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myerson: 向海萨尼学习博弈论(2)  

2009-07-13 16:11:36|  分类: 默认分类 |  标签: |举报 |字号 订阅

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 二、海萨尼完成了博弈论的统一事业


First and foremost,what made John Harsanyi's work so special was his consistent focus on analyticalgenerality. The key to understanding his work may have been best expressed in ashort paper on theoretical analysis in social science that he published in 1961 in the Australian Journal ofPolitics and History. There he wrote:

首先,John Harsanyi的研究之所以如此地独一无二,就在于他一以贯之地侧重于分析解的一般性研究。要理解他的工作,关键就在于他的那篇关于社会科学理论分析的短文,这篇文章发表于1961年的Australian Journal of Politics andHistory。他写道:

Theunusually rapid social, economic, and political changes of our period, theconflicts between rival economic and political systems, the hot and cold wars,revolutions and other social crises that we have been experiencing, representan intellectual and practical challenge that cannot be met by a meredescription of the facts but only by theoretical analysis, by explaining andevaluating these facts in terms of a general theoretical framework. (Harsanyi, 1961a, p 60.)

在我们这个时代,发生了很不寻常的社会、经济和政治变化,发生了相互对立的经济体系和政治体系之间的冲突,发生了热战和冷战,发生了革命,也发生了其他的各种社会危机,这正是我们所经历的事情。这给我们提出了智识和实践上的挑战。我们不能只是描述事实,而应该用理论分析来展现这种挑战。我们要用一个普适性的理论框架,来解释这些事实,来评估这些事实。(Harsanyi, 1961a, p.60

The madness of theNazi and Communist systems which had persecuted him cried out for explanation.He responded in his own way, not by dwelling on the social evils that he hadexperienced, but by working systematically to reconstruct the logicalfoundations of social theory, so that people in the future might better understandthe dynamics of social institutions. In this labor, he drew deeply on themathematical and philosophical skills that he developed in Hungary, duringthe years when scholarship was not forbidden to him.

迫害过他的纳粹制度等,是最需要解释的现象。他用自己的方式进行了响应,他并没有停留于他所经历的社会邪恶之上,而是进行了系统的研究,重构了社会理论的逻辑基础。这样,未来的人们,就可以更好地理解社会制度的动态演变了。在他的工作中,他充分地利用了自己在匈牙利所发展出来的数学工具和哲学工具。要知道,那些年里,他的学者身份可是要受到一定的限制的。

In this 1961 paper hesketched the logical progression that led him to game theory. He began withsome references to other general structures that he had studied in socialscience, including those of Max Weber and Talcott Parsons. But he went on toexplain carefully why he found the most effective social theories to be thosewhich explain people's behavior. in terms of their individual preferences, andthis led him to game theory.

在这篇文章中,他描述了引导他去研究博弈论的每一步逻辑过程。文章一开始,他提到了在社会科学领域里他研究过的几个一般性的理论框架,包括Max WeberTalcott Parsons。接着,他仔细地解释了,为什么他会觉得最有效的社会理论,是那些从个人偏好的角度对人类行动进行解释的理论,由此,他走向了博弈论。 

The game theory thathe found in the 1950s was a new subfield where a small but extraordinary groupof mathematicians and economists wrestled with basic questions of methodology.There was a proliferation of different solution concepts, but most of themcould be applied only to special types of games, either to games where players'payoffs were transferable like money, or to games where there were only twoplayers. Many theories could yield multiple solutions or no solutions at allfor a game.

 他在1950年代建立的博弈论,是一个全新的子领域,有一小群杰出的数学家和经济学家,当时正在全力解决方法论上的基本问题。当时,在解概念上,存在大量的不同看法,而且,大部分的解,都只适用于某些特定的博弈型,或者适用于局中人的支付为“货币”式可转移支付的博弈;或者适用于只有两个局中人的博弈。许多理论,都有多重解,或者根本就没有解。

John Harsanyi's viewof the field was clarified by his insistence that a good solution conceptshould yield one well-defined solution to any game. And in the mid 1950s, ifyou looked for game theoretic solution concepts that yielded unique solutionsto broad classes of games, you would find two. Lloyd Shapley's (1953) solutionyielded a unique value with any number of players, but was only defined forgames where payoffs were transferable. John Nash's (1950, 1953) bargainingsolution did not require transferable payoffs, but was only defined for gameswith two players. In 1956, Harsanyi showed that Nash's bargaining solutioncould be derived from an earlier theory of bargaining by the Danish economistFrederik Zeuthen (1930). Then in 1959 and 1963, John Harsanyi published papersto show how the Nash bargaining solution and the Shapley value could be unifiedinto one general solution concept that could be applied to any cooperative gamewith complete information. This 1963paper, with its remarkable unification ofthe two nicest solution concepts in game theory, was the paper that got mestarted in game theory. (I still treasure the photocopy of it that I made in1972.)

John Harsanyi对这个领域所持的观点,就是:他一贯坚信“存在一个好的解概念,它应该能对任一种博弈给出一个明确的解。”如果你检阅1950年代中期“对各种博弈型,都给出惟一解的博弈理论解概念”的文献,你会找到两个人。Lloyd Shapley (1953)的解,对于任意数量的局中人,给出了一个惟一值,但是,这个解是定义在“博弈的支付为可转移”的情况下的。John Nash (1950, 1953)的解,不需要支付为可转移,但是,只定义在“局中人为两人”的情形下。在1956年,Harsanyi说明了:Nash的讨价还价解,可以从更早期的丹麦经济学家Frederik Zeuthen的讨价还价理论中推导出来。接着,在1959年和1963年,JohnHarsanyi发表了两篇论文,说明了:Nash的讨价还价解与Shapley值,是可以统一到一个一般性的解概念中的,而且,它适用于完全信息下的任意一种博弈。正是这篇1963年的论文,它完美地将前面两种最漂亮的解概念,统一了起来;正是这篇论文,引领着我,使我开始了博弈论的研究。(在1972年时,我影印了这篇文章。这个影印本,我至今无比珍惜。)

 (待续)

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