Fixed Point Theorems with Applications to Economics and Game Theory

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Publisher : Cambridge University Press
ISBN 13 : 9780521388085
Total Pages : 144 pages
Book Rating : 4.3/5 (88 download)

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Book Synopsis Fixed Point Theorems with Applications to Economics and Game Theory by : Kim C. Border

Download or read book Fixed Point Theorems with Applications to Economics and Game Theory written by Kim C. Border and published by Cambridge University Press. This book was released on 1985 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores fixed point theorems and its uses in economics, co-operative and noncooperative games.

Computing Equilibria and Fixed Points

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Publisher : Springer Science & Business Media
ISBN 13 : 1475748396
Total Pages : 349 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Computing Equilibria and Fixed Points by : Zaifu Yang

Download or read book Computing Equilibria and Fixed Points written by Zaifu Yang and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computing Equilibria and Fixed Points is devoted to the computation of equilibria, fixed points and stationary points. This volume is written with three goals in mind: (i) To give a comprehensive introduction to fixed point methods and to the definition and construction of Gröbner bases; (ii) To discuss several interesting applications of these methods in the fields of general equilibrium theory, game theory, mathematical programming, algebra and symbolic computation; (iii) To introduce several advanced fixed point and stationary point theorems. These methods and topics should be of interest not only to economists and game theorists concerned with the computation and existence of equilibrium outcomes in economic models and cooperative and non-cooperative games, but also to applied mathematicians, computer scientists and engineers dealing with models of highly nonlinear systems of equations (or polynomial equations).

Analysis and Computation of Fixed Points

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Publisher : Academic Press
ISBN 13 : 1483266028
Total Pages : 424 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Analysis and Computation of Fixed Points by : Stephen M. Robinson

Download or read book Analysis and Computation of Fixed Points written by Stephen M. Robinson and published by Academic Press. This book was released on 2014-05-10 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: Analysis and Computation of Fixed Points contains the proceedings of a Symposium on Analysis and Computation of Fixed Points, held at the University of Wisconsin-Madison on May 7-8, 1979. The papers focus on the analysis and computation of fixed points and cover topics ranging from paths generated by fixed point algorithms to strongly stable stationary solutions in nonlinear programs. A simple reliable numerical algorithm for following homotopy paths is also presented. Comprised of nine chapters, this book begins by describing the techniques of numerical linear algebra that possess attractive stability properties and exploit sparsity, and their application to the linear systems that arise in algorithms that solve equations by constructing piecewise-linear homotopies. The reader is then introduced to two triangulations for homotopy fixed point algorithms with an arbitrary grid refinement, followed by a discussion on some generic properties of paths generated by fixed point algorithms. Subsequent chapters deal with topological perturbations in the numerical study of nonlinear eigenvalue and bifurcation problems; general equilibrium analysis of taxation policy; and solving urban general equilibrium models by fixed point methods. The book concludes with an evaluation of economic equilibrium under deformation of the economy. This monograph should be of interest to students and specialists in the field of mathematics.

Discrete and System Models

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Publisher : Springer
ISBN 13 : 1461254434
Total Pages : 372 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Discrete and System Models by : W.F. Lucas

Download or read book Discrete and System Models written by W.F. Lucas and published by Springer. This book was released on 2013-12-19 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this four volume series is to make available for college teachers and students samples of important and realistic applications of mathematics which can be covered in undergraduate programs. The goal is to provide illustrations of how modem mathematics is actually employed to solve relevant contemporary problems. Although these independent chapters were prepared primarily for teachers in the general mathematical sciences, they should prove valuable to students, teachers, and research scientists in many of the fields of application as well. Prerequisites for each chapter and suggestions for the teacher are provided. Several of these chapters have been tested in a variety of classroom settings, and all have undergone extensive peer review and revision. Illustrations and exercises be covered in one class, are included in most chapters. Some units can whereas others provide sufficient material for a few weeks of class time. Volume 1 contains 23 chapters and deals with differential equations and, in the last four chapters, problems leading to partial differential equations. Applications are taken from medicine, biology, traffic systems and several other fields. The 14 chapters in Volume 2 are devoted mostly to problems arising in political science, but they also address questions appearing in sociology and ecology. Topics covered include voting systems, weighted voting, proportional representation, coalitional values, and committees. The 14 chapters in Volume 3 emphasize discrete mathematical methods such as those which arise in graph theory, combinatorics, and networks.

