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神经经济学:将微观经济学向更微处推进(推荐)  

2009-04-02 13:36:03|  分类: 默认分类 |  标签: |举报 |字号 订阅

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Can Neural Data Improve Economics?


  Eric Maskin


  神经学的数据能改进经济学吗?


  马斯金[著]
Eugene Chen[译]


  (此文发表在【科学】2008年9月刊)


  Modern neuroimaging techniques---functional magnetic resonance imaging(fMRI), positron emission tomography scans, and so on---allow us topeer inside the brain and see what is going on when experimentalsubjects make economic decisions such as how to bid in auctions. Thedata on, say, dopamine release in the nucleus accumbens, or---asDelgado et al. (1) report on page 1849 of this issue---blood oxygen inthe striatum, are certainly fascinating in their own right. But canthey improve our understanding of economic behavior?


  现代神经影像技术——如功能性核磁共振造影(fMRI)、正电子发射断层扫描等——能让我们得以窥视实验对象在做诸如拍卖如何喊价竞标之类的经济决策时脑内的活动。伏隔核多巴胺释放的数据、或纹状体血氧浓度的数据——见【科学】期刊现期1849页德尔加多等人的文章(1)——本身就的确令人神往。问题是这些数据是否也能改进我们对经济行为的理解?


  Opinions diverge on this question.Neuroeconomists Camerer et al. recently predicted that “We willeventually be able to replace the simple mathematical ideas that havebeen used in economics with more neurally-detailed descriptions” (2).By contrast, economic theorists Gul and Pesendorfer maintain thatneuroscience evidence is irrelevant to economics because “the lattermakes no assumptions and draws no conclusions about the physiology ofthe brain” (3). Limited to current practice in economics, theGul-Pesendorfer assertion is correct. In a standard economic model, adecision-maker is confronted with several options, and the purpose ofthe exercise is to predict which one the subject will select. The modelassumes and asserts nothing about the subject’s brain states, nor isthere any call for it to do so as long as the prediction is accurate.But predictions based on standard choice models are sometimes far fromsatisfactory, and so in principle, we might improve matters by allowingpredicted behavior. in the model to depend not only on the economicoptions but also on neurophysiological information.


  对这个问题的回答,众口不一。神经经济学家卡墨勒等人最近曾预言“总有一天,我们会有办法用神经学上的精细描述代替在经济学上沿用已久的简单数理概念。”(2)与其相反,经济理论家古尔以及培森多佛则主张神经学数据与经济学无甚瓜葛,因为“经济学对人脑的生理既不作假设也不下结论。”(3)囿于时下经济学惯常的研究方法,古尔-培森多佛的断言是对的。 因为在一个标准的经济模型里,决策者总是面临数种选择, 而求解这个模型的目的就是要预言该研究对象会采取哪种选择。这种模型对研究对象的大脑状态既不作任何假设,也不作任何断言;只要预言能搞得准确,也没有必要作什么假设、或作什么断言。不过,以该标准选择模型为根据所作的预测有时远远不能令人满意; 因此,从原则上讲, 在这个方面, 我们或许还能有所作为;办法就是让模型的预测行为不仅依赖于不同的经济选择, 而且也依赖于神经生理学方面的数据。


  So far, the field of neuroeconomics has not developed such an expandedmodel. Moreover, even when it does so, there are knotty problems ofobtrusiveness and privacy to be resolved before one could perform.brain scans outside the laboratory. The field has been moving quicklyenough so that there is cause for optimism that all this willultimately transpire, but integrating neural information into everydayeconomics is probably a good many years off.


  可是神经经济学界迄今还没建构成这样的一种扩展型(译者注:即增加神经学新变量为解释性变量)的模型。 此外,即便这种模型建构得成, 要想在实验室之外的环境里进行人脑扫描,还要解决两个棘手的难题, 那就是强人所难的唐突如何规避,个人隐私如何保护。不过,这个领域进展很快,我们很有理由对最终的水到渠成抱乐观的态度,尽管神经学数据与例行日见的经济学之整合也许还是很多年后的事情。


  What can be done withbrain scans before that happy time? One possibility advocated byDelgado et al. is to use them for discriminating among standardeconomic models, in which neurophysiological variables (such as changesin blood oxygen levels) do not appear. Most puzzling economic phenomenaadmit quite a few conceivable alternative explanations, and neural datacan streamline the process of finding the best one---suggestingfollow-up experiments or new hypotheses. The authors use this approachto try to illuminate subjects’ behavior. in high-bid auctionexperiments. While they are probably right about how neural data can beuseful, their application of this principle to auctions does not seementirely successful.


