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9.3 Reciprocity: The Experimental Evidence
【阳民读书】互惠实验证据的行为经济学
今天是十一长假的第四天，阳民接着读书。今天的内容比较简单，以前也学过，阳民在行为经济学课程里也给同学们讲过。但还是要重复一下。今天不一一介绍，重点说一下如下的重点。
第一，行为经济学家提出了一系列关于个人如何对非利己的“社会偏好”采取行动的假设。其中一个最重要的假设是，个人对互惠有偏好。
第二，作者一开始介绍的这个囚徒困境是博弈论必讲的经典案例，但现实发现与理论推导恰恰相反，即人们往往宁愿保证个人不理性也要保证集体理性的现实，也就是说，不是人人都是自私的，人人都具有利他的偏好，或者亲社会偏好。
第三，无数的信任博弈和公益博弈的大量证据证明，许多人有动机回报他人的合作行为（这就是积极的互惠，这是相对于作者后文提到的消极互惠，当然这是阳民加注的，作者并没有标注）。互惠的概念现在在行为经济学中使用得如此普遍，以至于读者可能很难理解几十年前新古典主义经济学家认为互惠是完全违背直觉的不可想象的词汇。
第四，关于社会偏好的第三个博弈范式已经被看成是消极互惠的重要证据了，即以眼还眼以牙还牙。呵呵，这也是阳民的行为模式，尽管这种消极互惠也有代价高昂的惩罚相随。
第五，尽管人们已经接受了经济学关于互惠能够被激励的观点，但是如何进行激励却是公说公有理婆说婆有理，尤其是不同的理解支持了市场互动和非市场社会生活之间关系的概念的不同理解，行为经济学的解释机制呈现出很大的不同。
【英文原文】
Behavioural economists have proposed a range of hypothesesabout how individuals act on non-self-interested ‘social preferences’. One ofthe most important of these hypotheses is that individuals have preferences forreciprocity. In this section, I describe some of the experimental evidence thathas led to the formation of this hypothesis. I begin with the Trust Game. Thisis now one of the paradigm games of the literature on social preferences. Inits modern manifestation as an experimental design, it is due to Joyce Berg,John Dickhaut, and Kevin McCabe (1995), but (as I pointed out in Sections 1.3and 3.1), it can be traced back to Thomas Hobbes’s (1651/1962) discussion ofthe prisoner of war who is released in return for a promise to pay a ransom.The game tree for the stripped-down version I will discuss here is shown inFigure 9.1.
Of course, the whole idea of representingan interaction between individuals as a game in the formal sense of game theoryattributes more rationality to those individuals than I needed to attribute toconsumers in Chapters 6 and 7. But in this section, and in the rest of thischapter, I am concerned with how behavioural economists have understoodpro-social behaviour. For this purpose, I need to use modelling frameworks thatare standard in behavioural economics. My own model of pro-social behaviour,which I will present in Chapter 10, rests on less demanding assumptions aboutrationality.
The numbers shown in Figure 9.1 representthe possible payoffs of the game to the two players, A (listed first) and B(listed second). Payoffs are to be interpreted as normalized measures of thevalues of the relevant outcomes to the individual players, these ‘values’ beingunderstood in terms of the players’ own interests, as they perceive them at thetime the game is being played. To aid intuition, I will assume that payoffs arealso measures of the material outcomes of the game, expressed as increments ofsome good (say, money) that both players value. I do not assume that eachplayer necessarily acts so as to maximize his or her expected payoff. Thus, theformal description of the game does not predetermine what each player will (orrationally ought to) do. A moves first, choosing between hold and send. If hechooses hold, the game ends, with a baseline payoff of zero for each player.A’s choice of send can be interpreted as the action of investing one unit ofmaterial payoff in an activity which will generate a gross return of fiveunits. If A chooses send, B then chooses between two alternative distributionsof the costs and benefits of this activity. If she chooses keep, A loses thecost of his investment and B gains all the gross returns. If B chooses return,the cost of A’s investment is returnedto him and the net surplus of four units is divided equally between the twoplayers.
If both players act on self-interest and ifeach knows that this is true of the other, the outcome is (0, 0). (If A were tosend, B would keep; knowing this, A chooses hold.) However, it is a matter ofcommon experience that in situations of this general kind, individuals in A’sposition sometimes (but not always) choose send, and individuals in B’sposition sometimes (but not always) respond by choosing return. Relative to thebaseline of self-interested behaviour, the combination of send and returnbenefits both players. This pattern of behaviour has been observed in experimentswith many variants of the Trust Game, even when games are played only once andeven when players do not know one another’s identities. In anonymousexperiments, perhaps disappointingly, B-players typically do not choose returnquite often enough (or, in versions in which B-players can choose how much toreturn, do not return quite enough) to make send a beneficial strategy for anA-player to use when facing an unknown B. It is natural to conjecture thatA-players in experiments are drawing on their experience of non-anonymousinteractions in everyday social life and so are overestimating the willingnessof B-players to return when everything is anonymous. In any event, experimentalTrust Games show that a significant proportion of people succeed in achieving mutualbenefit in situations in which self-interested individuals would fail. It mightseem that, in trying to explain this success, the only real problem is toexplain why B chooses return, since if A expects this, it is in hisself-interest to choose send. One possibility is to invoke a theory of socialpreferences in which each player’s utility is a function of the profile ofmaterial payoffs to the two players. Then return would be individually rationalfor B if her utility from the payoff profile (2, 2) was greater than herutility from (–1, 5), which would be the case if she were sufficientlyaltruistic or if, as in the theories of inequality-averse social preferencesproposed by Ernst Fehr and Klaus Schmidt (1999) and Gary Bolton and Axel Ockenfels(2000), she were sufficiently averse to being on the advantageous side ofinequality. But if that were the correct explanation of return, the tendencyfor B-players in experiments to choose (2, 2) rather than (–1, 5) would beindependent of any previous choices by A-players. It turns out that ifA-players have no opportunity to make any choice and if B-players face the samechoice as they would in a Trust Game in which their co-player had chosen send,the (2, 2) choice is much less common (McCabe et al., 2003). This suggests thatsome intention of reciprocity is involved in B’s choice of return in the TrustGame.
