馬斯金：神經(jīng)數(shù)據(jù)能改進(jìn)經(jīng)濟(jì)學(xué)嗎？

　　 現(xiàn)代神經(jīng)影像技術(shù)——如功能性核磁共振造影（fMRI）、正電子發(fā)射斷層掃描等——能讓我們得以窺視實(shí)驗(yàn)對(duì)象在做諸如拍賣如何喊價(jià)競(jìng)標(biāo)之類的經(jīng)濟(jì)決策時(shí)腦內(nèi)的活動(dòng)。伏隔核多巴胺釋放的數(shù)據(jù)、或紋狀體血氧濃度的數(shù)據(jù)——見《科學(xué)》期刊現(xiàn)期1849頁德爾加多等人的文章(1)——本身就的確令人神往。問題是這些數(shù)據(jù)是否也能改進(jìn)我們對(duì)經(jīng)濟(jì)行為的理解？

　　 對(duì)這個(gè)問題的回答，眾口不一。神經(jīng)經(jīng)濟(jì)學(xué)家卡墨勒等人最近曾預(yù)言“總有一天，我們會(huì)有辦法用神經(jīng)學(xué)上的精細(xì)描述代替在經(jīng)濟(jì)學(xué)上沿用已久的簡(jiǎn)單數(shù)理概念。”（2）與其相反，經(jīng)濟(jì)理論家古爾以及培森多佛則主張神經(jīng)學(xué)數(shù)據(jù)與經(jīng)濟(jì)學(xué)無甚瓜葛，因?yàn)椤敖?jīng)濟(jì)學(xué)對(duì)人腦的生理既不作假設(shè)也不下結(jié)論�！保�3）囿于時(shí)下經(jīng)濟(jì)學(xué)慣常的研究方法，古爾-培森多佛的斷言是對(duì)的。因?yàn)樵谝粋�(gè)標(biāo)準(zhǔn)的經(jīng)濟(jì)模型里，決策者總是面臨數(shù)種選擇，而求解這個(gè)模型的目的就是要預(yù)言該研究對(duì)象會(huì)采取哪種選擇。這種模型對(duì)研究對(duì)象的大腦狀態(tài)既不作任何假設(shè)，也不作任何斷言；
只要預(yù)言能搞得準(zhǔn)確，也沒有必要作什么假設(shè)、或作什么斷言。不過，以該標(biāo)準(zhǔn)選擇模型為根據(jù)所作的預(yù)測(cè)有時(shí)遠(yuǎn)遠(yuǎn)不能令人滿意；
因此，從原則上講， 在這個(gè)方面，我們或許還能有所作為；
辦法就是讓模型的預(yù)測(cè)行為不僅依賴于不同的經(jīng)濟(jì)選擇，而且也依賴于神經(jīng)生理學(xué)方面的數(shù)據(jù)。

　　 可是神經(jīng)經(jīng)濟(jì)學(xué)界迄今還沒建構(gòu)成這樣的一種擴(kuò)展型（譯者注：即增加神經(jīng)學(xué)新變量為解釋性變量）的模型。此外，即便這種模型建構(gòu)得成，要想在實(shí)驗(yàn)室之外的環(huán)境里進(jìn)行人腦掃描，還要解決兩個(gè)棘手的難題，那就是強(qiáng)人所難的唐突如何規(guī)避，個(gè)人隱私如何保護(hù)。不過，這個(gè)領(lǐng)域進(jìn)展很快，我們很有理由對(duì)最終的水到渠成抱樂觀的態(tài)度，盡管神經(jīng)學(xué)數(shù)據(jù)與例行日見的經(jīng)濟(jì)學(xué)之整合也許還是很多年后的事情。

　　 問題是在這個(gè)美妙的日子到來之前，人腦掃描的數(shù)據(jù)能不能派上什么用場(chǎng)？德爾加多等人所倡導(dǎo)的一種可能的應(yīng)用就是以該數(shù)據(jù)區(qū)判各種標(biāo)準(zhǔn)的、不帶神經(jīng)生理學(xué)變量（例如血氧水平變化）的經(jīng)濟(jì)模型。經(jīng)濟(jì)現(xiàn)象中令人不解者，大部分都允許相當(dāng)多個(gè)、可以想象到的、各自不同但又互作候補(bǔ)的解釋。神經(jīng)學(xué)的數(shù)據(jù)在這個(gè)方面可資利用，通過對(duì)后續(xù)試驗(yàn)作出建議、或通過提出新的假說，來提高對(duì)這些解釋好中選優(yōu)的挑揀效率。以上的作者們就是取此途徑試圖闡釋實(shí)驗(yàn)對(duì)象在高喊價(jià)者贏的拍賣（譯者注：此即所謂“第一價(jià)格暗標(biāo)拍賣”，喊最高價(jià)者贏，并付此最高價(jià)換取標(biāo)的物。）實(shí)驗(yàn)中的行為。神經(jīng)學(xué)數(shù)據(jù)可派用場(chǎng)，這一點(diǎn)他們或許弄對(duì)了；
但是把這條道理應(yīng)用到拍賣之上，他們還不像是已經(jīng)獲得完全成功。

