不动点理论是假设给定的集合中有一个解并且可以用它来决定市场是不是处于平衡态中。书中重在强调实践中的应用,让读者了解应用不动点理论到经济和合作与非合作博弈中平衡点的存在性的数学技巧。将数学理论和其在经济中的应用既巧妙结合又有机区分,对于数学家和经济学家这都是一本很有价值的基础手头参考书。
Preface
1 Introduction: models and mathematics
2 Convexity
3 Simplexes
4 Sperner's lemma
5 The Knaster-Kuratowski-Mazurkiewicz lemma
6 Brouwer's fixed point theorem
7 Maximization of binary relations
8 Variational inequalities, price equilibrium, and complementarity
9 Some interconnections
10 What good is a completely labeled subsimplex
11 Continuity of correspondences
12 The maximum theorem
13 Approximation of correspondences
14 Selection theorems for correspondences
15 Fixed point theorems for correspondences
16 Sets with convex sections and a minimax theorem
17 The Fan-Browder theorem
18 Equilibrium of excess demand correspondences
19 Nash equilibrium of games and abstract economies
20 Walrasian equilibrium of an economy
21 More interconnections
22 The Knaster-Kuratowski-Mazurkiewicz-Shapley iemma
23 Cooperative equilibria of games
References
Index