Fixed Points And Economic Equilibria
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Fixed Points And Economic Equilibria
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Author : Ken Urai
language : en
Publisher: World Scientific
Release Date : 2010
Fixed Points And Economic Equilibria written by Ken Urai and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Business & Economics categories.
1. Introduction. 1.1. Mathematics is language. 1.2. Notes on some mathematical tools in this book. 1.3. Basic mathematical concepts and definitions -- 2. Fixed-point theorems. 2.1. Classical results and basic extensions. 2.2. Convexity and duality for general spaces. 2.3. Extension of classical results to general spaces -- 3. Nash equilibrium and abstract economy. 3.1. Multi-agent product settings for games. 3.2. Nash equilibrium. 3.3. Abstract economy -- 4. Gale-Nikaido-Debreu's theorem. 4.1. Gale-Nikaido-Debreu's theorem. 4.2. Market equilibria in general vector spaces. 4.3. Demand-supply coincidence in general spaces -- 5. General economic equilibrium. 5.1. General preferences and basic existence theorems. 5.2. Pareto optimal allocations. 5.3. Existence of general equilibrium -- 6. The C̮ech type homology theory and fixed points. 6.1. Basic concepts in algebraic topology. 6.2. Vietoris-Begle mapping and local connectedness. 6.3. Nikaido's analogue of Sperner's lemma. 6.4. Eilenberg-Montgomery's theorem -- 7. Convex structure and fixed-point index. 7.1. Lefschetz's fixed-point theorem and its extensions. 7.2. Cohomology theory for general spaces. 7.3. Dual-system structure and differentiability. 7.4. Linear Approximation for Isolated Fixed Points. 7.5. Indices for compact set of fixed points -- 8. Applications to related topics. 8.1. KKM, KKMS, and core existence. 8.2. Eaves' theorem. 8.3. Fan-Browder's coincidence theorem. 8.4. L-majorized mappings. 8.5. Variational inequality problem. 8.6. Equilibrium with cooperative concepts. 8.7. System of inequalities and affine transformations -- 9. Mathematics and social science. 9.1. Basic concepts in axiomatic set theory. 9.2. Individuals and rationality. 9.3. Society and values -- 10. Concluding discussions. 10.1. Fixed points and economic equilibria. 10.2. Rationality and fixed-point views of the world
Fixed Points And Economic Equilibria
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Author : Ken Urai
language : en
Publisher: World Scientific
Release Date : 2010-05-13
Fixed Points And Economic Equilibria written by Ken Urai and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-05-13 with Mathematics categories.
This book presents a systematic approach to problems in economic equilibrium based on fixed-point arguments and rigorous set-theoretical (axiomatic) methods. It describes the highest-level research on the classical theme, fixed points and economic equilibria, in the theory of mathematical economics, and also presents basic results in this area, especially in the general equilibrium theory and non-co-operative game theory. The arguments also contain distinguishable developments of the main theme in the homology theory for general topological spaces, in the model theory and mathematical logic, and in the methodology and philosophy of social sciences. It can thus serve as a graduate-level textbook on mathematical economics as well as an advanced monograph for students and researchers who are concerned about rigorous mathematical treatment in the social sciences.
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.
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.
Equilibrium Problems And Applications
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Author : Gábor Kassay
language : en
Publisher: Academic Press
Release Date : 2018-10-09
Equilibrium Problems And Applications written by Gábor Kassay and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-09 with Business & Economics categories.
Equilibrium Problems and Applications develops a unified variational approach to deal with single-valued, set-valued and quasi-equilibrium problems. The authors promote original results in relationship with classical contributions to the field of equilibrium problems. The content evolved in the general setting of topological vector spaces and it lies at the interplay between pure and applied nonlinear analysis, mathematical economics, and mathematical physics. This abstract approach is based on tools from various fields, including set-valued analysis, variational and hemivariational inequalities, fixed point theory, and optimization. Applications include models from mathematical economics, Nash equilibrium of non-cooperative games, and Browder variational inclusions. The content is self-contained and the book is mainly addressed to researchers in mathematics, economics and mathematical physics as well as to graduate students in applied nonlinear analysis. - A rigorous mathematical analysis of Nash equilibrium type problems, which play a central role to describe network traffic models, competition games or problems arising in experimental economics - Develops generic models relevant to mathematical economics and quantitative modeling of game theory, aiding economists to understand vital material without having to wade through complex proofs - Reveals a number of surprising interactions among various equilibria topics, enabling readers to identify a common and unified approach to analysing problem sets - Illustrates the deep features shared by several types of nonlinear problems, encouraging readers to develop further this unifying approach from other viewpoints into economic models in turn
Constructing Fixed Points And Economic Equilibria
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Author : Matthew Ralph John Hendtlass
language : en
Publisher:
Release Date : 2013
Constructing Fixed Points And Economic Equilibria written by Matthew Ralph John Hendtlass and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with categories.
Constructing Fixed Points And Economic Equilibria
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Author : Matthew Ralph John Hendtlass
language : en
Publisher:
Release Date : 2013
Constructing Fixed Points And Economic Equilibria written by Matthew Ralph John Hendtlass and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with categories.
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 : 2010-01-16
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 2010-01-16 with Business & Economics categories.
One of the problems in economics that economists have devoted a considerable amount of attention in prevalent years has been to ensure consistency in the models they employ. Assuming markets to be generally in some state of equilibrium, it is asked under what circumstances such equilibrium is possible. The fundamental mathematical tools used to address this concern are fixed point theorems: the conditions under which sets of assumptions have a solution. This book gives the reader access to the mathematical techniques involved and goes on to apply fixed point theorems to proving the existence of equilibria for economics and for co-operative and noncooperative games. Special emphasis is given to economics and games in cases where the preferences of agents may not be transitive. The author presents topical proofs of old results in order to further clarify the results. He also proposes fresh results, notably in the last chapter, that refer to the core of a game without transitivity. This book will be useful as a text or reference work for mathematical economists and graduate and advanced undergraduate students.
Computable Foundations For Economics
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Author : K. Vela Velupillai
language : en
Publisher: Routledge
Release Date : 2012-07-26
Computable Foundations For Economics written by K. Vela Velupillai and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-07-26 with Business & Economics categories.
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.
Economic Theory Of Fuzzy Equilibria
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Author : Antoine Billot
language : en
Publisher: Springer
Release Date : 2013-04-17
Economic Theory Of Fuzzy Equilibria written by Antoine Billot and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Business & Economics categories.
Fuzzy set theory, which started not much more than 20 years ago as a generalization of classical set theory, has in the meantime evolved into an area which scientifically, as well as from the point of view of applications, is recognized as a very valuable contribution to the existing knowledge. To an increasing degree, however, fuzzy set theory is also used in a descriptive, factual sense or as a decision making technology. Most of these applications of fuzzy set theory are in the areas of fuzzy control, multi-criteria analysis, descriptive decision theory and expert systems design. In economics, the application of fuzzy set theory is still very rare. Apart from Professor Ponsard and his group, who have obviously recognized the potential offuzzy set theory in economics much better than others, only very few economists are using this new tool in order to model economic systems in a more realistic way than often possible by traditional approaches, and to gain more insight into structural interdependences of economic systems. I consider it, therefore, particularly valuable that Dr. Billot, in his book, makes a remarkable contribution in this direction. There seems to be one major difference between Dr.