  问题是在这个美妙的日子到来之前,人脑扫描的数据能不能派上什么用场?德尔加多等人所倡导的一种可能的应用就是以该数据区判各种标准的、不带神经生理学变量(例如血氧水平变化)的经济模型。 经济现象中令人不解者,大部分都允许相当多个、可以想象到的、各自不同但又互作候补的解释。神经学的数据在这个方面可资利用,通过对后续试验作出建议、或通过提出新的假说,来提高对这些解释好中选优的挑拣效率。以上的作者们就是取此途径试图阐释实验对象在高喊价者赢的拍卖(译者注:此即所谓“第一价格暗标拍卖”, 喊最高价者赢, 并付此最高价换取标的物。)实验中的行为。神经学数据可派用场, 这一点他们或许弄对了;但是把这条道理应用到拍卖之上, 他们还不像是已经获得完全成功。


  In ahigh-bid auction, each potential buyer for the item being sold makes asealed bid (i.e., quotes an amount of money without disclosing thatamount to the other buyers). The buyer making the highest bid wins theitem and pays the seller that bid. High-bid auctions call for strategicbehavior. by buyers. If the item is worth v to a buyer, she will bidstrictly less than v, because bidding her actual valuation would gainher nothing: She would get something worth v but also pay v. How muchshe “shades” her bid---that is, bidding below what the item is worth toher---will depend on what she expects others will do. Game theorypredicts that each buyer will bid so as to maximize her expectedpayoff, given that all other buyers do the same. The result is what iscalled an equilibrium.


  在一个高喊价者赢的拍卖里,标的物的潜在买者们各自投入暗标(亦即各自喊价,但互相保密)。开标后, 喊最高价者赢, 并付此最高价给卖者换取标的物。 高喊价者赢的拍卖要求买者在竞标时采用策略性的行为。如果对于一个标的物买者评价为v, 她的喊价必得严格地小于v,因为如果喊价等于她的实际评价,就是赢了也没有赚头:所获标的物评价为v,但她的付出也是v。 那么, 她的喊价要削掉多少——亦即喊价要比她对标的物评价少掉几分——则取决于她对于其他竞标者行为之期望。博弈论预言了每一个买者在竞标时应如此行事, 亦即,在假定其他所有买者均比照自己一样行事的条件下,须得将自己的期望所得极大化。 这种结果,即所谓的均衡。


  In one of the Delgado et al. experiments, thereare two buyers, whose assigned valuations for the item being sold aredrawn independently from a uniform. distribution on the numbers between0 and 100. If the buyers are risk-neutral---that is, if a buyer’sexpected payoff is her net gain from winning (valuation minus bid)times the probability of winning---then in equilibrium, the buyer willbid half her valuation. However, Delgado et al. found---as have manyother similar experiments---that subjects generally bid more than this:They “overbid.”


  在德尔加多等人的一个实验里,有两个买者,他们对标的物评价的赋值可看作是独立且随机地从一个数值由0到100的均匀概率分布中取出。如果两个买者都是风险-中性——这就是说,买者的期望所得等于她的赢标净利(标的物评价减去喊价)乘以赢标概率——那么, 在均衡的时候, 买者们喊价都应只等于评价的一半。(译者注:请见文末附录之证明)可是, 德尔加多等人却发现——许多别的类似的实验也有同样的发现——实验对象往往喊价高于如上结果:也就是说,他们“喊价过高。”


  Delgado et al. discuss two standard explanationsfor overbidding. One is that subjects are risk-averse rather thanrisk-neutral---they strictly prefer the expectation of a monetarygamble to the gamble itself. The other is that they get an extrapsychic benefit from beating out another buyer. What the authors do notmention, however, is that both hypotheses are now considered somewhatdubious: Recent experimental evidence seems in conflict with each ofthem (4). Thus, it is welcome that Delgado et al. propose their ownexplanation, based on fMRI studies they performed.


  德尔加多等人讨论了有关喊价过高的两个标准解释。 其一是, 实验对象不应是风险-中性, 而应是风险-嫌恶的——这也就是说, 在一个以货币计输赢的赌局里,实验对象对赌局期望值(译者注:期望值是一个确定的数值)之偏爱严格地胜过对赌局本身(译者注:赌局本身可大赢也可大输,是一个或然值)之偏爱。其二是,战胜对方可给赢方带来一种额外的心理满足感。不过,以上作者们未曾提及的是,他们所讨论的这两个假说现在已都被认为是不无问题,不甚可靠的了:最近的一些实验证据似乎都与两者存有冲突(4)。 令人欣慰的是, 德尔加多等人也提出他们自己的、建立在他们所做的fMRI研究基础之上的解释 。


  Unfortunately, it is not completely clear what this new hypothesis is.The fMRI data show that subjects experience a lower blood oxygen levelin the striatum in response to losing an auction, but no significantchange in reaction to wining one. The authors interpret this result assuggesting that subjects experience “fear of losing” and that this fearaccounts for their overbidding. But actually modeling fearexplicitly---making it precise---does not seem straightforward.


