Fixed Point Theorems with Applications to Economics and Game Theory
Edition: Reprint
Publisher: Cambridge University Press
Published: 1999
Place of publication: Cambridge, UK
Language: eng
Format: Paperback
Number of pages: 144
ISBN-13: 9780521388085
Copyright date: 1985
Subjects: Economic theory & philosophy; Topology; Mathematics; Mathematical Models In Economics; Business & Economics; Business/Economics; Calculus; Economic History; Game Theory; Business & Economics / Economic History; Business & Economics-Economic History; Fixed point theory; Fixed point theory Fixed point theory; Mathematics / Calculus; Mathematics-Game Theory
First sentence: Denote the reals by R, the nonnegative reals by R+ and the strictly positive reals by R++.
Description: Fixed point theorems outline the conditions under which sets of assumptions have a solution and can be used to determine if it is possible for a market to be in equilibrium. This book gives the reader access to the mathematical techniques involved and goes on to apply fixed point theorems to prove the existence of equilibria for economics and for cooperative and non-cooperative games. Special emphasis is given to economies and games in cases where the preferences of agents may not be transitive.
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Table of contents: title: Preface; title: 1. Introduction: models and mathematics; title: 2. Convexity; title: 3. Simplexes; title: 4. Sperner's lemma; title: 5. The Knaster-Kuratowski-Mazurkiewicz lemma; title: 6. Brouwer's fixed point theorem; title: 7. Maximization of binary relations; title: 8. Variational inequalities, price equilibrium, and complementarity; title: 9. Some interconnections; title: 10. What good is a completely labelled subsimplex?; title: 11. Continuity of correspondences; title: 12. The maximum theorem; title: 13. Approximation of correspondence; title: 14. Selection theorems for correspondences; title: 15. Fixed point theorems for correspondences; title: 16. Sets with convex sections and a minimax theorem; title: 17. The Fan-Browder theorem; title: 18. Equilibrium of excess demand correspondences; title: 19. Nash equilibrium of games and abstract economies; title: 20. Walrasian equilibrium of an economy; title: 21. More interconnections; title: 22. The Knaster-Kuratowski-Mazurkiewicz-Shapley lemma; title: 23. Cooperative equilibria of games; title: References; title: Index.