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驗對象在做諸如拍賣如何喊價競標之類的經(jīng)濟決策時腦內(nèi)的活動。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)是否也能改進我們對經(jīng)濟行為的理解？

　　 對這個問題的回答，眾口不一。神經(jīng)經(jīng)濟學(xué)家卡墨勒等人最近曾預(yù)言“總有一天，我們會有辦法用神經(jīng)學(xué)上的精細描述代替在經(jīng)濟學(xué)上沿用已久的簡單數(shù)理概念�！保�2）與其相反，經(jīng)濟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)濟學(xué)無甚瓜葛，因為“經(jīng)濟學(xué)對人腦的生理既不作假設(shè)也不下結(jié)論�！保�3）囿于時下經(jīng)濟學(xué)慣常的研究方法，古爾-培森多佛的斷言是對的。因為在一個標準的經(jīng)濟模型里，決策者總是面臨數(shù)種選擇，而求解這個模型的目的就是要預(yù)言該研究對象會采取哪種選擇。這種模型對研究對象的大腦狀態(tài)既不作任何假設(shè)，也不作任何斷言；
只要預(yù)言能搞得準確，也沒有必要作什么假設(shè)、或作什么斷言。不過，以該標準選擇模型為根據(jù)所作的預(yù)測有時遠遠不能令人滿意；
因此，從原則上講， 在這個方面，我們或許還能有所作為；
辦法就是讓模型的預(yù)測行為不僅依賴于不同的經(jīng)濟選擇，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)濟學(xué)界迄今還沒建構(gòu)成這樣的一種擴展型（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，要想在實驗室之外的環(huán)境里進行人腦掃描，還要解決兩個棘手的難題，那就是強人所難的唐突如何規(guī)避，個人隱私如何保護。不過，這個領(lǐng)域進展很快，我們很有理由對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)濟學(xué)之整合也許還是很多年后的事情。

　　 問題是在這個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？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)判各種標準的、不帶神經(jīng)生理學(xué)變量（例如血氧水平變化）的經(jīng)濟模型。經(jīng)濟現(xiàn)象中令人不解者，大部分都允許相當(dāng)多個、可以想象到的、各自不同但又互作候補的解釋。神經(jīng)學(xué)的數(shù)據(jù)在這個方面可資利用，通過對后續(xù)試驗作出建議、或通過提出新的假說，來提高對這些解釋好中選優(yōu)的挑揀效率。以上的作者們就是取此途徑試圖闡釋實驗對象在高喊價者贏的拍賣（譯者注：此即所謂“第一價格暗標拍賣”，喊最高價者贏，并付此最高價換取標的物。）實驗中的行為。神經(jīng)學(xué)數(shù)據(jù)可派用場，這一點他們或許弄對了；
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。

　　 在一個高喊價者贏的拍賣里，標的物的潛在買者們各自投入暗標（亦即各自喊價，但互相保密）。開標后，喊最高價者贏，并付此最高價給賣者換取標的物。高喊價者贏的拍賣要求買者在競標時采用策略性的行為。如果對于一個標的物買者評價為v，她的喊價必得嚴格地小于v，因為如果喊價等于她的實際評價，就是贏了也沒有賺頭：所獲標的物評價為v， 但她的付出也是v。那么，她的喊價要削掉多少——亦即喊價要比她對標的物評價少掉幾分——則取決于她對于其他競標者行為之期望。博弈論預(yù)言了每一個買者在競標時應(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實驗里，有兩個買者，他們對標的物評價的賦值可看作是獨立且隨機地從一個數(shù)值由0到100的均勻概率分布中取出。如果兩個買者都是風(fēng)險-中性——這就是說，買者的期望所得等于她的贏標凈利（標的物評價減去喊價）乘以贏標概率——那么，在均衡的時候，買者們喊價都應(yīng)只等于評價的一半�？墒牵聽柤佣嗟热藚s發(fā)現(xiàn)——許多別的類似的實驗也有同樣的發(fā)現(xiàn)——實驗對象往往喊價高于如上結(jié)果：也就是說，他們“喊價過高�！�

