Fixed Point Theorems with Applications to Economics and Game Theory (REP SUB)

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Fixed Point Theorems with Applications to Economics and Game Theory (REP SUB)

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  • 製本 Paperback:紙装版/ペーパーバック版
  • 言語 ENG
  • 商品コード 9780521388085
  • DDC分類 330

Full Description


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.

Table of Contents

Preface                                            vii
Introduction: models and mathematics 1 (8)
Convexity 9 (10)
Simplexes 19 (4)
Sperner's lemma 23 (3)
The Knaster-Kuratowski-Mazurkiewicz lemma 26 (2)
Brouwer's fixed point theorem 28 (3)
Maximization of binary relations 31 (7)
Variational inequalities, price equilibrium, 38 (6)
and complementarity
Some interconnections 44 (6)
What good is a completely labeled subsimplex 50 (3)
Continuity of correspondences 53 (10)
The maximum theorem 63 (4)
Approximation of correspondences 67 (2)
Selection theorems for correspondences 69 (2)
Fixed point theorems for correspondences 71 (3)
Sets with convex sections and a minimax 74 (4)
theorem
The Fan-Browder theorem 78 (3)
Equilibrium of excess demand correspondences 81 (7)
Nash equilibrium of games and abstract 88 (7)
economies
Walrasian equilibrium of an economy 95 (9)
More interconnections 104(5)
The Knaster-Kuratowski-Mazurkiewicz-Shapley 109(3)
lemma
Cooperative equilibria of games 112(10)
References 122(5)
Index 127