary Biology, Conflict and Cooperation, Multi-Criteria Optimization, Collective Choice, Replicator Dynamics, Financial Mathematics, Rainbow Options, Structural Stability, Lyapunov Stability, Multi-Criteria Optimization, Turnpikes

Suggested Citation

Kolokoltsov, Vassili N. and Malafeyev, Oleg, Understanding Game Theory: Introduction to the Analysis of Many Agent Systems with Competition and Cooperation (January 20, 2010). UNDERSTANDING GAME THEORY , Available at SSRN: https://ssrn.com/abstract=1589193

Vassili N. Kolokoltsov (Contact Author)

University of Warwick - Department of Statistics ( email )

Gibbet Hill Rd.
Coventry, West Midlands CV4 8UW
United Kingdom

HOME PAGE: http://www2.warwick.ac.uk/fac/sci/statistics/staff/academic/kolokoltsov/

Oleg Malafeyev

Saint Petersburg State University - Faculty of Applied Mathematics and Control Processes ( email )

Universitetskii prospekt 35
Petergof
Saint Petersburg, 198504
Russia

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