Fixed points and economic equilibria

• Main Author: Urai, Ken.
• Corporate Author: World Scientific (Firm)
• Format: Electronic
• Language: English
• Published: Singapore ; Hackensack, N.J. : World Scientific Pub. Co., c2010.
• Series: Series on mathematical economics and game theory ; v. 5.
• Subjects: Equilibrium (Economics); Fixed point theory.; Economics > Mathematical models.; Electronic books.
• Online Access: View fulltext via EzAccess

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,...

Table of 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.