  不幸的是, 他们的这个新假说究竟是什么还不是完全清楚。 fMRI的数据显示,实验对象拍卖失标的反应,表现为纹状体血氧水平降低,但在赢标时血氧水平并未因此而有显著改变。作者们解释了这个结果, 认为这暗示了实验对象体验着一种“失标恐惧感”,而且正是这种恐惧感成了喊价过高的原因。不过, 要对恐惧感做到形式显明的建模—— 使之精准正确——却不是一件轻而易举的事情。


  A natural modeling device would be simply to subtract something fromthe subject’s payoff when she loses. However, such a modification wouldnot accord with the authors’ findings in their subsequent experiment.In the follow-up, there were two treatments: one in which a subject isinitially given a bonus sum of money S but told that she has to returnit if she loses the auction; the other in which the subject is promisedthat if she wins she will get S. The two treatments are, ex post,identical: In both cases, the subject ends up with the bonus if andonly if she wins. However, in practice, subjects bid more in the formertreatment than the latter. Such behavior. sharply contradicts the“payment subtraction” hypothesis, under which behavior. in the twotreatments would be the same. Moreover, it seems difficult to find anatural alternative formulation of the “fear of losing” idea thatexplains the results simultaneously from both Delgado et al.experiments. Even so, there is a well-known principle that couldaccount for the behavioral discrepancy between the two treatments inthe follow-up experiment: the “endowment” effect (5). When a subject isgiven a bonus S at the outset, she may become possessive and so movemore aggressively to retain it than she would act to obtain acontingent bonus at the end of the experiment.


  倒有一个浑然天成的建模窍门,那就是只要在实验对象拍卖失标的时候 从她的所得里减去某个数量。 作者们做了如此的实验改动, 但结果却与作者们在后续实验里之所见不相一致。在这些后续实验里,采用了两种不同的处理手段:其一,事先给了实验对象一笔奖金S,不过她也被告知,万一失标,这笔钱要交还;其二,承诺实验对象,如她赢标, 她会拿到奖金S. 这两种手段,从事后看,是等效的:无论是哪一种,当且仅当她赢标时,才能拿到奖金。可是,实际上,实验对象却在前者情形里比在后者情形里喊价更高。 这种行为与“支付裁减”假说(之预言)大相径庭,因为如果该假说为真,竞标者在以上两种情形里的行为应当一致。 此外,要想找到一种既浑然天成又可作替代的“失标恐惧感”的建模构想使之能同时解释德尔加多等人所做的两个实验的结果,看起来相当困难。即便如此,还有一个著名的原理,可以解释后续实验中两种处理所带来的行为差异:这个原理即“禀赋效果”(5)。当实验对象一开头就被给了一笔奖金S,她有可能心生占有欲;从而,较之先得行事之后才有可能在实验终了时获取一笔或然性奖金的情形,她就有可能更积极地行事以求保住奖金。

  

  As forwhy subjects overbid, perhaps the answer is that high-bid auctions arejust too complex for a typical buyer to analyze completelysystematically. The buyer will easily see that she has to shade her bid(bid strictly below v) to get a positive payoff. Still, she won’t wantto shade too much because shading reduces her probability of winning. Asimple rule of thumb would be to shade just a little. But this leadsimmediately to overbidding, because risk-neutral equilibrium biddingentails a great deal of shading: A buyer will bid only one-half hervaluation.


  至于说研究对象为何喊价过高,其答案也许是高喊价者赢的拍卖太复杂了,令典型的竞标者无法做到全然系统的分析。 竞标者轻易即可看出她得削减喊价(使之严格小于评价v)才能有赚头。 不过,她仍不想将喊价削减过多,因为削减喊价也减少了她赢标的概率。 一个简单的经验法则就是只将喊价稍稍削减。 不过其直接的结果就是喊价过高,因为风险-中性的竞标者在均衡时的喊价要求作相当程度的削减:竞标者的喊价只能是其评价的一半。


  In short,Delgado et al.’s discovery of a dip in striatal blood oxygen levelswhen buyers lose in an auction is an intriguing neurophysiologicalfinding, although it is not so clear that it has yet led to a bettereconomic model of buyers’ behavior. Still, the philosophy of Delgado etal.---that neural findings show great potential for improving economicanalysis---is one that should be endorsed, well before the time whenneuroscience and economics become one.


