博弈論(Game Theory)很有意思,大家可能首先想到的就是賭博,據說博弈論最早源於賭博策略和數學,下面是來自維基百科的解釋:

博弈論(英語:game theory),又譯為對策論,或者賽局理論,應用數學的一個分支,1944年馮·諾伊曼與奧斯卡·摩根斯特恩合著《博弈論與經濟行為》,標誌著現代系統博弈理論的的初步形成,因此他被稱為「博弈論之父」。博弈論被認為是20世紀經濟學最偉大的成果之一。目前在生物學、經濟學、國際關係、計算機科學、政治學、軍事戰略和其他很多學科都有廣泛的應用。主要研究公式化了的激勵結構(遊戲或者博弈)間的相互作用。是研究具有鬥爭或競爭性質現象的數學理論和方法。也是運籌學的一個重要學科。

作為互聯網廣告研發人員,應該或多或少了解一點計算廣告學,其中支撐Google, 百度等互聯網巨頭廣告業務的競價排名機制的核心之一就是博弈論。另外經濟學中有很多博弈論的影子,電影「美麗心靈」中的主角數學家約翰納什,由於他與另外兩位數學家在非合作博弈的均衡分析理論方面做出了開創性的貢獻,對博弈論和經濟學產生了重大影響,而獲得1994年諾貝爾經濟學獎,納什均衡則是博弈論課程中不可或缺的一節課。Coursera上有好幾門博弈論(Game Theory)相關的課程,這裡做個匯總整理。

1. 斯坦福大學的 博弈論(Game Theory)

這門課程早在Coursera誕生之初就有了,後經多次優化,現在有上和下兩個部分,這門課程屬於博弈論上,重在博弈論基礎,需要學習者有一定的數學思維和數學基礎,例如基礎的概率理論和一些微積分基礎知識:

This course is aimed at students, researchers, and practitioners who wish to understand more about strategic interactions. You must be comfortable with mathematical thinking and rigorous arguments. Relatively little specific math is required; but you should be familiar with basic probability theory (for example, you should know what a conditional probability is), and some very light calculus would be helpful.

2. 斯坦福大學的 博弈論二: 高級應用(Game Theory II: Advanced Applications)

上門博弈論課程的續集,關注博弈論的應用,包括機制設計,拍賣機制等:

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.

3. 東京大學的 博弈論入門課程(Welcome to Game Theory)

入門級博弈論課程,由東京大學推出,英文授課:

This course provides a brief introduction to game theory. Our main goal is to understand the basic ideas behind the key concepts in game theory, such as equilibrium, rationality, and cooperation. The course uses very little mathematics, and it is ideal for those who are looking for a conceptual introduction to game theory. Business competition, political campaigns, the struggle for existence by animals and plants, and so on, can all be regarded as a kind of 「game,」 in which individuals try to do their best against others. Game theory provides a general framework to describe and analyze how individuals behave in such 「strategic」 situations. This course focuses on the key concepts in game theory, and attempts to outline the informal basic ideas that are often hidden behind mathematical definitions. Game theory has been applied to a number of disciplines, including economics, political science, psychology, sociology, biology, and computer science. Therefore, a warm welcome is extended to audiences from all fields who are interested in what game theory is all about.

4. 喬治亞理工學院的 組合博弈論(Games without Chance: Combinatorial Game Theory)

這門課程主要關注組合博弈論,覆蓋不靠運氣遊戲背後的數學理論和分析:This course will cover the mathematical theory and analysis of simple games without chance moves.

本課程將講解如何運用數學理論,分析不含運氣步驟(隨機步驟)的簡單遊戲。本課程將探索不含運氣步驟(隨機步驟)的兩個玩家遊戲中的數學理論。我們將討論如何簡化遊戲,什麼情況下遊戲等同於數字運算,以及怎樣的遊戲才算公正。許多例子都是有關一此簡單的遊戲,有的你可能還沒有聽說過:Hackenbush(「無向圖刪邊」遊戲)、Nim(「拈」遊戲)、Push(推箱子遊戲)、Toads and Frogs(「蟾蜍和青蛙」遊戲),等。雖然完成這門課程並不能讓你成為國際象棋或圍棋高手,但是會讓你更深入了解遊戲的結構。

5. 國立台灣大學的 實驗經濟學: 行為博弈論 (Experimental Economics I: Behavioral Game Theory)

台灣大學王道一副教授 (Associate Professor)的實驗經濟學課程-行為博弈論:

人是否會如同理論經濟學的預測進行決策?這門課將透過每周的課程視頻以及課後作業帶你了解實驗經濟學的基本概念。每周將會有習題練習以及指定閱讀的期刊論文。你將會參與一些在線的實驗、報告論文並且互評其他同學的報告。?課程介紹(About the course)這是一門進階的經濟學課程,課程目標為介紹實驗經濟學的基本概念,並且讓學生們能開始在這個領域從事自己的相關研究。詳細課程目標如下:1.實驗經濟學的介紹:在上完這堂課之後,學生應能列舉經濟學各個領域的數個知名實驗,並且解釋實驗結果如何驗證或否證經濟理論及其他實地數據。2.評論近期相關領域研究:上完這堂課之後,學生應能閱讀並評論實驗經濟學相關的期刊論文。在課堂中,學生將會閱讀指定的期刊論文,並且(在視頻中)親自上台報告一篇論文。?授課形式(Course format)1.本堂課將以視頻的形式為主,搭配課後作業的形式來進行。每個同學將閱讀一篇實驗經濟學論文,並錄像成兩段各10分鐘的介紹視頻並後上傳至Coursera(或上傳到Youku,再複製連接到作業上傳區)。第一段期中報告視頻請同學介紹該論文所描述的實驗設計,第二段,也就是期末報告視頻則介紹實驗結果。此外每位同學至少需觀看其他兩位同學的呈現內容,並給予評論。2.這堂課將簡單地運用以下賽局(博弈)概念:奈許均衡/納什均衡(Nash Equilibrium)混合策略均衡(Mixed Strategy Equilibrium)子賽局完美均衡/子博弈精練納什均衡(SPNE)共識/共同知識(Common Knowledge)信念(Belief)

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