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Mathematical Methods of Game and Economic Theory

Author: Jean-Pierre Aubin

Publisher: Courier Corporation

Published: 2007-01-01

Total Pages: 658

ISBN-13: 048646265X

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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.

Book Synopsis Mathematical Methods of Game and Economic Theory by : Jean-Pierre Aubin

Download or read book Mathematical Methods of Game and Economic Theory written by Jean-Pierre Aubin and published by Courier Corporation. This book was released on 2007-01-01 with total page 658 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Mathematical Methods of Game and Economic Theory

Author: Jean-Pierre Aubin

Publisher: Dover Publications

Published: 2013-12-23

Total Pages: 656

ISBN-13: 9780486789354

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This text begins with optimization theory and convex analysis, followed by topics in game theory and mathematical economics, and concluding with an introduction to nonlinear analysis and control theory. 1982 edition.

Book Synopsis Mathematical Methods of Game and Economic Theory by : Jean-Pierre Aubin

Download or read book Mathematical Methods of Game and Economic Theory written by Jean-Pierre Aubin and published by Dover Publications. This book was released on 2013-12-23 with total page 656 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text begins with optimization theory and convex analysis, followed by topics in game theory and mathematical economics, and concluding with an introduction to nonlinear analysis and control theory. 1982 edition.

Mathematical Methods and Theory in Games, Programming, and Economics

Author: Samuel Karlin

Publisher: Elsevier

Published: 2014-05-12

Total Pages: 444

ISBN-13: 1483222985

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Matrix Games, Programming, and Mathematical Economics deals with game theory, programming theory, and techniques of mathematical economics in a single systematic theory. The principles of game theory and programming are applied to simplified problems related to economic models, business decisions, and military tactics. The book explains the theory of matrix games and some of the tools used in the analysis of matrix games. The text describes optimal strategies for matrix games which have two basic properties, as well as the construction of optimal strategies. The book investigates the structure of sets of solutions of discrete matrix games, with emphasis on the class of games whose solutions are unique. The examples show the use of dominance concepts, symmetries, and probabilistic arguments that emphasize the principles of game theory. One example involves two opposing political parties in an election campaign, particularly, how they should distribute their advertising efforts for wider exposure. The text also investigates how to determine an optimal program from several choices that results with the maximum or minimum objective. The book also explores the analogs of the duality theorem, the equivalence of game problems to linear programming problems, and also the inter-industry nonlinear activity analysis model requiring special mathematical methods. The text will prove helpful for students in advanced mathematics and calculus. It can be appreciated by mathematicians, engineers, economists, military strategists, or statisticians who formulate decisions using mathematical analysis and linear programming.

Book Synopsis Mathematical Methods and Theory in Games, Programming, and Economics by : Samuel Karlin

Download or read book Mathematical Methods and Theory in Games, Programming, and Economics written by Samuel Karlin and published by Elsevier. This book was released on 2014-05-12 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: Matrix Games, Programming, and Mathematical Economics deals with game theory, programming theory, and techniques of mathematical economics in a single systematic theory. The principles of game theory and programming are applied to simplified problems related to economic models, business decisions, and military tactics. The book explains the theory of matrix games and some of the tools used in the analysis of matrix games. The text describes optimal strategies for matrix games which have two basic properties, as well as the construction of optimal strategies. The book investigates the structure of sets of solutions of discrete matrix games, with emphasis on the class of games whose solutions are unique. The examples show the use of dominance concepts, symmetries, and probabilistic arguments that emphasize the principles of game theory. One example involves two opposing political parties in an election campaign, particularly, how they should distribute their advertising efforts for wider exposure. The text also investigates how to determine an optimal program from several choices that results with the maximum or minimum objective. The book also explores the analogs of the duality theorem, the equivalence of game problems to linear programming problems, and also the inter-industry nonlinear activity analysis model requiring special mathematical methods. The text will prove helpful for students in advanced mathematics and calculus. It can be appreciated by mathematicians, engineers, economists, military strategists, or statisticians who formulate decisions using mathematical analysis and linear programming.

Mathematical Methods and Theory in Games, Programming, and Economics

Author: Samuel Karlin

Publisher: Courier Corporation

Published: 2003-01-01

Total Pages: 838

ISBN-13: 0486495272

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This single-volume edition of a 2-volume set, discusses the theory of matrix games, linear and nonlinear programming, and mathematical economics while clarifying key mathematical concepts and demonstrates their applicability. 1959 edition.

Book Synopsis Mathematical Methods and Theory in Games, Programming, and Economics by : Samuel Karlin

Download or read book Mathematical Methods and Theory in Games, Programming, and Economics written by Samuel Karlin and published by Courier Corporation. This book was released on 2003-01-01 with total page 838 pages. Available in PDF, EPUB and Kindle. Book excerpt: This single-volume edition of a 2-volume set, discusses the theory of matrix games, linear and nonlinear programming, and mathematical economics while clarifying key mathematical concepts and demonstrates their applicability. 1959 edition.

Understanding Game Theory

Author: Vasilij Nikiti? Kolokol'cov

Publisher: World Scientific

Published: 2010

Total Pages: 301

ISBN-13: 9814291722

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This work offers 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.

