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Fixed point theorems with applications to economics and game theory / Kim C. Border.
Author
Border, Kim C.
[Browse]
Format
Book
Language
English
Published/Created
Cambridge [Cambridgeshire] ; New York : Cambridge University Press, 1985.
Description
viii, 129 pages : illustrations ; 24 cm
Availability
Copies in the Library
Location
Call Number
Status
Location Service
Notes
Lewis Library - Stacks
QA329.9 .B67 1985
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Details
Subject(s)
Fixed point theory
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Economics, Mathematical
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Game theory
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Summary note
One of the problems in economics that economists have devoted a considerable amount of attention in prevalent years has been to ensure consistency in the models they employ. Assuming markets to be generally in some state of equilibrium, it is asked under what circumstances such equilibrium is possible. The fundamental mathematical tools used to address this concern are fixed point theorems: the conditions under which sets of assumptions have a solution. This book gives the reader access to the mathematical techniques involved and goes on to apply fixed point theorems to proving the existence of equilibria for economics and for co-operative and noncooperative games. Special emphasis is given to economics and games in cases where the preferences of agents may not be transitive. The author presents topical proofs of old results in order to further clarify the results. He also proposes fresh results, notably in the last chapter, that refer to the core of a game without transitivity. This book will be useful as a text or reference work for mathematical economists and graduate and advanced undergraduate students.
Notes
Includes index.
Bibliographic references
Bibliography: p. [122]-126.
Contents
Introduction: models and mathematics
Convexity
Simplexes
Sperner's lemma
The Knaster-Kuratowski-Mazurkiewicz lemma
Brouwer's fixed point theorem
Maximization of binary relations
Variational inequalities, price equilibrium, and complementarity
Some interconnections
What good is a completely labeled subsimplex
Continuity of correspondences
The maximum theorem
Approximation of correspondences
Selection theorems for correspondences
Fixed point theorems for correspondences
Sets with convex sections and a minimax theorem
The Fan-Browder theorem
Equilibrium of excess demand correspondences
Nash equilibrium of games and abstract economies
Walrasian equilibrium of an economy.
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ISBN
0521388082
9780521388085
0521265649 ((U.S.))
9780521265645 ((U.S.))
9780511625756 ((ebook))
0511625758
LCCN
84019925
OCLC
11133342
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Fixed point theorems with applications to economics and game theory / Kim C. Border.
id
SCSB-5984456
Fixed point theorems with applications to economics and game theory / Kim C. Border.
id
SCSB-2403468