　　 在一個(gè)高喊價(jià)者贏的拍賣里，標(biāo)的物的潛在買者們各自投入暗標(biāo)（亦即各自喊價(jià)，但互相保密）。開標(biāo)后，喊最高價(jià)者贏，并付此最高價(jià)給賣者換取標(biāo)的物。高喊價(jià)者贏的拍賣要求買者在競(jìng)標(biāo)時(shí)采用策略性的行為。如果對(duì)于一個(gè)標(biāo)的物買者評(píng)價(jià)為v，她的喊價(jià)必得嚴(yán)格地小于v，因?yàn)槿绻�喊價(jià)等于她的實(shí)際評(píng)價(jià)，就是贏了也沒有賺頭：所獲標(biāo)的物評(píng)價(jià)為v， 但她的付出也是v。那么，她的喊價(jià)要削掉多少——亦即喊價(jià)要比她對(duì)標(biāo)的物評(píng)價(jià)少掉幾分——?jiǎng)t取決于她對(duì)于其他競(jìng)標(biāo)者行為之期望。博弈論預(yù)言了每一個(gè)買者在競(jìng)標(biāo)時(shí)應(yīng)如此行事，亦即，在假定其他所有買者均比照自己一樣行事的條件下，須得將自己的期望所得極大化。這種結(jié)果，即所謂的均衡。

　　 在德爾加多等人的一個(gè)實(shí)驗(yàn)里，有兩個(gè)買者，他們對(duì)標(biāo)的物評(píng)價(jià)的賦值可看作是獨(dú)立且隨機(jī)地從一個(gè)數(shù)值由0到100的均勻概率分布中取出。如果兩個(gè)買者都是風(fēng)險(xiǎn)-中性——這就是說，買者的期望所得等于她的贏標(biāo)凈利（標(biāo)的物評(píng)價(jià)減去喊價(jià)）乘以贏標(biāo)概率——那么，在均衡的時(shí)候，買者們喊價(jià)都應(yīng)只等于評(píng)價(jià)的一半。可是，德爾加多等人卻發(fā)現(xiàn)——許多別的類似的實(shí)驗(yàn)也有同樣的發(fā)現(xiàn)——實(shí)驗(yàn)對(duì)象往往喊價(jià)高于如上結(jié)果：也就是說，他們“喊價(jià)過高。”

　　 德爾加多等人討論了有關(guān)喊價(jià)過高的兩個(gè)標(biāo)準(zhǔn)解釋。其一是，實(shí)驗(yàn)對(duì)象不應(yīng)是風(fēng)險(xiǎn)-中性，而應(yīng)是風(fēng)險(xiǎn)-嫌惡的——這也就是說，在一個(gè)以貨幣計(jì)輸贏的賭局里，實(shí)驗(yàn)對(duì)象對(duì)賭局期望值（譯者注：期望值是一個(gè)確定的數(shù)值）之偏愛嚴(yán)格地勝過對(duì)賭局本身（譯者注：賭局本身可大贏也可大輸，是一個(gè)或然值）之偏愛。其二是，戰(zhàn)勝對(duì)方可給贏方帶來一種額外的心理滿足感。不過，以上作者們未曾提及的是，他們所討論的這兩個(gè)假說現(xiàn)在已都被認(rèn)為是不無問題，不甚可靠的了：最近的一些實(shí)驗(yàn)證據(jù)似乎都與兩者存有沖突(4)。令人欣慰的是，德爾加多等人也提出他們自己的、建立在他們所做的fMRI研究基礎(chǔ)之上的解釋 。

　　 不幸的是，他們的這個(gè)新假說究竟是什么還不是完全清楚。fMRI的數(shù)據(jù)顯示，實(shí)驗(yàn)對(duì)象拍賣失標(biāo)的反應(yīng)，表現(xiàn)為紋狀體血氧水平降低，但在贏標(biāo)時(shí)血氧水平并未因此而有顯著改變。作者們解釋了這個(gè)結(jié)果，認(rèn)為這暗示了實(shí)驗(yàn)對(duì)象體驗(yàn)著一種“失標(biāo)恐懼感”，而且正是這種恐懼感成了喊價(jià)過高的原因。不過，要對(duì)恐懼感做到形式顯明的建�！�—使之精準(zhǔn)正確——卻不是一件輕而易舉的事情。

