Fixed points and economic equilibria /:
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,...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Singapore ; Hackensack, NJ :
World Scientific,
©2010.
|
| Schriftenreihe: | Series on mathematical economics and game theory ;
v. 5. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | 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, a. |
| Beschreibung: | 1 online resource (xvii, 292 pages) : illustrations |
| Bibliographie: | Includes bibliographical references (pages 277-284) and index. |
| ISBN: | 9789812837196 9812837191 9786612760723 6612760729 |
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| 505 | 0 | |a 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. | |
| 650 | 0 | |a Equilibrium (Economics) |x Mathematical models. | |
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| contents | 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. |
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| dewey-search | 339.5 |
| dewey-sort | 3339.5 |
| dewey-tens | 330 - Economics |
| discipline | Wirtschaftswissenschaften |
| format | Electronic eBook |
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| indexdate | 2024-11-27T13:17:34Z |
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| series | Series on mathematical economics and game theory ; |
| series2 | Series on mathematical economics and game theory ; |
| spelling | Urai, Ken, 1962- https://id.oclc.org/worldcat/entity/E39PCjMgFVvmqBHhddqMdH3KHP http://id.loc.gov/authorities/names/no2010132071 Fixed points and economic equilibria / Ken Urai. Singapore ; Hackensack, NJ : World Scientific, ©2010. 1 online resource (xvii, 292 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier Series on mathematical economics and game theory ; v. 5 Includes bibliographical references (pages 277-284) and index. Print version record. 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, a. 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. Equilibrium (Economics) Mathematical models. Fixed point theory. http://id.loc.gov/authorities/subjects/sh85048934 Théorème du point fixe. POLITICAL SCIENCE Economic Conditions. bisacsh BUSINESS & ECONOMICS Economics Macroeconomics. bisacsh Equilibrium (Economics) Mathematical models fast Fixed point theory fast has work: Fixed points and economic equilibria (Text) https://id.oclc.org/worldcat/entity/E39PCFK3tMRVg6QMwdyR3dH6cd https://id.oclc.org/worldcat/ontology/hasWork Print version: Urai, Ken, 1962- Fixed points and economic equilibria. Singapore ; Hackensack, NJ : World Scientific, ©2010 9789812837189 (OCoLC)477296982 Series on mathematical economics and game theory ; v. 5. http://id.loc.gov/authorities/names/no2004056822 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=340809 Volltext |
| spellingShingle | Urai, Ken, 1962- Fixed points and economic equilibria / Series on mathematical economics and game theory ; 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. Equilibrium (Economics) Mathematical models. Fixed point theory. http://id.loc.gov/authorities/subjects/sh85048934 Théorème du point fixe. POLITICAL SCIENCE Economic Conditions. bisacsh BUSINESS & ECONOMICS Economics Macroeconomics. bisacsh Equilibrium (Economics) Mathematical models fast Fixed point theory fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85048934 |
| title | Fixed points and economic equilibria / |
| title_auth | Fixed points and economic equilibria / |
| title_exact_search | Fixed points and economic equilibria / |
| title_full | Fixed points and economic equilibria / Ken Urai. |
| title_fullStr | Fixed points and economic equilibria / Ken Urai. |
| title_full_unstemmed | Fixed points and economic equilibria / Ken Urai. |
| title_short | Fixed points and economic equilibria / |
| title_sort | fixed points and economic equilibria |
| topic | Equilibrium (Economics) Mathematical models. Fixed point theory. http://id.loc.gov/authorities/subjects/sh85048934 Théorème du point fixe. POLITICAL SCIENCE Economic Conditions. bisacsh BUSINESS & ECONOMICS Economics Macroeconomics. bisacsh Equilibrium (Economics) Mathematical models fast Fixed point theory fast |
| topic_facet | Equilibrium (Economics) Mathematical models. Fixed point theory. Théorème du point fixe. POLITICAL SCIENCE Economic Conditions. BUSINESS & ECONOMICS Economics Macroeconomics. Equilibrium (Economics) Mathematical models Fixed point theory |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=340809 |
| work_keys_str_mv | AT uraiken fixedpointsandeconomicequilibria |