Introduction to Numerical Continuation Methods

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Publisher : SIAM
ISBN 13 : 9780898719154
Total Pages : 413 pages
Book Rating : 4.7/5 (191 download)

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Book Synopsis Introduction to Numerical Continuation Methods by : Eugene L. Allgower

Download or read book Introduction to Numerical Continuation Methods written by Eugene L. Allgower and published by SIAM. This book was released on 2003-01-01 with total page 413 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical continuation methods have provided important contributions toward the numerical solution of nonlinear systems of equations for many years. The methods may be used not only to compute solutions, which might otherwise be hard to obtain, but also to gain insight into qualitative properties of the solutions. Introduction to Numerical Continuation Methods, originally published in 1979, was the first book to provide easy access to the numerical aspects of predictor corrector continuation and piecewise linear continuation methods. Not only do these seemingly distinct methods share many common features and general principles, they can be numerically implemented in similar ways. The book also features the piecewise linear approximation of implicitly defined surfaces, the algorithms of which are frequently used in computer graphics, mesh generation, and the evaluation of surface integrals. To help potential users of numerical continuation methods create programs adapted to their particular needs, this book presents pseudo-codes and Fortran codes as illustrations. Since it first appeared, many specialized packages for treating such varied problems as bifurcation, polynomial systems, eigenvalues, economic equilibria, optimization, and the approximation of manifolds have been written. The original extensive bibliography has been updated in the SIAM Classics edition to include more recent references and several URLs so users can look for codes to suit their needs. Audience: this book continues to be useful for researchers and graduate students in mathematics, sciences, engineering, economics, and business. A background in elementary analysis and linear algebra are adequate prerequisites for reading this book; some knowledge from a first course in numerical analysis may also be helpful.

Recent Advances in Modeling and Forecasting Kaiyu

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Publisher : Springer Nature
ISBN 13 : 9819912415
Total Pages : 620 pages
Book Rating : 4.8/5 (199 download)

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Book Synopsis Recent Advances in Modeling and Forecasting Kaiyu by : Saburo Saito

Download or read book Recent Advances in Modeling and Forecasting Kaiyu written by Saburo Saito and published by Springer Nature. This book was released on with total page 620 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Advanced Fixed Point Theory for Economics

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Author :
Publisher : Springer
ISBN 13 : 9811307105
Total Pages : 441 pages
Book Rating : 4.8/5 (113 download)

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Book Synopsis Advanced Fixed Point Theory for Economics by : Andrew McLennan

Download or read book Advanced Fixed Point Theory for Economics written by Andrew McLennan and published by Springer. This book was released on 2018-07-03 with total page 441 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book develops the central aspect of fixed point theory – the topological fixed point index – to maximal generality, emphasizing correspondences and other aspects of the theory that are of special interest to economics. Numerous topological consequences are presented, along with important implications for dynamical systems. The book assumes the reader has no mathematical knowledge beyond that which is familiar to all theoretical economists. In addition to making the material available to a broad audience, avoiding algebraic topology results in more geometric and intuitive proofs. Graduate students and researchers in economics, and related fields in mathematics and computer science, will benefit from this book, both as a useful reference and as a well-written rigorous exposition of foundational mathematics. Numerous problems sketch key results from a wide variety of topics in theoretical economics, making the book an outstanding text for advanced graduate courses in economics and related disciplines.

Mathematical Programming The State of the Art

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Publisher : Springer Science & Business Media
ISBN 13 : 3642688748
Total Pages : 662 pages
Book Rating : 4.6/5 (426 download)

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Book Synopsis Mathematical Programming The State of the Art by : A. Bachem

Download or read book Mathematical Programming The State of the Art written by A. Bachem and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 662 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the late forties, Mathematical Programming became a scientific discipline in its own right. Since then it has experienced a tremendous growth. Beginning with economic and military applications, it is now among the most important fields of applied mathematics with extensive use in engineering, natural sciences, economics, and biological sciences. The lively activity in this area is demonstrated by the fact that as early as 1949 the first "Symposium on Mathe matical Programming" took place in Chicago. Since then mathematical programmers from all over the world have gath ered at the intfrnational symposia of the Mathematical Programming Society roughly every three years to present their recent research, to exchange ideas with their colleagues and to learn about the latest developments in their own and related fields. In 1982, the XI. International Symposium on Mathematical Programming was held at the University of Bonn, W. Germany, from August 23 to 27. It was organized by the Institut fUr Okonometrie und Operations Re search of the University of Bonn in collaboration with the Sonderforschungs bereich 21 of the Deutsche Forschungsgemeinschaft. This volume constitutes part of the outgrowth of this symposium and docu ments its scientific activities. Part I of the book contains information about the symposium, welcoming addresses, lists of committees and sponsors and a brief review about the Ful kerson Prize and the Dantzig Prize which were awarded during the opening ceremony.

