Computing Equilibria And Fixed Points
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Computing Equilibria And Fixed Points
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Author : Zaifu Yang
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Computing Equilibria And Fixed Points written by Zaifu Yang and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Business & Economics categories.
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).
Computing Equilibria And Fixed Points
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Author : Zaifu Yang
language : en
Publisher:
Release Date : 2014-01-15
Computing Equilibria And Fixed Points written by Zaifu Yang and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
The Computation Of Fixed Points And Applications
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Author : M. J. Todd
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
The Computation Of Fixed Points And Applications written by M. J. Todd and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
Fixed-point algorithms have diverse applications in economics, optimization, game theory and the numerical solution of boundary-value problems. Since Scarf's pioneering work [56,57] on obtaining approximate fixed points of continuous mappings, a great deal of research has been done in extending the applicability and improving the efficiency of fixed-point methods. Much of this work is available only in research papers, although Scarf's book [58] gives a remarkably clear exposition of the power of fixed-point methods. However, the algorithms described by Scarf have been super~eded by the more sophisticated restart and homotopy techniques of Merrill [~8,~9] and Eaves and Saigal [1~,16]. To understand the more efficient algorithms one must become familiar with the notions of triangulation and simplicial approxi- tion, whereas Scarf stresses the concept of primitive set. These notes are intended to introduce to a wider audience the most recent fixed-point methods and their applications. Our approach is therefore via triangu- tions. For this reason, Scarf is cited less in this manuscript than his contri- tions would otherwise warrant. We have also confined our treatment of applications to the computation of economic equilibria and the solution of optimization problems. Hansen and Koopmans [28] apply fixed-point methods to the computation of an invariant optimal capital stock in an economic growth model. Applications to game theory are discussed in Scarf [56,58], Shapley [59], and Garcia, Lemke and Luethi [24]. Allgower [1] and Jeppson [31] use fixed-point algorithms to find many solutions to boundary-value problems.
Fixed Point Theorems With Applications To Economics And Game Theory
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Author : Kim C. Border
language : en
Publisher: Cambridge University Press
Release Date : 1985
Fixed Point Theorems With Applications To Economics And Game Theory written by Kim C. Border and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with Business & Economics categories.
This book explores fixed point theorems and its uses in economics, co-operative and noncooperative games.
Analysis And Computation Of Fixed Points
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Author : Stephen M. Robinson
language : en
Publisher: Academic Press
Release Date : 2014-05-10
Analysis And Computation Of Fixed Points written by Stephen M. Robinson and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-10 with Mathematics categories.
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.
Pathways To Solutions Fixed Points And Equilibria
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Author : Willard I. Zangwill
language : en
Publisher: Prentice Hall
Release Date : 1981
Pathways To Solutions Fixed Points And Equilibria written by Willard I. Zangwill and has been published by Prentice Hall this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with Mathematics categories.
Finite Dimensional Variational Inequalities And Complementarity Problems
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Author : Francisco Facchinei
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-06-14
Finite Dimensional Variational Inequalities And Complementarity Problems written by Francisco Facchinei and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-06-14 with Mathematics categories.
The ?nite-dimensional nonlinear complementarity problem (NCP) is a s- tem of ?nitely many nonlinear inequalities in ?nitely many nonnegative variables along with a special equation that expresses the complementary relationship between the variables and corresponding inequalities. This complementarity condition is the key feature distinguishing the NCP from a general inequality system, lies at the heart of all constrained optimi- tion problems in ?nite dimensions, provides a powerful framework for the modeling of equilibria of many kinds, and exhibits a natural link between smooth and nonsmooth mathematics. The ?nite-dimensional variational inequality (VI), which is a generalization of the NCP, provides a broad unifying setting for the study of optimization and equilibrium problems and serves as the main computational framework for the practical solution of a host of continuum problems in the mathematical sciences. The systematic study of the ?nite-dimensional NCP and VI began in the mid-1960s; in a span of four decades, the subject has developed into a very fruitful discipline in the ?eld of mathematical programming. The - velopments include a rich mathematical theory, a host of e?ective solution algorithms, a multitude of interesting connections to numerous disciplines, and a wide range of important applications in engineering and economics. As a result of their broad associations, the literature of the VI/CP has bene?ted from contributions made by mathematicians (pure, applied, and computational), computer scientists, engineers of many kinds (civil, ch- ical, electrical, mechanical, and systems), and economists of diverse exp- tise (agricultural, computational, energy, ?nancial, and spatial).
General Equilibrium
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Author : Hayo Reinders
language : en
Publisher: Springer
Release Date : 1989-03-01
General Equilibrium written by Hayo Reinders and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989-03-01 with Business & Economics categories.
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.
Advanced Fixed Point Theory For Economics
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Author : Andrew McLennan
language : en
Publisher: Springer
Release Date : 2018-07-03
Advanced Fixed Point Theory For Economics written by Andrew McLennan and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-03 with Business & Economics categories.
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 outstandingtext for advanced graduate courses in economics and related disciplines.
Irving Fisher
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Author : Robert W. Dimand
language : en
Publisher: Springer
Release Date : 2019-03-29
Irving Fisher written by Robert W. Dimand and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-03-29 with Business & Economics categories.
Acclaimed by Joseph Schumpeter as ‘The greatest economist the United States has ever produced’, this book examines the life and work of American economist and statistician Irving Fisher (1867–1947). Fisher’s reputation suffered for decades after his incorrect predictions for the stock market in October 1929 and the impact of Keynesian macroeconomics, but the importance of his work came to be recognized through the advocacy of many prestigious scholars including Milton Friedman, Hyman Minsky and James Tobin. With pivotal contributions including his Debt-Deflation Theory, Fisher Diagram and Ideal Index Number, his research in neoclassical economics influenced policymaking in his own day as well as during the recent financial crisis. This volume will be of interest to all those interested in the twentieth century transformation of economics.