不动点定理和应用
2009-6
世界图书出版公司
伯德
129
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Fixed point theorems are the basic mathematical tools used inshowing the existence of solution concepts in game theory andeconomics. While there are many excellent texts available on fixedpoint theory， most of them are inaccessible to a typical well-trainedeconomist. These notes are intended to be a nonintimidating intro-duction to the subject of fixed point theory with particular emphasison economic applications. While I have tried to integrate themathematics and applications， these notes arc not a comprehensiveintroduction to either general equilibrium theory or game theory.There are already a number of excellent texts in these areas. Debreu[1959] and Luce and Ralffa [1957] are classics. More recent textsinclude Hildenbrand and Kirman [1976]， Ichiisbi [1983]， Moulln[1982] and Owen [1982]， Instead I have tried to cover material thatgets left out of these texts， and to present it in such a way as to makeit quickly and easily accessible to people who want to apply fixedpoint theorems， not refine them. I have made an effort to presentuseful theorems fairly early on in the text. This leads to a certainamount of compromise. In order to keep prerequisites to aminimum， the theorems are not generally stated in their most generalform and the proofs presented are not necessarily the most elegant. Ihave tried to keep the level of mathematical sophistication on a parwith， say， Rudin [1976]. In particular， only finite-dimensional spacesarc used. While many of the theorems presented here are true in arbi-trary locally convex spaces， no attempt has been made to cover theinfinite-dimensional results. I have however deliberately tried topresent proofs that generalize easily to infinite dimensional spaceswhenever pssible.
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。
Preface1 Introduction: models and mathematics2 Convexity3 Simplexes4 Sperner's lemma5 The Knaster-Kuratowski-Mazurkiewicz lemma Brouwer's fixed point theorem Maximization of binary relations Variational inequalities, price equilibrium, and complementarity9 Some interconnections10 What good is a completely labeled subsimplex11 Continuity of correspondences12 The maximum theorem13 Approximation of correspondences14 Selection theorems for correspondences15 Fixed point theorems for correspondences16 Sets with convex sections and a minimax theorem17 The Fan-Browder theorem18 Equilibrium of excess demand correspondences19 Nash equilibrium of games and abstract economies20 Walrasian equilibrium of an economy21 More interconnections22 The Knaster-Kuratowski-Mazurkiewicz-Shapley iemma23 Cooperative equilibria of gamesReferencesIndex
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感觉印刷质量还是不错的，送货比较快。
老师一直推荐我买这本书，今天终于买了，很不错！
还没有读完，书是不错的
应该是不错的，给弟弟买的。