Fixed points and economic equilibria /

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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,...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Urai, Ken, 1962-
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Singapore ; Hackensack, NJ : World Scientific, ©2010.
Colección:Series on mathematical economics and game theory ; v. 5.
Temas:
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
Acceso en línea:Texto completo
Tabla de Contenidos:
  • 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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