Book Synopsis Understanding Game Theory by : Vasilij Nikiti? Kolokol'cov

Download or read book Understanding Game Theory written by Vasilij Nikiti? Kolokol'cov and published by World Scientific. This book was released on 2010 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work offers 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.

Understanding Game Theory: Introduction To The Analysis Of Many Agent Systems With Competition And Cooperation (Second Edition)

Author: Vasily N Kolokoltsov

Publisher: World Scientific

Published: 2020-08-21

Total Pages: 411

ISBN-13: 9811214875

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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.

Book Synopsis Understanding Game Theory: Introduction To The Analysis Of Many Agent Systems With Competition And Cooperation (Second Edition) by : Vasily N Kolokoltsov

Download or read book Understanding Game Theory: Introduction To The Analysis Of Many Agent Systems With Competition And Cooperation (Second Edition) written by Vasily N Kolokoltsov and published by World Scientific. This book was released on 2020-08-21 with total page 411 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Handbook of Game Theory with Economic Applications

Author: R.J. Aumann

Publisher: Elsevier

Published: 1992

Total Pages: 824

ISBN-13: 9780444894274

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This is the second of three volumes surveying the state of the art in Game Theory and its applications to many and varied fields, in particular to economics. The chapters in the present volume are contributed by outstanding authorities, and provide comprehensive coverage and precise statements of the main results in each area. The applications include empirical evidence. The following topics are covered: communication and correlated equilibria, coalitional games and coalition structures, utility and subjective probability, common knowledge, bargaining, zero-sum games, differential games, and applications of game theory to signalling, moral hazard, search, evolutionary biology, international relations, voting procedures, social choice, public economics, politics, and cost allocation. This handbook will be of interest to scholars in economics, political science, psychology, mathematics and biology. For more information on the Handbooks in Economics series, please see our home page on http://www.elsevier.nl/locate/hes

Book Synopsis Handbook of Game Theory with Economic Applications by : R.J. Aumann

Download or read book Handbook of Game Theory with Economic Applications written by R.J. Aumann and published by Elsevier. This book was released on 1992 with total page 824 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the second of three volumes surveying the state of the art in Game Theory and its applications to many and varied fields, in particular to economics. The chapters in the present volume are contributed by outstanding authorities, and provide comprehensive coverage and precise statements of the main results in each area. The applications include empirical evidence. The following topics are covered: communication and correlated equilibria, coalitional games and coalition structures, utility and subjective probability, common knowledge, bargaining, zero-sum games, differential games, and applications of game theory to signalling, moral hazard, search, evolutionary biology, international relations, voting procedures, social choice, public economics, politics, and cost allocation. This handbook will be of interest to scholars in economics, political science, psychology, mathematics and biology. For more information on the Handbooks in Economics series, please see our home page on http://www.elsevier.nl/locate/hes

Game and Economic Theory

Author: Sergiu Hart

Publisher: University of Michigan Press

Published: 1995

Total Pages: 478

ISBN-13: 9780472106738

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Outstanding works showing the application of game theory to economic theory.

Book Synopsis Game and Economic Theory by : Sergiu Hart

Download or read book Game and Economic Theory written by Sergiu Hart and published by University of Michigan Press. This book was released on 1995 with total page 478 pages. Available in PDF, EPUB and Kindle. Book excerpt: Outstanding works showing the application of game theory to economic theory.

Game Theory for Economic Analysis

Author: Tatsuro Ichiishi

Publisher: Elsevier

Published: 2014-06-28

Total Pages: 177

ISBN-13: 1483295060

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Game Theory for Economic Analysis

Book Synopsis Game Theory for Economic Analysis by : Tatsuro Ichiishi

Download or read book Game Theory for Economic Analysis written by Tatsuro Ichiishi and published by Elsevier. This book was released on 2014-06-28 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt: Game Theory for Economic Analysis

Game Theory and Applications

Author: Tatsuro Ichiishi

Publisher: Academic Press

Published: 2014-06-28

Total Pages: 449

ISBN-13: 1483295052

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Game Theory and Applications outlines game theory and proves its validity by examining it alongside the neoclassical paradigm. This book contends that the neoclassical theory is the exceptional case, and that game theory may indeed be the rule. The papers and abstracts collected here explore its recent development and suggest new research directions. Explains many of the recent central developments in game theory Highlights new research directions in economic theory which surpass the neoclassical paradigm Includes game-theoretical analyses in economics, political science, and biology Written by leading game theorists, economists, political scientists, and biologists

Book Synopsis Game Theory and Applications by : Tatsuro Ichiishi

Download or read book Game Theory and Applications written by Tatsuro Ichiishi and published by Academic Press. This book was released on 2014-06-28 with total page 449 pages. Available in PDF, EPUB and Kindle. Book excerpt: Game Theory and Applications outlines game theory and proves its validity by examining it alongside the neoclassical paradigm. This book contends that the neoclassical theory is the exceptional case, and that game theory may indeed be the rule. The papers and abstracts collected here explore its recent development and suggest new research directions. Explains many of the recent central developments in game theory Highlights new research directions in economic theory which surpass the neoclassical paradigm Includes game-theoretical analyses in economics, political science, and biology Written by leading game theorists, economists, political scientists, and biologists