Mathematical Methods of Game and Economic Theory
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.

Mathematical Methods and Models for Economists
Mathematical Methods and Models for Economists

Author: Angel de la Fuente

Publisher: Cambridge University Press

Published: 2000-01-28

Total Pages: 630

ISBN-13: 9780521585293

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A textbook for a first-year PhD course in mathematics for economists and a reference for graduate students in economics.

An Introduction to Mathematical Analysis for Economic Theory and Econometrics
An Introduction to Mathematical Analysis for Economic Theory and Econometrics

Author: Dean Corbae

Publisher: Princeton University Press

Published: 2009-02-17

Total Pages: 696

ISBN-13: 1400833086

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Providing an introduction to mathematical analysis as it applies to economic theory and econometrics, this book bridges the gap that has separated the teaching of basic mathematics for economics and the increasingly advanced mathematics demanded in economics research today. Dean Corbae, Maxwell B. Stinchcombe, and Juraj Zeman equip students with the knowledge of real and functional analysis and measure theory they need to read and do research in economic and econometric theory. Unlike other mathematics textbooks for economics, An Introduction to Mathematical Analysis for Economic Theory and Econometrics takes a unified approach to understanding basic and advanced spaces through the application of the Metric Completion Theorem. This is the concept by which, for example, the real numbers complete the rational numbers and measure spaces complete fields of measurable sets. Another of the book's unique features is its concentration on the mathematical foundations of econometrics. To illustrate difficult concepts, the authors use simple examples drawn from economic theory and econometrics. Accessible and rigorous, the book is self-contained, providing proofs of theorems and assuming only an undergraduate background in calculus and linear algebra. Begins with mathematical analysis and economic examples accessible to advanced undergraduates in order to build intuition for more complex analysis used by graduate students and researchers Takes a unified approach to understanding basic and advanced spaces of numbers through application of the Metric Completion Theorem Focuses on examples from econometrics to explain topics in measure theory

Mathematical Optimization and Economic Theory
Mathematical Optimization and Economic Theory

Author: Michael D. Intriligator

Publisher: SIAM

Published: 2002-01-01

Total Pages: 515

ISBN-13: 0898715113

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A classic account of mathematical programming and control techniques and their applications to static and dynamic problems in economics.

Mathematical Methods for Economic Theory 1
Mathematical Methods for Economic Theory 1

Author: James C. Moore

Publisher: Springer Science & Business Media

Published: 1999-10-19

Total Pages: 436

ISBN-13: 9783540662358

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This two-volume work functions both as a textbook for graduates and as a reference for economic scholars. Assuming only the minimal mathematics background required of every second-year graduate, the two volumes provide a self-contained and careful development of mathematics through locally convex topological vector spaces, and fixed-point, separation, and selection theorems in such spaces. Volume One covers basic set theory, sequences and series, continuous and semi-continuous functions, an introduction to general linear spaces, basic convexity theory, and applications to economics.

Handbook of Mathematical Economics
Handbook of Mathematical Economics

Author: Kenneth J. Arrow

Publisher: North Holland

Published: 1981

Total Pages: 408

ISBN-13:

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V.2: Mathematical approaches to microeconomic theory. Mathematical approaches to competitive equilibrium.

Mathematical Methods for Economic Theory 2
Mathematical Methods for Economic Theory 2

Author: James C. Moore

Publisher: Springer Science & Business Media

Published: 2013-03-14

Total Pages: 344

ISBN-13: 3662085445

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This two-volume work functions both as a textbook for graduates and as a reference for economic scholars. Assuming only the minimal mathematics background required of every second-year graduate in economics, the two volumes provide a self-contained and careful development of mathematics through locally convex topological vector spaces, and fixed-point, separation, and selection theorems in such spaces. This second volume introduces general topology, the theory of correspondences on and into topological spaces, Banach spaces, topological vector spaces, and maximum, fixed-point, and selection theorems for such spaces

The Fecundity of Mathematical Methods in Economic Theory
The Fecundity of Mathematical Methods in Economic Theory

Author: H.W. Brand

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 64

ISBN-13: 940103673X

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The question of how far mathematical methods of reasoning and inves tigation are applicable in economic theorising has long been a matter of debate. The first part of this question needing to be answered was whether, outside the range of ordinary statistical methods, such application is in fact possible. In my opinion the controversy on this point has been a fruitful one, which has led, as might have been expected, to an affirmative answer. What, however, has not yet been decided - for the simple reason that hitherto it has not been investigated - is whether the application of mathematical methods to our science is expedient. From the point of view of economic methodology this seems to me the more important part of the question, although the only considerations hitherto brought to bear upon it have been of a rather general character, based on uncer tain ideas which have led to uncertain conclusions. That is why I welcome this attempt of Dr. Heinz W. Brand to bring the solution nearer by his present work. The conclusion he reaches here is that mathematical methods cannot unreservedly be employed in our science. The arguments which he carefully weighs, in the course of a criticism which is never destructive, are centred on his own criterion of asking whether it is not merely possible, but at the same time profitable, to apply mathematics in economic science.