What is a game? Classically, a game is perceived as something played by human beings. Its mathematical analysis is human-centered, explores the structures of particular games, economic or social environments and tries to model supposedly "rational" human behavior in search of appropriate "winning strategies". This point of view places game theory into a very special scientific corner where mathematics, economics and psychology overlap and mingle.This book takes a novel approach to the subject. Its focus is on mathematical models that apply to game theory in particular but exhibit a universal character and thus extend the scope of game theory considerably.This textbook addresses anyone interested in a general game-theoretic view of the world. The reader should have mathematical knowledge at the level of a first course in real analysis and linear algebra. However, possibly more specialized aspects are further elaborated and pointers to relevant supplementary literature are given. Moreover, many examples invite the reader to participate "actively" when going through the material. The scope of the book can be covered in one course on Mathematical Game Theory at advanced undergraduate or graduate level.Key FeaturesA novel approach to the mathematics of game theory is presented, which no other textbook has taken so far (to the author’s best knowledge). By reducing game-theoretic models to their mathematical structure, the role of mathematical game theory in general game theory is akin to the role of theoretical physics in general physics. Under this unifying structural realm, the strong links between game theory, mathematical optimization, information theory, economic modeling and quantum theory become evidentThe text treats the classical topics of game theory in this setting and connects them with the afore-mentioned fields mathematically. It should be a welcome addition to any mathematically oriented course on game theory. Moreover, it should be of interest to anyone in the fields of applied mathematics and mathematical economics and, generally, to anyone interested in a game-theoretic picture of the mathematics of the real world

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