Fixed Point Theorems with Applications to Economics and Game Theory 0521265649, 9780521265645, 0521388082, 9780521388085
One of the problems in economics that economists have devoted a considerable amount of attention in prevalent years has
309 39 301KB
English Pages 138 Year 1985
Table of contents :
Cover......Page 1
Fixed point theorems with applications to economics and game theory......Page 4
Copyright......Page 5
Contents......Page 6
Preface......Page 8
1. Introduction: Models and mathematics......Page 10
2. Convexity......Page 18
3. Simplexes......Page 28
4. Sperner's lemma......Page 32
5. The Knaster-Kuratowski-Mazurkiewicz lemma......Page 35
6. Brouwer's fixed point theorem......Page 37
7. Maximization of binary relations......Page 40
8. Variational inequalities, price equilibrium, and complementarity......Page 47
9. Some interconnections......Page 53
10. What good is a completely labeled subsimplex......Page 59
11. Continuity of correspondences......Page 62
12. The maximum theorem......Page 72
13. Approximation of correspondences......Page 76
14. Selection theorems for correspondences......Page 78
15. Fixed point theorems for correspondences......Page 80
16. Sets with convex sections and a minimax theorem......Page 83
17. The Fan-Browder theorem......Page 87
18. Equilibrium of excess demand correspondences......Page 90
19. Nash equilibrium of games and abstract economies......Page 97
20. Walrasian equilibrium of an economy......Page 104
21. More interconnections......Page 113
22. The Knaster-Kuratowski-Mazurkiewicz Shapley lemma......Page 118
23. Cooperative equilibria of games......Page 121
References......Page 131
Index......Page 136
Cover......Page 1
Fixed point theorems with applications to economics and game theory......Page 4
Copyright......Page 5
Contents......Page 6
Preface......Page 8
1. Introduction: Models and mathematics......Page 10
2. Convexity......Page 18
3. Simplexes......Page 28
4. Sperner's lemma......Page 32
5. The Knaster-Kuratowski-Mazurkiewicz lemma......Page 35
6. Brouwer's fixed point theorem......Page 37
7. Maximization of binary relations......Page 40
8. Variational inequalities, price equilibrium, and complementarity......Page 47
9. Some interconnections......Page 53
10. What good is a completely labeled subsimplex......Page 59
11. Continuity of correspondences......Page 62
12. The maximum theorem......Page 72
13. Approximation of correspondences......Page 76
14. Selection theorems for correspondences......Page 78
15. Fixed point theorems for correspondences......Page 80
16. Sets with convex sections and a minimax theorem......Page 83
17. The Fan-Browder theorem......Page 87
18. Equilibrium of excess demand correspondences......Page 90
19. Nash equilibrium of games and abstract economies......Page 97
20. Walrasian equilibrium of an economy......Page 104
21. More interconnections......Page 113
22. The Knaster-Kuratowski-Mazurkiewicz Shapley lemma......Page 118
23. Cooperative equilibria of games......Page 121
References......Page 131
Index......Page 136
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