Fixed points and economic equilibria:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New Jersey, NJ [u.a.]
World Scientific
2010
|
| Series: | Series on mathematical economics and game theory
5 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Item Description: | Literaturverz. S. 277 - 284 |
| Physical Description: | XVII, 292 S. Ill., graph. Darst. |
| ISBN: | 9812837183 9789812837189 |
Staff View
MARC
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface
vii
1
Introduction
1
1.1
Mathematics is Language
.................. 1
1.2
Notes on Some Mathematical Tools
in This Book
......................... 2
1.3
Basic Mathematical Concepts and Definitions
...... 12
2
Fixed-Point Theorems
27
2.1
Classical Results and Basic Extensions
.......... 27
2.2
Convexity and Duality for General Spaces
........ 39
2.3
Extension of Classical Results to General Spaces
..... 46
3
Nash Equilibrium and Abstract Economy
57
3.1
Multi-
Agent Product Settings for Games
......... 57
3.2
Nash Equilibrium
...................... 67
3.3
Abstract Economy
...................... 75
4
Gale-Nikaido-Debreu s Theorem
87
4.1
Gale-Nikaido-Debreu s Theorem
.............. 87
4.2
Market Equilibria in General Vector Spaces
........ 91
4.3
Demand-Supply Coincidence in General Spaces
..... 99
xvi
Fixed Points and Economic Equilibria
5
General Economic Equilibrium
101
5.1
General Preferences and Basic Existence Theorems
. . . 101
5.2
Pareto Optimal Allocations
................. 109
5.3
Existence of General Equilibrium
.............
Ill
6
The
Čech
Type Homology Theory and Fixed Points
125
6.1
Basic Concepts in Algebraic Topology
........... 125
6.2
Vietoris-Begle Mapping and Local Connectedness
.... 142
6.3
Nikaido s Analogue of Sperner s Lemma
.......... 150
6.4
Eilenberg-Montgomery s Theorem
............. 164
7
Convex Structure and Fixed-Point Index
167
7.1
Lefschetz s Fixed-Point Theorem and
Its Extensions
........................ 167
7.2
Cohomology Theory for General Spaces
.......... 175
7.3
Dual-System Structure and Differentiability
....... 177
7.4
Linear Approximation for Isolated Fixed Points
..... 177
7.5
Indices for Compact Set of Fixed Points
.......... 180
8
Applications to Related Topics
183
8.1
KKM, KKMS, and Core Existence
............. 183
8.2
Eaves Theorem
....................... 187
8.3
Fan-Browder s Coincidence Theorem
........... 189
8.4
L-majorized Mappings
................... 190
8.5
Variational Inequality Problem
............... 191
8.6
Equilibrium with Cooperative Concepts
.......... 192
8.7
System of Inequalities and
Affine
Transformations
.... 195
9
Mathematics and Social Science
201
9.1
Basic Concepts in Axiomatic Set Theory
......... 201
9.2
Individuals and Rationality
................. 218
9.3
Society and Values
..................... 232
10
Concluding Discussions
243
10.1
Fixed Points and Economic Equilibria
........... 243
10.2
Rationality and Fixed-Point Views of the World
..... 250
Contents xvii
Mathematical
Appendix
I
257
Mathematical Appendix II
263
Mathematical Appendix III
273
References
277
Index
285
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, and also presents basic
results in this area, especially in the general equilibrium
theory and non-cooperative 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.
ISBN-13
978-981-283-718-9
... , . _ . ....
ISBN-10
981-283-718-3
World Scientific
www.worldscientific.com
ľUľhc
|
| any_adam_object | 1 |
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| dewey-hundreds | 300 - Social sciences 500 - Natural sciences and mathematics |
| dewey-ones | 339 - Macroeconomics and related topics 515 - Analysis |
| dewey-raw | 339.5 515.7248 |
| dewey-search | 339.5 515.7248 |
| dewey-sort | 3339.5 |
| dewey-tens | 330 - Economics 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| format | Book |
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| id | DE-604.BV024629420 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:03:23Z |
| institution | BVB |
| isbn | 9812837183 9789812837189 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018601031 |
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| physical | XVII, 292 S. Ill., graph. Darst. |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | World Scientific |
| record_format | marc |
| series | Series on mathematical economics and game theory |
| series2 | Series on mathematical economics and game theory |
| spelling | Urai, Ken Verfasser aut Fixed points and economic equilibria Ken Urai New Jersey, NJ [u.a.] World Scientific 2010 XVII, 292 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Series on mathematical economics and game theory 5 Literaturverz. S. 277 - 284 Gleichgewichtstheorie (DE-588)4071876-1 gnd rswk-swf Nichtkooperatives Spiel (DE-588)4042085-1 gnd rswk-swf Fixpunkt (DE-588)4154496-1 gnd rswk-swf Wirtschaftsmathematik (DE-588)4066472-7 gnd rswk-swf Wirtschaftsmathematik (DE-588)4066472-7 s Gleichgewichtstheorie (DE-588)4071876-1 s Fixpunkt (DE-588)4154496-1 s Nichtkooperatives Spiel (DE-588)4042085-1 s b DE-604 Series on mathematical economics and game theory 5 (DE-604)BV021836771 5 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018601031&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018601031&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Urai, Ken Fixed points and economic equilibria Series on mathematical economics and game theory Gleichgewichtstheorie (DE-588)4071876-1 gnd Nichtkooperatives Spiel (DE-588)4042085-1 gnd Fixpunkt (DE-588)4154496-1 gnd Wirtschaftsmathematik (DE-588)4066472-7 gnd |
| subject_GND | (DE-588)4071876-1 (DE-588)4042085-1 (DE-588)4154496-1 (DE-588)4066472-7 |
| 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 | Gleichgewichtstheorie (DE-588)4071876-1 gnd Nichtkooperatives Spiel (DE-588)4042085-1 gnd Fixpunkt (DE-588)4154496-1 gnd Wirtschaftsmathematik (DE-588)4066472-7 gnd |
| topic_facet | Gleichgewichtstheorie Nichtkooperatives Spiel Fixpunkt Wirtschaftsmathematik |
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