Author: R. Henn
Publisher: Springer Science & Business Media
ISBN: 3642454941
Category : Business & Economics
Languages : en
Pages : 714

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Author: Jean-Pierre Aubin
Publisher: Courier Corporation
ISBN: 048646265X
Category : Mathematics
Languages : en
Pages : 658

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Book Description
Mathematical economics and game theory approached with the fundamental mathematical toolbox of nonlinear functional analysis are the central themes of this text. Both optimization and equilibrium theories are covered in full detail. The book's central application is the fundamental economic problem of allocating scarce resources among competing agents, which leads to considerations of the interrelated applications in game theory and the theory of optimization. Mathematicians, mathematical economists, and operations research specialists will find that it provides a solid foundation in nonlinear functional analysis. This text begins by developing linear and convex analysis in the context of optimization theory. The treatment includes results on the existence and stability of solutions to optimization problems as well as an introduction to duality theory. The second part explores a number of topics in game theory and mathematical economics, including two-person games, which provide the framework to study theorems of nonlinear analysis. The text concludes with an introduction to non-linear analysis and optimal control theory, including an array of fixed point and subjectivity theorems that offer powerful tools in proving existence theorems.

Author: Julio González-Díaz
Publisher: American Mathematical Society
ISBN: 1470465736
Category : Mathematics
Languages : en
Pages : 324

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Book Description
Game theory provides a mathematical setting for analyzing competition and cooperation in interactive situations. The theory has been famously applied in economics, but is relevant in many other sciences, such as political science, biology, and, more recently, computer science. This book presents an introductory and up-to-date course on game theory addressed to mathematicians and economists, and to other scientists having a basic mathematical background. The book is self-contained, providing a formal description of the classic game-theoretic concepts together with rigorous proofs of the main results in the field. The theory is illustrated through abundant examples, applications, and exercises. The style is distinctively concise, while offering motivations and interpretations of the theory to make the book accessible to a wide readership. The basic concepts and results of game theory are given a formal treatment, and the mathematical tools necessary to develop them are carefully presented. Cooperative games are explained in detail, with bargaining and TU-games being treated as part of a general framework. The authors stress the relation between game theory and operations research. The book is suitable for a graduate or an advanced undergraduate course on game theory.

Author: Herve Moulin
Publisher: NYU Press
ISBN: 0814764231
Category : Business & Economics
Languages : en
Pages : 291

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Book Description
The second edition of Herve Moulin's highly successful book outlines the fundamental concepts of game theory—one of the most provocative and fruitful applications of mathematics to the human sciences—and demonstrates its uses in economic and political discourse. Thoroughly revised, and now published with an accompanying workbook of 89 exercises, this rigorous yet accessible test explains the uses of game theory in largely nontechnical terms. Moulin carefully discusses the behavioral scenarios underlying the various equilibrium concepts. He provides a self-contained exposition of basic equilibrium concepts for strategic games: perfect (sophisticated) equilibrium, Nash's noncooperative example, Aumann's strong and correlated example, and several versions of the core. The author is concerned less with mathematical refinements than with helping the reader understand the strategic stories backing these concepts. HIs examples therefore give a fair account of the current game models used in economics, politics, and sociology. Addressed here are oligopoly theory, the provision of public gtoods, auctions, voting procedures, and cost allocation problems, as well as the classic prisoner's dilemma, tic-tac-toe, and Marienbad games. Extremely popular in its original French edition and in its first English version, Moulin's excellent introductory text is now, more than ever, the book to answer the essential questions about the application of game theory to the social sciences.

Author: Samuel Karlin
Publisher:
ISBN:
Category : Economics, Mathematical
Languages : en
Pages : 408

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Author: Tatsuro Ichiishi
Publisher: Elsevier
ISBN: 1483295060
Category : Mathematics
Languages : en
Pages : 177

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Book Description
Game Theory for Economic Analysis

Author: A. J. Jones
Publisher: Horwood Publishing
ISBN: 9781898563143
Category : Mathematics
Languages : en
Pages : 304

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Book Description
This modern, still relevant text is suitable for senior undergraduate and graduate students, teachers and professionals in mathematics, operational research, economics, sociology; and psychology, defence and strategic studies, and war games. Engagingly written with agreeable humor, the book can also be understood by non-mathematicians. It shows basic ideas of extensive form, pure and mixed strategies, the minimax theorem, non-cooperative and co-operative games, and a ''first class'' account of linear programming, theory and practice. The text is self-contained with comprehensive source references. Based on a series of lectures given by the author in the theory of games at Royal Holloway College, it gives unusually comprehensive but concise treatment of co-operative games, an original account of bargaining models, with a skilfully guided tour through the Shapely and Nash solutions for bimatrix games and a carefully illustrated account of finding the best threat strategies.

Author: James N. Webb
Publisher: Springer Science & Business Media
ISBN: 1846286360
Category : Mathematics
Languages : en
Pages : 237

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Book Description
The outstanding feature of this book is that it provides a unified account of three types of decision problem. It covers the basic ideas of decision theory, classical game theory, and evolutionary game theory in one volume. No background knowledge of economics or biology is required as examples have been carefully selected for their accessibility. Detailed solutions to the numerous exercises are provided at the back of the book, making it ideal for self-study. This introduction to game theory is intended as a first course for undergraduate students of mathematics, but it will also interest advanced students or researchers in biology and economics.

Author: Otto Moeschlin
Publisher: North Holland
ISBN:
Category : Business & Economics
Languages : en
Pages : 486

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Author: Robert J. Aumann
Publisher: American Mathematical Soc.
ISBN: 9780821805251
Category : Business & Economics
Languages : en
Pages : 306

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Book Description
Since the publication of "Theory of Games and Economic Behavior" by von Neumann and Morgenstern, the concept of games has played an increasing role in economics. It also plays a role of growing importance in other sciences, including biology, political science, and psychology. Many scientists have made seminal advances and continue to be leaders in the field, including Harsanyi, Shapley, Shubik, and Selten. Professor Robert Aumann, in addition to his important contributions to game theory and economics, made a number of significant contributions to mathematics. This volume provides a collection of essays in mathematical economics and game theory, including cutting-edge research on noncooperative game theory and its foundations, bargaining theory, and general equilibrium theory. Also included is a reprint of Aumann's classic paper, "Acceptable Points in General Cooperative n-Person Games" and of the oft-cited, yet hard to find, paper by Maschler, "The Worth of a Cooperative Enterprise to Each Member". This book illustrates the wide range of applications of mathematics to economics, game theory, and social choice. The volume is dedicated to Professor Robert J. Aumann, Hebrew University, Jerusalem, Israel, for his contributions in mathematics and social sciences.