博弈论2:高级应用经典课程

Game Theory II: Advanced Applications

本课程是斯坦福大学的慕课,属高级课程,考虑的是如何使两个主体之间相互作用,以达到良好的社会效果。主要涵盖三个主题:社会选择理论(即集体决策)、机制设计和拍卖。

斯坦福大学

Coursera

经济

难(高级)

14 小时

  • 英语
  • 2481

课程概况

本课程是斯坦福大学的慕课,属高级课程,考虑的是如何使两个主体之间相互作用,以达到良好的社会效果。主要涵盖三个主题:社会选择理论(即集体决策)、机制设计和拍卖。

博弈论是理性和非理性主体之间策略互动的数学建模,它因电影,如:《美丽心灵》被人们所熟知。在四周的讲座中,这门高级课程考虑的是如何使两个主体之间相互作用,以达到良好的社会效果。主要涵盖三个主题:社会选择理论(即集体决策)、机制设计和拍卖。

第一周我们考虑的问题聚集不同主体的偏好,讨论投票规则和集体决策所面临的挑战。在这块我们提出了一些最重要的理论结果:值得注意的是,阿罗定理,该定理证明了没有“完美”的选举制度,同时也提出了齐柏-托维定理和穆勒-托维定理。我们继续考虑做出集体决策的问题。此时,主体都是自私自利的,并且会战略性地谎报自己的偏好。我们解释“机制设计”——一个用于设计自私自利的主体者之间相互作用的广泛框架,并且给出一些重要的理论结果。第三周我们关注的是设计出一种能使主体总体福利最大化的机制,同时介绍维克雷-克拉克-格罗夫斯机制的强大体系。 本课程用四周的时间考虑如何在自私自利的主体之间分配稀缺资源的问题,并且讲一下拍卖理论的导论。

Popularized by movies such as “A Beautiful Mind”, game theory is the mathematical modeling of strategic interaction among rational (and irrational) agents. Over four weeks of lectures, this advanced course considers how to design interactions between agents in order to achieve good social outcomes. Three main topics are covered: social choice theory (i.e., collective decision making and voting systems), mechanism design, and auctions.

In the first week we consider the problem of aggregating different agents’ preferences, discussing voting rules and the challenges faced in collective decision making. We present some of the most important theoretical results in the area: notably, Arrow’s Theorem, which proves that there is no “perfect” voting system, and also the Gibbard-Satterthwaite and Muller-Satterthwaite Theorems. We move on to consider the problem of making collective decisions when agents are self interested and can strategically misreport their preferences. We explain “mechanism design” — a broad framework for designing interactions between self-interested agents — and give some key theoretical results. Our third week focuses on the problem of designing mechanisms to maximize aggregate happiness across agents, and presents the powerful family of Vickrey-Clarke-Groves mechanisms. The course wraps up with a fourth week that considers the problem of allocating scarce resources among self-interested agents, and that provides an introduction to auction theory.

You can find a full syllabus and description of the course here: http://web.stanford.edu/~jacksonm/GTOC-II-Syllabus.html

There is also a predecessor course to this one, for those who want to learn or remind themselves of the basic concepts of game theory: https://www.coursera.org/learn/game-theory-1

An intro video can be found here: http://web.stanford.edu/~jacksonm/Game-Theory-2-Intro.mp4

课程大纲

第1周:社会选择
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第2周:机制设计
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第3周:有效机制
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第4周:拍卖
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第5周:期末考试
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预备知识

您必须有较强的数学思维和严谨的逻辑论证思维。还需要一些特定的数学基础;课程包括少量的概率论(例如,你应该知道什么是条件概率)和非常少量的的微积分(例如,导数)。

参考资料

以下背景阅读资料提供了更多的课程材料的详细范围:Yoav Shoham和 Kevin Leyton-Brown所写的《多智能体系统:算法、博弈论和逻辑基础》,剑桥出版社,2009年。这本书和该课程有相同的结构,并涵盖了大部分相同的材料。你可以从上面的链接中下载免费的PDF版或购买书籍(如):amazon.com.
Matthew O.Jackson所写的《博弈论基础知识简明介绍》。这本书速介绍了博弈论的基础知识;他们可以下载免费的PDF版。

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