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Computing Equilibria And Fixed Points
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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).
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 . This book was released on 2014-01-15 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Fixed Points and Economic Equilibria by : Ken Urai
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: Wuthering Heights
Book Synopsis Computing Fixed Points with Applications to Economic Equilibrium Models by : Michael J. Todd
Download or read book Computing Fixed Points with Applications to Economic Equilibrium Models written by Michael J. Todd and published by . This book was released on 1976 with total page 102 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
Book Synopsis Twenty Lectures on Algorithmic Game Theory by : Tim Roughgarden
Download or read book Twenty Lectures on Algorithmic Game Theory written by Tim Roughgarden and published by Cambridge University Press. This book was released on 2016-08-30 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computer science and economics have engaged in a lively interaction over the past fifteen years, resulting in the new field of algorithmic game theory. Many problems that are central to modern computer science, ranging from resource allocation in large networks to online advertising, involve interactions between multiple self-interested parties. Economics and game theory offer a host of useful models and definitions to reason about such problems. The flow of ideas also travels in the other direction, and concepts from computer science are increasingly important in economics. This book grew out of the author's Stanford University course on algorithmic game theory, and aims to give students and other newcomers a quick and accessible introduction to many of the most important concepts in the field. The book also includes case studies on online advertising, wireless spectrum auctions, kidney exchange, and network management.
Book Synopsis Applying General Equilibrium by : John B. Shoven
Download or read book Applying General Equilibrium written by John B. Shoven and published by Cambridge University Press. This book was released on 1992-05-29 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: The central idea underlying this work is to convert the Walrasian general equilibrium structure (formalized in the 1950s by Kenneth Arrow, Gerard Debreu and others) from an abstract representation of an economy into realistic models of actual economies.
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.
Book Synopsis Pathways to Solutions, Fixed Points, and Equilibria by : Willard I. Zangwill
Download or read book Pathways to Solutions, Fixed Points, and Equilibria written by Willard I. Zangwill and published by Prentice Hall. This book was released on 1981 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Hardness of Approximation Between P and NP by : Aviad Rubinstein
Download or read book Hardness of Approximation Between P and NP written by Aviad Rubinstein and published by Morgan & Claypool. This book was released on 2019-06-07 with total page 319 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nash equilibrium is the central solution concept in Game Theory. Since Nash’s original paper in 1951, it has found countless applications in modeling strategic behavior of traders in markets, (human) drivers and (electronic) routers in congested networks, nations in nuclear disarmament negotiations, and more. A decade ago, the relevance of this solution concept was called into question by computer scientists, who proved (under appropriate complexity assumptions) that computing a Nash equilibrium is an intractable problem. And if centralized, specially designed algorithms cannot find Nash equilibria, why should we expect distributed, selfish agents to converge to one? The remaining hope was that at least approximate Nash equilibria can be efficiently computed. Understanding whether there is an efficient algorithm for approximate Nash equilibrium has been the central open problem in this field for the past decade. In this book, we provide strong evidence that even finding an approximate Nash equilibrium is intractable. We prove several intractability theorems for different settings (two-player games and many-player games) and models (computational complexity, query complexity, and communication complexity). In particular, our main result is that under a plausible and natural complexity assumption ("Exponential Time Hypothesis for PPAD"), there is no polynomial-time algorithm for finding an approximate Nash equilibrium in two-player games. The problem of approximate Nash equilibrium in a two-player game poses a unique technical challenge: it is a member of the class PPAD, which captures the complexity of several fundamental total problems, i.e., problems that always have a solution; and it also admits a quasipolynomial time algorithm. Either property alone is believed to place this problem far below NP-hard problems in the complexity hierarchy; having both simultaneously places it just above P, at what can be called the frontier of intractability. Indeed, the tools we develop in this book to advance on this frontier are useful for proving hardness of approximation of several other important problems whose complexity lies between P and NP: Brouwer’s fixed point, market equilibrium, CourseMatch (A-CEEI), densest k-subgraph, community detection, VC dimension and Littlestone dimension, and signaling in zero-sum games.
Book Synopsis The Computation of Fixed Points and Applications by : M. J. Todd
Download or read book The Computation of Fixed Points and Applications written by M. J. Todd and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Computing Equilibria written by Jerzy Łoś and published by Elsevier Science & Technology. This book was released on 1976 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Advances in Global Optimization by : David Gao
Download or read book Advances in Global Optimization written by David Gao and published by Springer. This book was released on 2014-11-11 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt: This proceedings volume addresses advances in global optimization—a multidisciplinary research field that deals with the analysis, characterization and computation of global minima and/or maxima of nonlinear, non-convex and nonsmooth functions in continuous or discrete forms. The volume contains selected papers from the third biannual World Congress on Global Optimization in Engineering & Science (WCGO), held in the Yellow Mountains, Anhui, China on July 8-12, 2013. The papers fall into eight topical sections: mathematical programming; combinatorial optimization; duality theory; topology optimization; variational inequalities and complementarity problems; numerical optimization; stochastic models and simulation and complex simulation and supply chain analysis.
Book Synopsis Herbert Scarf's Contributions to Economics, Game Theory and Operations Research by : Z. Yang
Download or read book Herbert Scarf's Contributions to Economics, Game Theory and Operations Research written by Z. Yang and published by Springer. This book was released on 2017-01-19 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: Herbert Scarf is a distinguished economist and has made a number of extraordinarily significant contributions to economics, game theory and operations research. This work has generated a major research field in economics termed Applied General Equilibrium Analysis. This book comprises all his research articles and consists of four volumes.
Book Synopsis The Elgar Companion to Recent Economic Methodology by : J. B. Davis
Download or read book The Elgar Companion to Recent Economic Methodology written by J. B. Davis and published by Edward Elgar Publishing. This book was released on 2011-01-01 with total page 553 pages. Available in PDF, EPUB and Kindle. Book excerpt: Economic methodology has traditionally been associated with logical positivism in the vein of Milton Friedman, Karl Popper, Imre Lakatos and Thomas Kuhn. However, the emergence and proliferation of new research programs in economics have stimulated many novel developments in economic methodology. This impressive Companion critically examines these advances in methodological thinking, particularly those that are associated with the new research programs which challenge standard economic methodology. Bringing together a collection of leading contributors to this new methodological thinking, the authors explain how it differs from the past and point towards further concerns and future issues. The recent research programs explored include behavioral and experimental economics, neuroeconomics, new welfare theory, happiness and subjective well-being research, geographical economics, complexity and computational economics, agent-based modeling, evolutionary thinking, macroeconomics and Keynesianism after the crisis, and new thinking about the status of the economics profession and the role of the media in economics. This important compendium will prove invaluable for researchers and postgraduate students of economic methodology and the philosophy of economics. Practitioners in the vanguard of new economic thinking will also find plenty of useful information in this path-breaking book.
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.
Book Synopsis Complementarity, Equilibrium, Efficiency and Economics by : G. Isac
Download or read book Complementarity, Equilibrium, Efficiency and Economics written by G. Isac and published by Springer Science & Business Media. This book was released on 2002-06-30 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: In complementarity theory, which is a relatively new domain of applied mathematics, several kinds of mathematical models and problems related to the study of equilibrium are considered from the point of view of physics as well as economics. In this book the authors have combined complementarity theory, equilibrium of economical systems, and efficiency in Pareto's sense. The authors discuss the use of complementarity theory in the study of equilibrium of economic systems and present results they have obtained. In addition the authors present several new results in complementarity theory and several numerical methods for solving complementarity problems associated with the study of economic equilibrium. The most important notions of Pareto efficiency are also presented. Audience: Researchers and graduate students interested in complementarity theory, in economics, in optimization, and in applied mathematics.