　　 倒有一個(gè)渾然天成的建模竅門，那就是只要在實(shí)驗(yàn)對(duì)象拍賣失標(biāo)的時(shí)候 從她的所得里減去某個(gè)數(shù)量。作者們做了如此的實(shí)驗(yàn)改動(dòng)，但結(jié)果卻與作者們?cè)诤罄m(xù)實(shí)驗(yàn)里之所見不相一致。在這些后續(xù)實(shí)驗(yàn)里，采用了兩種不同的處理手段：其一，事先給了實(shí)驗(yàn)對(duì)象一筆獎(jiǎng)金S，不過她也被告知，萬一失標(biāo)，這筆錢要交還；
其二，承諾實(shí)驗(yàn)對(duì)象，如她贏標(biāo)，她會(huì)拿到獎(jiǎng)金S. 這兩種手段，從事后看，是等效的：無論是哪一種，當(dāng)且僅當(dāng)她贏標(biāo)時(shí)，才能拿到獎(jiǎng)金�？墒�， 實(shí)際上，實(shí)驗(yàn)對(duì)象卻在前者情形里比在后者情形里喊價(jià)更高。這種行為與“支付裁減”假說（之預(yù)言）大相徑庭，因?yàn)槿绻�該假說為真，競(jìng)標(biāo)者在以上兩種情形里的行為應(yīng)當(dāng)一致。此外，要想找到一種既渾然天成又可作替代的“失標(biāo)恐懼感”的建模構(gòu)想使之能同時(shí)解釋德爾加多等人所做的兩個(gè)實(shí)驗(yàn)的結(jié)果，看起來相當(dāng)困難。即便如此，還有一個(gè)著名的原理，可以解釋后續(xù)實(shí)驗(yàn)中兩種處理所帶來的行為差異：這個(gè)原理即“稟賦效果”（5）。當(dāng)實(shí)驗(yàn)對(duì)象一開頭就被給了一筆獎(jiǎng)金S，她有可能心生占有欲；
從而，較之先得行事之后才有可能在實(shí)驗(yàn)終了時(shí)獲取一筆或然性獎(jiǎng)金的情形，她就有可能更積極地行事以求保住獎(jiǎng)金。

　　 至于說研究對(duì)象為何喊價(jià)過高，其答案也許是高喊價(jià)者贏的拍賣太復(fù)雜了，令典型的競(jìng)標(biāo)者無法做到全然系統(tǒng)的分析。競(jìng)標(biāo)者輕易即可看出她得削減喊價(jià)（使之嚴(yán)格小于評(píng)價(jià)v）才能有賺頭。不過，她仍不想將喊價(jià)削減過多，因?yàn)橄鳒p喊價(jià)也減少了她贏標(biāo)的概率。一個(gè)簡(jiǎn)單的經(jīng)驗(yàn)法則就是只將喊價(jià)稍稍削減。不過其直接的結(jié)果就是喊價(jià)過高，因?yàn)轱L(fēng)險(xiǎn)-中性的競(jìng)標(biāo)者在均衡時(shí)的喊價(jià)要求作相當(dāng)程度的削減：競(jìng)標(biāo)者的喊價(jià)只能是其評(píng)價(jià)的一半。

　　 簡(jiǎn)言之，德爾加多等人對(duì)競(jìng)標(biāo)者在拍賣失標(biāo)時(shí)紋狀體血氧水平下降的揭示，確實(shí)是一個(gè)引人興趣的神經(jīng)生理學(xué)上的發(fā)現(xiàn)，雖然這個(gè)發(fā)現(xiàn)是不是已經(jīng)導(dǎo)致了對(duì)競(jìng)標(biāo)者行為建構(gòu)較佳的經(jīng)濟(jì)模型還不是很清楚。盡管如此，德爾加多等人的哲學(xué)思想——亦即，神經(jīng)學(xué)上的發(fā)現(xiàn)對(duì)改進(jìn)經(jīng)濟(jì)學(xué)分析具有甚大的潛力——是我們應(yīng)該認(rèn)可的思想，而且應(yīng)當(dāng)遠(yuǎn)在神經(jīng)科學(xué)與經(jīng)濟(jì)學(xué)結(jié)成一體之前就被認(rèn)可了。

　　附：原文

　　Can Neural Data Improve Economics?

