This note will be permanently deleted and cannot be recovered. Are you sure?
Are you sure you wish to share this note?
Sorry, you can only share notes on selected books with the reading experience feature.
Please choose the Show Notes option before creating a new note.
By Kim C. Border
Publisher: Cambridge University Press
Print Publication Year:1985
Online Publication Date:January 2010
Online ISBN:9780511625756
Hardback ISBN:9780521265645
Paperback ISBN:9780521388085
Book DOI: http://dx.doi.org/10.1017/CBO9780511625756
Subjects: Econometrics and mathematical methods , Economic thought, philosophy and methodology
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.
Reviews:
pp. i-iv
pp. v-vi
pp. vii-viii
1 - Introduction: models and mathematics: Read PDF
pp. 1-8
pp. 9-18
pp. 19-22
pp. 23-25
5 - The Knaster-Kuratowski-Mazurkiewicz lemma: Read PDF
pp. 26-27
6 - Brouwer's fixed point theorem: Read PDF
pp. 28-30
7 - Maximization of binary relations: Read PDF
pp. 31-37
8 - Variational inequalities, price equilibrium, and complementarity: Read PDF
pp. 38-43
9 - Some interconnections: Read PDF
pp. 44-49
10 - What good is a completely labeled subsimplex: Read PDF
pp. 50-52
11 - Continuity of correspondences: Read PDF
pp. 53-62
12 - The maximum theorem: Read PDF
pp. 63-66
13 - Approximation of correspondences: Read PDF
pp. 67-68
14 - Selection theorems for correspondences: Read PDF
pp. 69-70
15 - Fixed point theorems for correspondences: Read PDF
pp. 71-73
16 - Sets with convex sections and a minimax theorem: Read PDF
pp. 74-77
17 - The Fan-Browder theorem: Read PDF
pp. 78-80
18 - Equilibrium of excess demand correspondences: Read PDF
pp. 81-87
19 - Nash equilibrium of games and abstract economies: Read PDF
pp. 88-94
20 - Walrasian equilibrium of an economy: Read PDF
pp. 95-103
21 - More interconnections: Read PDF
pp. 104-108
22 - The Knaster-Kuratowski-Mazurkiewicz-Shapley lemma: Read PDF
pp. 109-111
23 - Cooperative equilibria of games: Read PDF
pp. 112-121
pp. 122-126
pp. 127-129
No references available.