Understanding Game Theory

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.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.This new edition has been updated and enlarged. In particular, two new chapters were added on statistical limit of games with many agents and on quantum games, reflecting possibly the two most stunning trends in the game theory of the 21st century.Contents: Basic Ideas:Around the Prisoner's DilemmaAuctions and NetworksWise Men and BusinessmenHawks and Doves, Lions and LambsCoalitions and DistributionPresidents and DictatorsAt the Doors of Quantum GamesIt's Party Time!Armed with Mathematics:A Rapid Course in Mathematical Game TheoryExamples of Game Models and MethodsElements of More Advanced AnalysisGames of Many Agents in Statistical LimitQuantum Games
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.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;Quantum Games0Key Features:The updated second edition contains two new chapters on statistical limit of games with many agents and on quantum gamesReveals information on game theory in relation to other fields of human culture, making the book accessible to a wider range of readers and stresses natural connections to a variety of sciences and human creative activities (biology, philosophy, sociology, politics, military strategy, etc)Provides a clear separation into two parts of elementary and advanced levels, allowing a grasps of ideas without spending too much time on unnecessary technicalitiesIncludes exercises with detailed hints to enhance the appreciation of the materials presentedHighly illustrated in graphics by world-renowned mathematician and mathematics imaging artist, A T Fomenko