  简言之,德尔加多等人对竞标者在拍卖失标时纹状体血氧水平下降的揭示,确实是一个引人兴趣的神经生理学上的发现,虽然这个发现是不是已经导致了对竞标者行为建构较佳的经济模型还不是很清楚。尽管如此, 德尔加多等人的哲学思想——亦即,神经学上的发现对改进经济学分析具有甚大的潜力——是我们应该认可的思想,而且应当远在神经科学与经济学结成一体之前就被认可。


  参考与注解:


  M. R. Delgado, A. Schotter, E. A. Ozbay, E. A. Phelps,

  Science 321, 1849 (2008).

  C. Camerer, G. Loewenstein, D. Prelec, J. Econ. Lit.

  43, 9 (2005).

  F. Gul, W. Pesendorfer, “The case for mindless

  Economics,”

  www.princeton.edu/-pesendor/mindless.pdf(2005).

  J. Kagel, D. Levin, “Auctions: A survey of

  experimental research, 1995-2008,”
  www.econ.ohio-state.edu/kagel/Auctions_Handbook_vol2.pdf(2008).

  R. Thaler, J. Econ. Behav. Org. 1. 39 (1980).

  I thank NSF for research support.


  附录(译者注:以下是一个标准教科书式证明的翻译)

  在一个简单的第一价格拍卖模型里,两个买者竞标同一个标的物。每一个买者都可以假设其对手对标的物的私下评价数值乃是随机取自一个在区间是[0,1]之上的均匀分布。其累积分布函数是  F(v) = v. (因为F对两个买者而言是对称的, 故这个拍卖模型对两个买者而言也是对称的。)假设:(i) 标的物对卖者价值为0, (ii) 卖者保留价格也为0, 那么, 每个买者的期望效用U作为其喊价p的函数就将等于该买者赢标时所获消费者剩余 (v-p) 乘以该买者竞标时喊价高过对手喊价B的概率。(对手喊价B可以 表为该对手对标的物评价vo的函数。)所以, 该概率可以写成Pr{p > B(vo)}.因此, U(p) = (v − p)Pr{p > B(vo)}.

又假设每个买者在均衡时的喊价是该买者对标的物评价的单调递增函数;这就意味着喊价函数B 有一个反函数。 令YB的反函数:Y = B−1. 那么就有 U(p) = (v − p)Pr{Y(p) > vo}.

因为 vo 分布为F(vo), Pr{Y(p) > vo} = F(Y(p)) = Y(p), 这就意味着 U(p) = (v − p)Y(p).U'(p) = 0 时, 喊价 pU 极大化. 将 Up 求导, 并令之为零。U’(p) = -Y(p)+(v-p)Y’(p)=0.  因为两个买者相互对称,在均衡时,一定有 p = B(v) 或 等效地,Y(p) = v. 因此,

-Y(p)+(Y(p)-p)Y’(p)=0. 这个微分方程的一个解 Y* 将是这个博弈纳许均衡策略解的反函数。此时, 我们可以猜测其唯一解具有线性型 Y*(p)=ap ,且对某些实数a,  有Y*’(p)=a . 将之代入U’(p)=0, − ap + (ap − p)a = 0 − p + (a − 1)p = 0. 解之得 a*=2. 因此 Y*(p) = 2p 满足U’(p) = 0. Y*(p) = a*p 意味着Y*(p)/a* = p,v/a* = B*(v). 所以这个博弈的唯一的纳许均衡策略解的喊价函数可以确定为 B*(v) = v/2 .

(中文博主注:已按Eugene提供的新地址,作了更新.)

(又注: 在原贴的讨论中,有一个网友的评论是:

(以前我读博士的时候,有个“神经科学经济学家”来我们学校作报告,我的博士论文指导教授问了她一个小问题:有什么经济现象是现有的经济学理论无法解决,而能够被神经经济学解决的呢?这个小问题难倒了报告人,因为连神经科学的很多理论都还停留在猜想阶段,还没有足够成熟到用来解决其他领域的问题。包括Maskin文中所说的风险倾向问题,也已经在Behavioral Economics有很多的研究,不过很不幸的事情是,就连BehavioralEconomics也遭到无数的批判。

(这可能是一个好问题,也可能是一个坏问题.)




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