　　Eric Maskin

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

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

　　 So far, the field of neuroeconomics has not developed such an expanded model. Moreover, even when it does so, there are knotty problems of obtrusiveness and privacy to be resolved before one could perform brain scans outside the laboratory. The field has been moving quickly enough so that there is cause for optimism that all this will ultimately transpire,(點(diǎn)擊此處閱讀下一頁)

　　 but integrating neural information into everyday economics is probably a good many years off.

　　 What can be done with brain scans before that happy time? One possibility advocated by Delgado et al. is to use them for discriminating among standard economic models, in which neurophysiological variables (such as changes in blood oxygen levels) do not appear. Most puzzling economic phenomena admit quite a few conceivable alternative explanations, and neural data can streamline the process of finding the best one---suggesting follow-up experiments or new hypotheses. The authors use this approach to try to illuminate subjects’ behavior in high-bid auction experiments. While they are probably right about how neural data can be useful, their application of this principle to auctions does not seem entirely successful.

　　 In a high-bid auction, each potential buyer for the item being sold makes a sealed bid (i.e., quotes an amount of money without disclosing that amount to the other buyers). The buyer making the highest bid wins the item and pays the seller that bid. High-bid auctions call for strategic behavior by buyers. If the item is worth v to a buyer, she will bid strictly less than v, because bidding her actual valuation would gain her nothing: She would get something worth v but also pay v. How much she “shades” her bid---that is, bidding below what the item is worth to her---will depend on what she expects others will do. Game theory predicts that each buyer will bid so as to maximize her expected payoff, given that all other buyers do the same. The result is what is called an equilibrium.

　　 In one of the Delgado et al. experiments, there are two buyers, whose assigned valuations for the item being sold are drawn independently from a uniform distribution on the numbers between 0 and 100. If the buyers are risk-neutral---that is, if a buyer’s expected payoff is her net gain from winning (valuation minus bid) times the probability of winning---then in equilibrium, the buyer will bid half her valuation. However, Delgado et al. found---as have many other similar experiments---that subjects generally bid more than this: They “overbid.”

　　 Delgado et al. discuss two standard explanations for overbidding. One is that subjects are risk-averse rather than risk-neutral---they strictly prefer the expectation of a monetary gamble to the gamble itself. The other is that they get an extra psychic benefit from beating out another buyer. What the authors do not mention, however, is that both hypotheses are now considered somewhat dubious: Recent experimental evidence seems in conflict with each of them (4). Thus, it is welcome that Delgado et al. propose their own explanation, based on fMRI studies they performed.

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

　　 A natural modeling device would be simply to subtract something from the subject’s payoff when she loses. However, such a modification would not accord with the authors’ findings in their subsequent experiment. In the follow-up, there were two treatments: one in which a subject is initially given a bonus sum of money S but told that she has to return it if she loses the auction; the other in which the subject is promised that 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 and only if she wins. However, in practice, subjects bid more in the former treatment than the latter. Such behavior sharply contradicts the “payment subtraction” hypothesis, under which behavior in the two treatments would be the same. Moreover, it seems difficult to find a natural alternative formulation of the “fear of losing” idea that explains the results simultaneously from both Delgado et al. experiments. Even so, there is a well-known principle that could account for the behavioral discrepancy between the two treatments in the follow-up experiment: the “endowment” effect (5). When a subject is given a bonus S at the outset, she may become possessive and so move more aggressively to retain it than she would act to obtain a contingent bonus at the end of the experiment.

　　 As for why subjects overbid, perhaps the answer is that high-bid auctions are just too complex for a typical buyer to analyze completely systematically. 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 want to shade too much because shading reduces her probability of winning.(點(diǎn)擊此處閱讀下一頁)

　　 A simple rule of thumb would be to shade just a little. But this leads immediately to overbidding, because risk-neutral equilibrium bidding entails a great deal of shading: A buyer will bid only one-half her valuation.

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

　　參考文獻(xiàn)：

　　 1.M. R. Delgado, A. Schotter, E. A. Ozbay, E. A. Phelps, Science 321, 1849 (2008).

　　 2.C. Camerer, G. Loewenstein, D. Prelec, J. Econ. Lit.43, 9 (2005).

　　 3.F. Gul, W. Pesendorfer, “The case for mindless Economics,”

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

　　 4.J. Kagel, D. Levin, “Auctions: A survey of experimental research, 1995-2008,”

　　 www.econ.ohio-state.edu/kagel/Auctions_Handbook_vol2.pdf (2008).

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

　　 6.I thank NSF for research support.

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