Numerical Continuation Methods

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Publisher : Springer Science & Business Media
ISBN 13 : 3642612571
Total Pages : 402 pages
Book Rating : 4.6/5 (426 download)

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Book Synopsis Numerical Continuation Methods by : Eugene L. Allgower

Download or read book Numerical Continuation Methods written by Eugene L. Allgower and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the past fifteen years two new techniques have yielded extremely important contributions toward the numerical solution of nonlinear systems of equations. This book provides an introduction to and an up-to-date survey of numerical continuation methods (tracing of implicitly defined curves) of both predictor-corrector and piecewise-linear types. It presents and analyzes implementations aimed at applications to the computation of zero points, fixed points, nonlinear eigenvalue problems, bifurcation and turning points, and economic equilibria. Many algorithms are presented in a pseudo code format. An appendix supplies five sample FORTRAN programs with numerical examples, which readers can adapt to fit their purposes, and a description of the program package SCOUT for analyzing nonlinear problems via piecewise-linear methods. An extensive up-to-date bibliography spanning 46 pages is included. The material in this book has been presented to students of mathematics, engineering and sciences with great success, and will also serve as a valuable tool for researchers in the field.

The Computation of Equilibrium Prices

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Publisher :
ISBN 13 :
Total Pages : 172 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis The Computation of Equilibrium Prices by : Herbert E. Scarf

Download or read book The Computation of Equilibrium Prices written by Herbert E. Scarf and published by . This book was released on 1979 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Fixed Points

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Publisher : Academic Press
ISBN 13 : 1483261131
Total Pages : 505 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Fixed Points by : Stepan Karamardian

Download or read book Fixed Points written by Stepan Karamardian and published by Academic Press. This book was released on 2014-05-10 with total page 505 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fixed Points: Algorithms and Applications covers the proceedings of the First International Conference on Computing Fixed Points with Applications, held in the Department of Mathematical Sciences at Clemson University, Clemson, South Carolina on June 26-28, 1974. This book is composed of 21 chapters and starts with reviews of finding roots of polynomials by pivoting procedures and the relations between convergence and labeling in approximation algorithm. The next chapters deal with the principles of complementary pivot theory and the Markovian decision chains; the method of continuation for Brouwer fixed point calculation; a fixed point approach to stability in cooperative games; and computation of fixed points in a nonconvex region. Other chapters discuss a computational comparison of fixed point algorithms, the fundamentals of union jack triangulations, and some aspects of Mann's iterative method for approximating fixed points. The final chapters consider the application of fixed point algorithms to the analysis of tax policies and the pricing for congestion in telephone networks. This book will prove useful to mathematicians, computer scientists, and advance mathematics students.

Economic Evolution and Equilibrium

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Publisher : Springer Science & Business Media
ISBN 13 : 3540686622
Total Pages : 265 pages
Book Rating : 4.5/5 (46 download)

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Book Synopsis Economic Evolution and Equilibrium by : Marco Lehmann-Waffenschmidt

Download or read book Economic Evolution and Equilibrium written by Marco Lehmann-Waffenschmidt and published by Springer Science & Business Media. This book was released on 2007-05-07 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work uses various model frameworks to study the evolution of equilibria in an open loop evolving economy in which the model characteristics evolve without any directional restrictions except for continuity. Applying mathematical methods, it is shown that equilibria can always be adapted in a piecewise gradual, non bang-bang way.

Applied General Equilibrium

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Publisher : Springer Science & Business Media
ISBN 13 : 3642247466
Total Pages : 126 pages
Book Rating : 4.6/5 (422 download)

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Book Synopsis Applied General Equilibrium by : Manuel Alejandro Cardenete

Download or read book Applied General Equilibrium written by Manuel Alejandro Cardenete and published by Springer Science & Business Media. This book was released on 2012-01-05 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt: This advanced textbook aims at providing a simple but fully operational introduction to applied general equilibrium. General equilibrium is the backbone of modern economic analysis and as such generation after generation of economics students are introduced to it. As an analytical tool in economics, general equilibrium provides one of the most complete views of an economy since it incorporates all economic agents (households, firms, government, foreign sector) in an integrated way that is compatible with microtheory and microdata. The integration of theory and data handling is required for successful modeling but it requires a double ability that is not found in standard books. With this book we aim at filling the gap and provide advanced students with the required tools, from the building of consistent and applicable general equilibrium models to the interpretation of the results that ensue from the adoption of policies. The topics include: model design, model development, computer code examples, calibration and data adjustments, practical policy examples.