George Akerlof (1982) has used a variant ofthe Trust Game as a theoretical model of how some labour contracts involve‘partial gift exchange’. Akerlof ’s idea is that an employer (correspondingwith player A in the Trust Game) can choose to pay more than the minimum wagenecessary to attract the labour she needs. A worker (corresponding with playerB) who is paid this higher wage can choose to work harder than self-interestwould dictate, given the limited ability of the employer to monitor individualeffort. In Akerlof ’s model, workers come to have ‘sentiment’ for the firm thatemploys them, and this sentiment leads them to supply more-than-minimum effortin response to more-than-minimum wages. Thus, through a mechanism ofreciprocity, employers and employees are able to realize mutual benefits that wouldbe unobtainable if everyone acted on self-interest. (The downside of thismechanism is that if all firms try to pay wages above the level necessary to securea supply of labour, equilibrium is possible only if there is a permanent poolof involuntarily unemployed workers.)
Another paradigm game that providesevidence about reciprocity is the Public Good Game. In the classic version ofthis game, there are n players (with n 2). Each player has the same endowment of‘tokens’. Simultaneously, each player chooses what proportion of his tokens toput into a ‘public account’, which is shared by all players; the remainder goesinto his own ‘privateaccount’. Tokens have a face value in money. Tokens placed in private accountskeep their face value, but the value of tokens in the public account is multipliedby some factor m, where 1 < m < n. At the end of the game, each playerreceives the value of the tokens in his private account, plus an equal share ofthe value of all the tokens in the public account. Thus, each token that aplayer puts in the public account yields him a private return of m/n (in token units),while each token put in his private account yields him a private return of 1.If all players put the same number of tokens in the public account, each playerreceives a return ofmfor each of the tokens that he puts in that account. Sincem > 1, the best symmetrical strategy for the players collectively is for themto put all their tokens in the public account. However, since m/n < 1, the dominantstrategy for a self-interested player is to put all his tokens in his privateaccount. So, like the Trust Game, the Public Good Game is a setting in whichindividuals have opportunities for mutual benefit that cannot be realized throughindividual self-interest. It can be interpreted as a model of a situation inwhich a public good can be supplied only through individuals’ voluntarycontributions.
Experimental research on this game has ledto three main conclusions. First, if m/n is not too close to zero, asignificant proportion of players make significant positive contributions,contrary to the assumption of self-interest. Second, if the game is playedrepeatedly, or if players make their contribution decisions sequentially ratherthan simultaneously, each player’s contribution tends to be positivelycorrelated with the previous contributions of her co-players. Third, as thegame is repeated, contributions to the public account decline. The bestexplanation of these findings seems to be that they result from interactionsbetween two types of players—free-riders (who never contribute) and conditionalreciprocators (who contribute if and only if others’ contributions aresufficiently large). Because of the presence of the free-riders and because ofthe ungenerous terms on which many conditional reciprocators are willing toreciprocate, the conditional reciprocators progressively withdraw fromcooperation (Bardsley and Moffatt, 2007; Fischbacher and Gächter, 2010). Itseems that, as in the Trust Game (and perhaps for the same reasons),experimental subjects initially over-estimate one another’s cooperativeness.
Fehr and Simon Gächter (2000) initiated anew line of research into the supply of public goods by establishing that thetendency for contributions to decline can be eliminated if, after eachrepetition of a Public Good Game, each subject is able to choose whether toimpose costly punishments on individual others. For this mechanism to work,there must be some subjects with a prosocial preference for punishingfree-riders, but Fehr and Gächter show theoretically that there can be high andstable rates of contributions even if the proportion of such individuals isquite small and even if their preferences for punishing are quite weak. Thereis now a large body of experimental evidence showing that, if the cost ofpunishing is low relative to the cost of being punished and if (which is rarelythe case in ordinary life) individuals who are punished do not have anyopportunity to retaliate, high rates of contributions can be sustained.7
Taken all round, the evidence from Trust and Public GoodGames suggests that many people are motivated to reciprocate other people’scooperative behaviour. The idea of reciprocity is now so commonly used inbehavioural economics that it may bedifficult for a reader to understand how counterintuitive it seemed toneoclassical economists only a few decades ago.
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