in my forthcoming book on the subject (see https://doi.org/10.1142/12540
for more details). The aim is a comprehensive mathematical basis of game
theory that is akin to the role played by mathematical physics in
natural sciences.
General description from the book cover:
"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."
Ulrich Faigle
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