Differential Equation Models

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Publisher : Springer Science & Business Media
ISBN 13 : 1461254272
Total Pages : 390 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Differential Equation Models by : Martin Braun

Download or read book Differential Equation Models written by Martin Braun and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this four volume series is to make available for college teachers and students samples of important and realistic applications of mathematics which can be covered in undergraduate programs. The goal is to provide illustrations of how modem mathematics is actually employed to solve relevant contemporary problems. Although these independent chapters were prepared primarily for teachers in the general mathematical sciences, they should prove valuable to students, teachers, and research scientists in many of the fields of application as well. Prerequisites for each chapter and suggestions for the teacher are provided. Several of these chapters have been tested in a variety of classroom settings, and all have undergone extensive peer review and revision. Illustrations and exercises are included in most chapters. Some units can be covered in one class, whereas others provide sufficient material for a few weeks of class time. Volume 1 contains 23 chapters and deals with differential equations and, in the last four chapters, problems leading to partial differential equations. Applications are taken from medicine, biology, traffic systems and several other fields. The 14 chapters in Volume 2 are devoted mostly to problems arising in political science, but they also address questions appearing in sociology and ecology. Topics covered include voting systems, weighted voting, proportional representation, coalitional values, and committees. The 14 chapters in Volume 3 emphasize discrete mathematical methods such as those which arise in graph theory, combinatorics, and networks.

Computational Techniques for Econometrics and Economic Analysis

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Publisher : Springer Science & Business Media
ISBN 13 : 9780792323563
Total Pages : 258 pages
Book Rating : 4.3/5 (235 download)

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Book Synopsis Computational Techniques for Econometrics and Economic Analysis by : D.A. Belsley

Download or read book Computational Techniques for Econometrics and Economic Analysis written by D.A. Belsley and published by Springer Science & Business Media. This book was released on 1994 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is unlikely that any frontier of economics/econometrics is being pushed faster, further than that of computational techniques. The computer has become a tool for performing as well as an environment in which to perform economics and econometrics, taking over where theory bogs down, allowing at least approximate answers to questions that defy closed mathematical or analytical solutions. Tasks may now be attempted that were hitherto beyond human potential, and all the forces available can now be marshalled efficiently, leading to the achievement of desired goals. Computational Techniques for Econometrics and Economic Analysis is a collection of recent studies which exemplify all these elements, demonstrating the power that the computer brings to the economic analysts. The book is divided into four parts: 1 -- the computer and econometric methods; 2 -- the computer and economic analysis; 3 -- computational techniques for econometrics; and 4 -- the computer and econometric studies.

General Equilibrium

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Publisher : Springer
ISBN 13 : 1349198021
Total Pages : 357 pages
Book Rating : 4.3/5 (491 download)

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Book Synopsis General Equilibrium by : Hayo Reinders

Download or read book General Equilibrium written by Hayo Reinders and published by Springer. This book was released on 1989-03-01 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an excerpt 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. This extract concentrates on the topic of general equilibrium.

Computable Foundations for Economics

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Author :
Publisher : Routledge
ISBN 13 : 1134253362
Total Pages : 514 pages
Book Rating : 4.1/5 (342 download)

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Book Synopsis Computable Foundations for Economics by : K. Vela Velupillai

Download or read book Computable Foundations for Economics written by K. Vela Velupillai and published by Routledge. This book was released on 2012-07-26 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computable Foundations for Economics is a unified collection of essays, some of which are published here for the first time and all of which have been updated for this book, on an approach to economic theory from the point of view of algorithmic mathematics. By algorithmic mathematics the author means computability theory and constructive mathematics. This is in contrast to orthodox mathematical economics and game theory, which are formalised with the mathematics of real analysis, underpinned by what is called the ZFC formalism, i.e., set theory with the axiom of choice. This reliance on ordinary real analysis and the ZFC system makes economic theory in its current mathematical mode completely non-algorithmic, which means it is numerically meaningless. The book provides a systematic attempt to dissect and expose the non-algorithmic content of orthodox mathematical economics and game theory and suggests a reformalization on the basis of a strictly rigorous algorithmic mathematics. This removes the current schizophrenia in mathematical economics and game theory, where theory is entirely divorced from algorithmic applicability – for experimental and computational exercises. The chapters demonstrate the uncomputability and non-constructivity of core areas of general equilibrium theory, game theory and recursive macroeconomics. The book also provides a fresh look at the kind of behavioural economics that lies behind Herbert Simon’s work, and resurrects a role for the noble classical traditions of induction and verification, viewed and formalised, now, algorithmically. It will therefore be of particular interest to postgraduate students and researchers in algorithmic economics, game theory and classical behavioural economics.