　　 德爾加多等人討論了有關(guān)喊價過高的兩個標準解釋。其一是，實驗對象不應(yīng)是風(fēng)險-中性，而應(yīng)是風(fēng)險-嫌惡的——這也就是說，在一個以貨幣計輸贏的賭局里，實驗對象對賭局期望值（譯者注：期望值是一個確定的數(shù)值）之偏愛嚴格地勝過對賭局本身（譯者注：賭局本身可大贏也可大輸，是一個或然值）之偏愛。其二是，戰(zhàn)勝對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假說現(xiàn)在已都被認為是不無問題，不甚可靠的了：最近的一些實驗證據(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，他們的這個新假說究竟是什么還不是完全清楚。fMRI的數(shù)據(jù)顯示，實驗對象拍賣失標的反應(yīng)，表現(xiàn)為紋狀體血氧水平降低，但在贏標時血氧水平并未因此而有顯著改變。作者們解釋了這個結(jié)果，認為這暗示了實驗對象體驗著一種“失標恐懼感”，而且正是這種恐懼感成了喊價過高的原因。不過，要對恐懼感做到形式顯明的建�！怪珳收_——卻不是一件輕而易舉的事情。

　　 倒有一個渾然天成的建模竅門，那就是只要在實驗對象拍賣失標的時候 從她的所得里減去某個數(shù)量。作者們做了如此的實驗改動，但結(jié)果卻與作者們在后續(xù)實驗里之所見不相一致。在這些后續(xù)實驗里，采用了兩種不同的處理手段：其一，事先給了實驗對象一筆獎金S，不過她也被告知，萬一失標，這筆錢要交還；
其二，承諾實驗對象，如她贏標，她會拿到獎金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)她贏標時，才能拿到獎金。可是， 實際上，實驗對象卻在前者情形里比在后者情形里喊價更高。這種行為與“支付裁減”假說（之預(yù)言）大相徑庭，因為如果該假說為真，競標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“失標恐懼感”的建模構(gòu)想使之能同時解釋德爾加多等人所做的兩個實驗的結(jié)果，看起來相當(dāng)困難。即便如此，還有一個著名的原理，可以解釋后續(xù)實驗中兩種處理所帶來的行為差異：這個原理即“稟賦效果”（5）。當(dāng)實驗對象一開頭就被給了一筆獎金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驗終了時獲取一筆或然性獎金的情形，她就有可能更積極地行事以求保住獎金。

　　 至于說研究對象為何喊價過高，其答案也許是高喊價者贏的拍賣太復(fù)雜了，令典型的競標者無法做到全然系統(tǒng)的分析。競標者輕易即可看出她得削減喊價（使之嚴格小于評價v）才能有賺頭。不過，她仍不想將喊價削減過多，因為削減喊價也減少了她贏標的概率。一個簡單的經(jīng)驗法則就是只將喊價稍稍削減。不過其直接的結(jié)果就是喊價過高，因為風(fēng)險-中性的競標者在均衡時的喊價要求作相當(dāng)程度的削減：競標者的喊價只能是其評價的一半。

　　 簡言之，德爾加多等人對競標者在拍賣失標時紋狀體血氧水平下降的揭示，確實是一個引人興趣的神經(jīng)生理學(xué)上的發(fā)現(xiàn)，雖然這個發(fā)現(xiàn)是不是已經(jīng)導(dǎo)致了對競標者行為建構(gòu)較佳的經(jīng)濟模型還不是很清楚。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)對改進經(jīng)濟學(xué)分析具有甚大的潛力——是我們應(yīng)該認可的思想，而且應(yīng)當(dāng)遠在神經(jīng)科學(xué)與經(jīng)濟學(xué)結(jié)成一體之前就被認可了。

　　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：

　　 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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