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"Covering both noncooperative and cooperative games, this comprehensive introduction to game theory also includes some advanced chapters on auctions, games with incomplete information, games with vector payoffs, stable matchings, and the bargaining set. Mathematically oriented, the book presents every theorem alongside a proof. The material is presented clearly and every concept is illustrated with concrete examples from a broad range of disciplines. With numerous exercises the book is a thorough and extensive guide to game theory from undergraduate through graduate courses in economics, mathematics, computer science, engineering, and life sciences to being an authoritative reference for researchers"--

This is an extract from the 4-volume dictionary of economics, a reference book which aims to define the subject of economics today. 1300 subject entries in the complete work cover the broad themes of economic theory. It concentrates on the topic of game theory.

Traditional game theory requires at least two individuals. This book extends game theory to the inner workings of a single person.Using game theory to analyse single individuals makes sense if one thinks of individuals as consisting of two or more relatively autonomous partitions that might have conflicting motives. This is not to say that individuals are literally made up from multiple selves; it only suffices that we adopt a portrayal of the individual as a multilayered entity or of a dual nature, in a manner similar to Adam Smith's depiction of an ""impartial spectator"" ex.

Front Cover; Game Theory and Applications; Copyright Page; Table of Contents; Contributors; Preface; Chapter 1. Refinement of Nash Equilibrium: The Main Ideas; 1. INTRODUCTION; 2. BACKWARD INDUCTION AND FORWARD INDUCTION; 3. INFORMAL APPLICATIONS; 4. THE PROBLEM OF INCONSISTENCY; 5. THE EXISTENCE THEOREM: VERSION I; 6. FORMAL APPLICATIONS; 7. CONSISTENCY OF BELIEFS; 8. ADMISSIBILITY; 9. RESTRICTIONS ON OUT-OF-EQUILIBRIUM BELIEFS; 10. ALTERNATIVE VIEWS OF ""IRRELEVANT ALTERNATIVES""; 11. DEDUCTIONS BEYOND IIA; 12. CONCLUDING REMARKS; ACKNOWLEDGMENTS; APPENDIX A; APPENDIX B: PROOF OF THEOREM 3.

"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"--