Description 
1 online resource (xvii, 292 pages) : illustrations 
Series 
Series on mathematical economics and game theory ; v. 5 

Series on mathematical economics and game theory ; v. 5

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. Fixedpoint 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. Multiagent product settings for games. 3.2. Nash equilibrium. 3.3. Abstract economy  4. GaleNikaidoDebreu's theorem. 4.1. GaleNikaidoDebreu's theorem. 4.2. Market equilibria in general vector spaces. 4.3. Demandsupply 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. VietorisBegle mapping and local connectedness. 6.3. Nikaido's analogue of Sperner's lemma. 6.4. EilenbergMontgomery's theorem  7. Convex structure and fixedpoint index. 7.1. Lefschetz's fixedpoint theorem and its extensions. 7.2. Cohomology theory for general spaces. 7.3. Dualsystem 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. FanBrowder's coincidence theorem. 8.4. Lmajorized 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 fixedpoint views of the world 
Summary 
This book presents a systematic approach to problems in economic equilibrium based on fixedpoint arguments and rigorous settheoretical (axiomatic) methods. It describes the highestlevel 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 noncooperative 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 
Bibliography 
Includes bibliographical references (pages 277284) and index 
Notes 
Print version record 
Subject 
Equilibrium (Economics)  Mathematical models.


Fixed point theory.

Form 
Electronic book

ISBN 
9789812837196 (electronic bk.) 

9812837191 (electronic bk.) 
