Fixed Point Theorems with Applications to Economics and Game Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Fixed Point Theorems with Applications to Economics and Game Theory write by Kim C. Border. This book was released on 1985. Fixed Point Theorems with Applications to Economics and Game Theory available in PDF, EPUB and Kindle. This book explores fixed point theorems and its uses in economics, co-operative and noncooperative games.
Fixed Points and Economic Equilibria
Fixed Points and Economic Equilibria - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Fixed Points and Economic Equilibria write by Ken Urai. This book was released on 2010. Fixed Points and Economic Equilibria available in PDF, EPUB and Kindle. 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
Fixed-point Theorems with Applications to Game Theory
Fixed-point Theorems with Applications to Game Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Fixed-point Theorems with Applications to Game Theory write by . This book was released on 2002. Fixed-point Theorems with Applications to Game Theory available in PDF, EPUB and Kindle. Nash's Theorem is an important game-theoretic result following from the fixed-point theorem of Kakutani, which is itself a generalization of Brouwer's Fixed-Point Theorem. This paper will present a detailed proof of Brouwer's Theorem, as well as an overview of the concepts of homology, homotopy, and degree which are necessary to the proof. Also included are discussion and less-detailed proofs of Kakutani's and Nash's theorems.
Fixed Point Theorems and Applications
Fixed Point Theorems and Applications - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Fixed Point Theorems and Applications write by Vittorino Pata. This book was released on 2019-09-22. Fixed Point Theorems and Applications available in PDF, EPUB and Kindle. This book addresses fixed point theory, a fascinating and far-reaching field with applications in several areas of mathematics. The content is divided into two main parts. The first, which is more theoretical, develops the main abstract theorems on the existence and uniqueness of fixed points of maps. In turn, the second part focuses on applications, covering a large variety of significant results ranging from ordinary differential equations in Banach spaces, to partial differential equations, operator theory, functional analysis, measure theory, and game theory. A final section containing 50 problems, many of which include helpful hints, rounds out the coverage. Intended for Master’s and PhD students in Mathematics or, more generally, mathematically oriented subjects, the book is designed to be largely self-contained, although some mathematical background is needed: readers should be familiar with measure theory, Banach and Hilbert spaces, locally convex topological vector spaces and, in general, with linear functional analysis.
Advanced Fixed Point Theory for Economics
Advanced Fixed Point Theory for Economics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Advanced Fixed Point Theory for Economics write by Andrew McLennan. This book was released on 2018-07-03. Advanced Fixed Point Theory for Economics available in PDF, EPUB and Kindle. This book develops the central aspect of fixed point theory – the topological fixed point index – to maximal generality, emphasizing correspondences and other aspects of the theory that are of special interest to economics. Numerous topological consequences are presented, along with important implications for dynamical systems. The book assumes the reader has no mathematical knowledge beyond that which is familiar to all theoretical economists. In addition to making the material available to a broad audience, avoiding algebraic topology results in more geometric and intuitive proofs. Graduate students and researchers in economics, and related fields in mathematics and computer science, will benefit from this book, both as a useful reference and as a well-written rigorous exposition of foundational mathematics. Numerous problems sketch key results from a wide variety of topics in theoretical economics, making the book an outstanding text for advanced graduate courses in economics and related disciplines.
