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myerson: 向海萨尼学习博弈论(3)  

2009-07-16 22:11:36|  分类: 默认分类 |  标签: |举报 |字号 订阅

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三、海萨尼的博弈论研究方法的转变之路

But this early workwas all in cooperative game theory. John Nash had introduced the basic conceptof noncooperative equilibrium in 1951, but in the decade thereafter there wasvery little work in noncooperative game theory. The most important advance inthis decade was Thomas Schelling's (1957, 1958) theory of the focal-pointeffect in games with multiple equilibria, which he advocated as a better way tounderstand bargaining in the real world. John Harsanyi responded to Schellingin a 1961 paper in the Journal of Conflict Resolution. In this paper, JohnHarsanyi argued that the distribution of power that is measured by acooperative solution concept can become the focal factor that selects among themany noncooperative equilibria of a bargaining game. To me, this paper stillstands as the definitive defense of cooperative game theory against thearguments of a noncooperative game theorist. But, in 1961, virtually all theactive game theorists except Schelling still wanted to do cooperative gametheory. The advance of noncooperative game theory really began in footnote 7 ofthis paper, where John Harsanyi promised to show, in a subsequent paper, howthe axioms of his general bargaining theory could be extended to noncooperativegames.

但是,早期的研究,全都是合作博弈理论。John Nash1951年时引入了非合作均衡的基本概念,但是,在此后的十年中,非合作博弈论方面的研究,极其少见。那个10年里,最重要的推进,是Thomas Schelling19571958)的“多重均衡博弈的聚点效应”理论,他提出这个理论,并认为它是理解现实世界中的讨价还价问题的一个更好方法。John Harsanyi1961年写了一篇文章,对Schelling的研究提出了回应,文章发表于Journal of Conflict Resolution上。在这篇文章中,John Harsanyi指出:用合作博弈概念来度量的权力分配,可以作为在某个讨价还价博弈的许多非合作均衡中进行选择的“聚点因素”。对我来说,这篇文章在“合作博弈理论与非合作博弈理论”之争中,是对合作博弈的一个确定性的辩护。但是,在1961年,除了Schelling之外,本质上来说,所有活跃的博弈理论家们,依然想研究合作博弈理论。非合作博弈论的推进,实际上,是从Harsanyi的这篇文章的“脚注7”开始的。在这个脚注中,Harsanyi承诺在后续研究中,说明:他的一般讨价还价理论的定理,可以拓展到非合作博弈。 

That subsequent paperbecame a series of papers (Harsanyi 1962a, 1964, 1966, 1975), and ultimately led to hisgreat book with Reinhard Selten (1988). Applying ideas like risk dominance toidentify a unique rational equilibrium for any noncooperative game proved to bea very hard problem. But as soon as he began to work on it, John Harsanyirealized the force of Nash's early arguments for the greater generality ofnoncooperative game theory over the cooperative approach. Thus Harsanyiswitched camps during the 1960s, and he became the leading advocate ofnoncooperative game theory. In this role, he began the search for theoreticalcriteria to select among multiple equilibria, because he understood first thatthe noncooperative approach could not become the standard methodology of gametheoretic analysis without some refinements of Nash's equilibrium concept.

他所说的后续论文,就成了一系列的论文(Harsanyi 1962a, 1964, 1966,1977),最终成就了他与Reinhard Selten(1988)的巨著。用“风险占优”的观点,来确定任一非合作博弈的惟一理性均衡,被证明是一件非常困难的事。但是,就在他刚开始研究这个问题时,他就认识到纳什早期关于“非合作博弈论”的观点,比合作博弈方法具有更大的一般性。因此,Harsanyi1960年代就改换门庭,并成了提倡非合作博弈理论的主要人物。在这个新角色中,他开始寻找多重均衡的理论选择标准,因为他首先认识到,如果不对纳什的均衡概念进行精炼,那么非合作方法就不能成为博弈理论分析的标准方法。

In 1962(b), JohnHarsanyi published a short speculative piece about bargaining when players areignorant about each others' preferences. He found some fundamental difficultieshere, because the tools of game-theoretic analysis could only be applied underthe assumption that all players know the complete structure of the game. So hebegan to think systematically about how to model incomplete information ingames, and he developed his ideas in discussions with Reinhard Selten and theother great game theorists in the now-legendary Mathematica arms controlproject. The result was a monumental three-part series of papers on games withincomplete information, which John Harsanyi published in 1967 and 1968. Here hecarefully and systematically showed how any kind of uncertainty about a gameshould be modeled by bringing the uncertainty into the game model itself. He defineda Bayesian game model in which each player has a set of possible types thatcharacterize the player's possible preferences and beliefs at the beginning ofthe game. Then each player is assumed to understand the whole structure of thisBayesian model and, in addition, to know his own actual type.

 1962(b)中,JohnHarsanyi发表了一篇纯理论的短文,探讨了局中人不知道彼此偏好的情况下的讨价还价。在文章中,他找出一些基本的困难,因为博弈理论分析只能适用于“所有局中人都知道博弈的完全结构”的假设。因此,他开始系统化地思考如何对“博弈中的不完全信息”模型化。他与Reinhard Selten和其他而今成为传奇的参与Mathematica军控项目的博弈理论家们进行了讨论,从而提出了自己的观点。这就是John Harsanyi1967年和1968年发表的里程碑三论文,这个系列的论文讨论了不完全信息的博弈。在这几篇文章中,他小心地、系统地说明了:如何将不确定性引入到博弈模型中来,对任一种博弈的不确定性进行建模。他定义了Bayesian博弈模型,在这个模型中,每一个局中人都有一组“在博弈之初,就确定局中人可能偏好和可能信念”的可能形式。这样,就可以假设每一个局中人都理解这个Bayesian模型的全部结构,另外也就知道了他自身的实际形式。

If this approachseemed counterintuitive at first, it was because the initial problem ofuncertainty about payoff functions in a game was solved by assuming insteadthat payoff functions were known in a much bigger and more complicated game.But John Harsanyi showed that, with an additional consistency assumption, theseBayesian games could themselves be understood as conventionalcomplete-information games where the beginning of the game has just been movedbackwards in time, so that a historical chance move could be introduced toaccount for the differences in players' information.

如果说,这个方法初看之下,似是“反直觉”的,那是因为博弈支付函数的初始不确定性,是通过假设“支付函数在一个更大的、更复杂的博弈中为已知”。但是,John Harsanyi说明了:只要再给出一个一致性假设,那么,这些Bayesian博弈,本身就可以理解为传统的完全信息博弈,在这种情况下,博弈的开始,只要向后移动,从而可以引入历史的机会移动,从而解释局中人的信息差异。


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