Download or read book Optima and Equilibria written by Jean-Pierre Aubin and published by Springer Science & Business Media. This book was released on 2002-11-18 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: Progress in the theory of economic equilibria and in game theory has proceeded hand in hand with that of the mathematical tools used in the field, namely nonlinear analysis and, in particular, convex analysis. Jean-Pierre Aubin, one of the leading specialists in nonlinear analysis and its application to economics, has written a rigorous and concise - yet still elementary and self-contained - textbook providing the mathematical tools needed to study optima and equilibria, as solutions to problems, arising in economics, management sciences, operations research, cooperative and non-cooperative games, fuzzy games etc. It begins with the foundations of optimization theory, and mathematical programming, and in particular convex and nonsmooth analysis. Nonlinear analysis is then presented, first game-theoretically, then in the framework of set valued analysis. These results are then applied to the main classes of economic equilibria. The book contains numerous exercises and problems: the latter allow the reader to venture into areas of nonlinear analysis that lie beyond the scope of the book and of most graduate courses.
Download or read book Optima and Equilibria written by Jean-Pierre Aubin and published by Springer. This book was released on 1993-05-17 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: By Way of Warning As in ordinary language, metaphors may be used in mathematics to explain a given phenomenon by associating it with another which is ( or is considered to be) more familiar. It is this sense of familiarity, whether individual or collective, innate or acquired by education, which enables one to convince oneself that one has understood the phenomenon in question. Contrary to popular opinion, mathematics is not simply a richer or more precise language. Mathematical reasoning is a separate faculty possessed by all human brains, just like the ability to compose or listen to music, to paint or look at paintings, to believe in and follow cultural or moral codes, etc. But it is impossible (and dangerous) to compare these various faculties within a hierarchical framework; in particular, one cannot speak of the superiority of the language of mathematics. Naturally, the construction of mathematical metaphors requires the autonomous development of the discipline to provide theories which may be substituted for or associated with the phenomena to be explained. This is the domain of pure mathematics. The construction of the mathematical corpus obeys its own logic, like that of literature, music or art. In all these domains, an aesthetic satisfaction is at once the objective of the creative activity and a signal which enables one to recognise successful works. (Likewise, in all these domains, fashionable phenomena - reflecting social consensus - are used to develop aesthetic criteria).
Download or read book Optima and Competitive Equilibria with Adverse Selection and Moral Hazard written by Edward C. Prescott and published by . This book was released on 1981 with total page 53 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book General Equilibrium Overlapping Generations Models and Optimal Growth Theory written by Truman F. Bewley and published by Harvard University Press. This book was released on 2009-07-01 with total page 615 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents an original exposition of general equilibrium theory for advanced undergraduate and graduate-level students of economics. It contains detailed discussions of economic efficiency, competitive equilibrium, the first and second welfare theorems, the Kuhn-Tucker approach to general equilibrium, the Arrow-Debreu model, and rational expectations equilibrium and the permanent income hypothesis. Truman Bewley also treats optimal growth and overlapping generations models as special cases of the general equilibrium model. He uses the model and the first and second welfare theorems to explain the main ideas of insurance, capital theory, growth theory, and social security. It enables him to present a unified approach to portions of macro- as well as microeconomic theory. The book contains problems sets for most chapters.
Download or read book Calculation of Optima and Equilibria in Dynamic Resource Extraction Problems written by Rajani Singh and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Fixed Points and Economic Equilibria written by Ken Urai and published by World Scientific. This book was released on 2010 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book On Pareto Optima and Competitive Equilibria Relationships among equilibria and optima written by James C. Moore and published by . This book was released on 1970 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Equilibria and Pareto Optima of Markets with Adverse Selection written by Douglas Gale and published by . This book was released on 1994 with total page 60 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book On Pareto Optima and Competitive Equilibria written by James C. Moore and published by . This book was released on 1970 with total page 86 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book General Equilibrium Analysis written by Monique Florenzano and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 187 pages. Available in PDF, EPUB and Kindle. Book excerpt: General Equilibrium Analysis is a systematic exposition of the Walrasian model of economic equilibrium with a finite number of agents, as formalized by Arrow, Debreu and McKenzie at the beginning of the fifties and since then extensively used, worked and studied. Existence and optimality of general equilibrium are developed repeatedly under different sets of hypothesis which define some general settings and delineate different approaches to the general equilibrium existence problem. The final chapter is devoted to the extension of the general equilibrium model to economies defined on an infinite dimensional commodity space. The objective of General Equilibrium Analysis is to give to each problem in each framework the most general solution, at least for the present state of art. The intended readers are graduate students, specialists and researchers in economics, especially in mathematical economics. The book is appropriate as a class text, or for self-study.
Download or read book Local Optima Local Equilibria and Convexity Assumptions written by Mohamed A. El-Hodiri and published by . This book was released on 197? with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book An Introduction to Mathematical Analysis for Economic Theory and Econometrics written by Dean Corbae and published by Princeton University Press. This book was released on 2009-02-17 with total page 696 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Advances in Equilibrium Theory written by C.D. Aliprantis and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
Download or read book Structural Information and Communication Complexity written by Andrea Werneck Richa and published by Springer Nature. This book was released on 2020-07-29 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed conference proceedings of the 27th International Colloquium on Structural Information and Communication Complexity, SIROCCO 2020, held in Paderborn, Germany, in June 2020.* The 19 full papers and 2 invited papers presented in this book were carefully reviewed and selected from 41 submissions. They are divided into seven sections, i.e. invited papers; mobile robots; dynamic graphs; network communication; multi-agent systems; communication complexity; and game theory. * The conference was held virtually due to the COVID-19 pandemic.
Download or read book The complexity of Nash Equilibria Local Optima and Pareto Optimal solutions written by Heiko Röglin and published by . This book was released on 2008 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Recursive Formulation of Traffic Optima and Equilibria written by Richard Steinberg and published by . This book was released on 2000 with total page 17 pages. Available in PDF, EPUB and Kindle. Book excerpt:
