Computing Equilibria and Fixed Points

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Publisher : Springer Science & Business Media
ISBN 13 : 9780792383956
Total Pages : 368 pages
Book Rating : 4.3/5 (839 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 1999 with total page 368 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).

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).

Computing Equilibria and Fixed Points

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Publisher :
ISBN 13 : 9781475748406
Total Pages : 364 pages
Book Rating : 4.7/5 (484 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 . This book was released on 2014-01-15 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Fixed Points and Economic Equilibria

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Publisher : World Scientific
ISBN 13 : 9812837191
Total Pages : 311 pages
Book Rating : 4.8/5 (128 download)

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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: 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

The Computation of Fixed Points and Applications

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Publisher : Springer
ISBN 13 :
Total Pages : 146 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis The Computation of Fixed Points and Applications by : Michael J. Todd

Download or read book The Computation of Fixed Points and Applications written by Michael J. Todd and published by Springer. This book was released on 1976 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Computing Equilibria

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Publisher :
ISBN 13 :
Total Pages : 358 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis Computing Equilibria by : Jerzy Łoś

Download or read book Computing Equilibria written by Jerzy Łoś and published by . This book was released on 1976 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Fixed Points

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Publisher :
ISBN 13 :
Total Pages : 512 pages
Book Rating : 4.:/5 (44 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 . This book was released on 1977 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Computing Fixed Points with Applications to Economic Equilibrium Models

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Publisher :
ISBN 13 :
Total Pages : 102 pages
Book Rating : 4.E/5 ( download)

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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:

Hardness of Approximation Between P and NP

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Publisher : Morgan & Claypool
ISBN 13 : 1947487213
Total Pages : 319 pages
Book Rating : 4.9/5 (474 download)

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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.

Fixed Points

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Publisher : University-Press.org
ISBN 13 : 9781230553054
Total Pages : 66 pages
Book Rating : 4.5/5 (53 download)

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Book Synopsis Fixed Points by : Source Wikipedia

Download or read book Fixed Points written by Source Wikipedia and published by University-Press.org. This book was released on 2013-09 with total page 66 pages. Available in PDF, EPUB and Kindle. Book excerpt: Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Pages: 64. Chapters: Nash equilibrium, Brouwer fixed point theorem, Contraction mapping, Banach fixed point theorem, Minimax, Fixed point combinator, Derangement, Weil conjectures, Renormalization group, Cycle detection, Kakutani fixed point theorem, Domain theory, Lotka-Volterra equation, Common knowledge, Functional renormalization group, Cycles and fixed points, Knaster-Tarski theorem, Thue-Morse sequence, Hairy ball theorem, Lefschetz fixed-point theorem, Sperner's lemma, Applied general equilibrium, Local zeta-function, Diagonal lemma, Iterated function, Infrared fixed point, Atiyah-Bott fixed-point theorem, Rencontres numbers, Rotation number, Fixed point property, Autonomous convergence theorem, Price of stability, Fixed-point lemma for normal functions, Bourbaki-Witt theorem, Conley index theory, Fixed points of isometry groups in Euclidean space, UV fixed point, Schauder fixed point theorem, Lefschetz zeta function, Caristi fixed point theorem, Nielsen theory, Markus Yamabe conjecture, Fixed point theorems in infinite-dimensional spaces, Fixed point index, Ryll-Nardzewski fixed point theorem, Artin-Mazur zeta function, Least fixed point, Knaster-Kuratowski-Mazurkiewicz lemma, Banks-Zaks fixed point, Coincidence point, Kleene fixed-point theorem, Fixed point space, Sullivan conjecture, Borel fixed-point theorem. Excerpt: In game theory, Nash equilibrium (named after John Forbes Nash, who proposed it) is a solution concept of a game involving two or more players, in which each player is assumed to know the equilibrium strategies of the other players, and no player has anything to gain by changing only his own strategy unilaterally. If each player has chosen a strategy and no player can benefit by changing his or her strategy while the other players keep theirs unchanged, then the current set of strategy...

Fixed Point Theory in Ordered Sets and Applications

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Publisher : Springer Science & Business Media
ISBN 13 : 1441975853
Total Pages : 482 pages
Book Rating : 4.4/5 (419 download)

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Book Synopsis Fixed Point Theory in Ordered Sets and Applications by : Siegfried Carl

Download or read book Fixed Point Theory in Ordered Sets and Applications written by Siegfried Carl and published by Springer Science & Business Media. This book was released on 2010-11-17 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph provides a unified and comprehensive treatment of an order-theoretic fixed point theory in partially ordered sets and its various useful interactions with topological structures. The material progresses systematically, by presenting the preliminaries before moving to more advanced topics. In the treatment of the applications a wide range of mathematical theories and methods from nonlinear analysis and integration theory are applied; an outline of which has been given an appendix chapter to make the book self-contained. Graduate students and researchers in nonlinear analysis, pure and applied mathematics, game theory and mathematical economics will find this book useful.

Fixed points theorems via nash equilibria

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Publisher :
ISBN 13 :
Total Pages : 5 pages
Book Rating : 4.:/5 (96 download)

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Book Synopsis Fixed points theorems via nash equilibria by : Juan Pablo Torres-Martínez

Download or read book Fixed points theorems via nash equilibria written by Juan Pablo Torres-Martínez and published by . This book was released on 2002 with total page 5 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Fixed Points

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Publisher : Booksllc.Net
ISBN 13 : 9781230792088
Total Pages : 62 pages
Book Rating : 4.7/5 (92 download)

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Book Synopsis Fixed Points by : Source Wikipedia

Download or read book Fixed Points written by Source Wikipedia and published by Booksllc.Net. This book was released on 2013-09 with total page 62 pages. Available in PDF, EPUB and Kindle. Book excerpt: Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Pages: 61. Chapters: Applied general equilibrium, Artin-Mazur zeta function, Autonomous convergence theorem, Banks-Zaks fixed point, Coincidence point, Common knowledge (logic), Conley index theory, Conley-Zehnder theorem, Contraction mapping, Cycles and fixed points, Cycle detection, Derangement, Domain theory, Fixed-point combinator, Fixed-point index, Fixed-point property, Fixed-point space, Fixed-point theorem, Fixed points of isometry groups in Euclidean space, Fixed point (mathematics), Functional renormalization group, Hairy ball theorem, Infrared fixed point, Iterated function, Knaster-Kuratowski-Mazurkiewicz lemma, Knaster-Tarski theorem, Least fixed point, Lefschetz zeta function, Local zeta-function, Lotka-Volterra equation, Markus-Yamabe conjecture, Minimax, Nash equilibrium, Nielsen theory, Price of stability, Rencontres numbers, Rotation number, Ryll-Nardzewski fixed-point theorem, Schauder fixed point theorem, Sperner's lemma, Sullivan conjecture, Thue-Morse sequence, UV fixed point, Weil conjectures. Excerpt: In game theory, the Nash equilibrium is a solution concept of a non-cooperative game involving two or more players, in which each player is assumed to know the equilibrium strategies of the other players, and no player has anything to gain by changing only his own strategy unilaterally. If each player has chosen a strategy and no player can benefit by changing strategies while the other players keep theirs unchanged, then the current set of strategy choices and the corresponding payoffs constitute a Nash equilibrium. Stated simply, Amy and Wili are in Nash equilibrium if Amy is making the best decision she can, taking into account Wili's decision, and Wili is making the best decision he can, taking into account Amy's decision. Likewise, a group of players are in Nash equilibrium if each one is...

Analysis and Computation of Fixed Points

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Publisher :
ISBN 13 :
Total Pages : 440 pages
Book Rating : 4.3/5 (91 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 . This book was released on 1980 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings from the Symposium on Analysis and Computation of Fixed Points held at The University of Wisconsin--Madison on May 7-8, 1979. Held under the auspices of the Mathematics Research Center, sponsored by the National Science Foundation and the United States Army. There are eight papers addressing aspects of homotopy theory, algebraic topology, and the economic implications of computable general equilibrium models. The ninth paper is a doctoral dissertation, in hopes that its contents will reach interested researchers.

Nonlinear Programming Techniques for Equilibria

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Publisher : Springer
ISBN 13 : 3030002055
Total Pages : 127 pages
Book Rating : 4.0/5 (3 download)

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Book Synopsis Nonlinear Programming Techniques for Equilibria by : Giancarlo Bigi

Download or read book Nonlinear Programming Techniques for Equilibria written by Giancarlo Bigi and published by Springer. This book was released on 2018-09-20 with total page 127 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book considers a range of problems in operations research, which are formulated through various mathematical models such as complementarity, variational inequalities, multiobjective optimization, fixed point problems, noncooperative games and inverse optimization. Moreover, the book subsumes all these models under a common structure that allows them to be formulated in a unique format: the Ky Fan inequality. It subsequently focuses on this unifying equilibrium format, providing a comprehensive overview of the main theoretical results and solution algorithms, together with a wealth of applications and numerical examples. Particular emphasis is placed on the role of nonlinear optimization techniques – e.g. convex optimization, nonsmooth calculus, proximal point and descent algorithms – as valuable tools for analyzing and solving Ky Fan inequalities.

Fixed Point Theorems Via Nash Equilibria

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Publisher :
ISBN 13 :
Total Pages : 5 pages
Book Rating : 4.:/5 (545 download)

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Book Synopsis Fixed Point Theorems Via Nash Equilibria by : Juan Pablo Torres-Martínez

Download or read book Fixed Point Theorems Via Nash Equilibria written by Juan Pablo Torres-Martínez and published by . This book was released on 2002 with total page 5 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Fixed Points, Equilibria and Homotopies

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Publisher :
ISBN 13 :
Total Pages : 85 pages
Book Rating : 4.:/5 (287 download)

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Book Synopsis Fixed Points, Equilibria and Homotopies by : Willard I. Zangwill

Download or read book Fixed Points, Equilibria and Homotopies written by Willard I. Zangwill and published by . This book was released on 1981 with total page 85 pages. Available in PDF, EPUB and Kindle. Book excerpt: