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Supermodularity and Complementarity
Donald M. Topkis
Cloth | 1998 | $105.00 / £62.00/312 pp. | 6 x 9
Princeton University Press
The economics literature is replete with examples of monotone comparative statics; that is, scenarios where optimal decisions or equilibria in a parameterized collection of models vary monotonically with the parameter. Most of these examples are manifestations of complementarity, with a common explicit or implicit theoretical basis in properties of a super-modular function on a lattice. Supermodular functions yield a characterization for complementarity and extend the notion of complementarity to a general setting that is a natural mathematical context for studying complementarity and monotone comparative statics. Concepts and results related to supermodularity and monotone comparative statics constitute a new and important formal step in the long line of economics literature on complementarity.
This monograph links complementarity to powerful concepts and results involving supermodular functions on lattices and focuses on analyses and issues related to monotone comparative statics. Don Topkis, who is known for his seminal contributions to this area, here presents a self-contained and up-to-date view of this field, including many new results, to scholars interested in economic theory and its applications as well as to those in related disciplines. The emphasis is on methodology. The book systematically develops a comprehensive, integrated theory pertaining to supermodularity, complementarity, and monotone comparative statics. It then applies that theory in the analysis of many diverse economic models formulated as decision problems, noncooperative games, and cooperative games.
Table of Contents:
Preface
Ch. 1 Introduction 3
Ch. 2 Lattices, Supermodular Functions, and Related Topics 7
Ch. 3 Optimal Decision Models 94
Ch. 4 Noncooperative Games 175
Ch. 5 Cooperative Games 207
Bibliography 263
Index 269
[此贴子已经被作者于2008-8-9 19:52:32编辑过]
不客气。我自己也只是在随性看这方面的东西，看法还谈不上，所知的也就是文献上的各种说法，没必要拿出来冒充自己的想法。既然有同好，那就再发点自己搜集的资料。
1.数学基础：超模博弈是建立在Lattice Theory基础上的，属于代数的范畴。在维基百科上看到推荐夏威夷大学的J.B. Nation的Notes on Lattice Theory，好像还不错，发上来供参考。
2.超模的专著：超模分析是本书的作者Topkis提出的，这本书是专门讨论超模博弈及其应用的，是理所当然的经典。这个领域中另一个重量级的学者是西班牙的Vavier Vives，他1999年在MIT出版社出版了Oligopoly Pricing: Old Ideas and New Tools，应用超模博弈对寡头垄断市场的分析进行了重新阐述，在论坛中有这本书的扫描版，但是效果不大好，很多地方看不清楚，下面这个文件是这本书在NetLibrary上的版本，可以跟扫描版对比着看。
3.超模的文章：Topkis1978、1979年的两篇文章（1978，Minimizing a Submodular Function on a Lattice；1979，Equilibrium Points in Nonzero-sum n-person Submodular Games）正式提出了超模和超模博弈的概念，尤其是后一篇被认为是开创性的文献；Vives1990年在Journal of Mathematical Economics上发表了Nash Equilibrium with Strategic Complementarities，也算是这一领域的开创性文献，后来Vives又写了不少这方面的文献，基本上都可以在他的个人主页（http://webprofesores.iese.edu/xvives/publications.asp）上下载到，值得一提的是Vives2005年在Journal of Economic Literature上发表了一篇关于互补和超模的综述Complementarities and Games: New Developments，感兴趣的可以在看其他文献之前先看一下这篇文章，以了解超模博弈及其现在的进展；应用领域则首推Stanford的Paul Milgrom，他和John Roberts1990年分别在AER和Econometrica上发表了两篇重要文献（AER：The Economics of Modern Manufacturing: Technology, Strategy, and Organization，中间有个定理有错误，Topkis等在1995年指出；Econometrica：Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities），在单调比较静态分析方面，Milgrom和Shanon1994年在Econometrica发表了Monotone Comparative Statics以及Milgrom的学生Susan Athey2002年发在QJE上的Monotone Comparative Statics under Uncertainty都是一些重要的文献；另外Jeremy I. Bulow、John D. Geanakoplos和Paul D. Klemperer1985年在JPE上发表了Multimarket Oligopoly: Strategic Substitutes and Complements，正式提出了策略替代和策略互补的概念和分析框架。另外Rabah Amir等人也分别在Games and Economic Behavior和Journal of Economic Theory上发表了一些关于超模博弈或单调比较静态的文章。
下面这个文件是这几篇文献，但是Topkis1979年的文献我还一直没找到，其完整信息为Topkis, D. (1979). “Equilibrium Points in Nonzero-Sum n-Person Submodular Games,” SIAM Journal of Control and Optimization 17, 773–787，如果哪位能找到发上来将不胜感谢。
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[此贴子已经被作者于2008-8-10 11:21:00编辑过]
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