Advanced Fixed Point Theory for Economics -  Andrew McLennan

Advanced Fixed Point Theory for Economics (eBook)

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2018 | 1st ed. 2018
XX, 432 Seiten
Springer Singapore (Verlag)
978-981-13-0710-2 (ISBN)
Systemvoraussetzungen
128,39 inkl. MwSt
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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.



Andrew McLennan received his PhD from Princeton in 1982 under the supervision of Hugo Sonnenschein, and is currently Professor at the University of Queensland School of Economics. His primary research interests are in game theory, mathematical economics and microeconomics.
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.

Andrew McLennan received his PhD from Princeton in 1982 under the supervision of Hugo Sonnenschein, and is currently Professor at the University of Queensland School of Economics. His primary research interests are in game theory, mathematical economics and microeconomics.

Chapter 1 Introduction and Summary.- Part I Topological Methods.- Chapter 2 Planes, Polyhedra, and Polytopes.- Chapter 3 Computing Fixed Points.- Chapter 4 Topologies on Spaces of Sets.- Chapter 5 Topologies on Functions and Correspondences.- Chapter 6 Metric Space Theory.- Chapter 7 Retracts.- Chapter 8 Essential Sets of Fixed Points.- Chapter 9 Approximation of Correspondences.- Part II Smooth Methods.- Chapter 10 Differentiable Manifolds.- Chapter 11 Sard’s Theorem.- Chapter 12 Degree Theory.- Chapter 13 The Fixed Point Index.- Part III Applications and Extensions.- Chapter 14 Topological Consequences.- Chapter 15 Vector Fields and their Equilibria.

Erscheint lt. Verlag 3.7.2018
Zusatzinfo XX, 432 p. 18 illus.
Verlagsort Singapore
Sprache englisch
Themenwelt Mathematik / Informatik Mathematik Angewandte Mathematik
Mathematik / Informatik Mathematik Finanz- / Wirtschaftsmathematik
Wirtschaft Allgemeines / Lexika
Wirtschaft Volkswirtschaftslehre
Schlagworte Brouwer fixed point theorem • differentiable manifold • Economic Modeling • Economic Theory • Eilenberg–Montgomery theorem • Fan–Glicksberg theorem • fixed point index • Fixed Point Theory • Game Theory • General Equilibrium Theory • Kakutani fixed point theorem • Lefschetz fixed point theorem • Mathematical economics • Metric space theory • Multivariate Calculus • Nash Equilibrium • Schauder Fixed Point Theorem • Topological degree • topological methods • Topology
ISBN-10 981-13-0710-5 / 9811307105
ISBN-13 978-981-13-0710-2 / 9789811307102
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