Incorporating Fairness into the Trust Game

EMANUELE CIRIOLO

Department of Applied Economics (Room H4.203), Free University of Brussels, 50, Avenue F. Roosevelt, 1050 Brussels, Belgium

eciriolo@ulb.ac.be, tel. +32.2.650 4126; fax +32.2.650 3825 Affiliations: DULBEA, ULB, Belgium

CORE, UCL, Belgium

November 2004

ABSTRACT

We analyse the trust game and show that it allows a behavioural measure of components

of Social Capital other than trust and trustworthiness. Introducing a fairness concern in the

analysis of the trust game coincides to subdivide untrustworthiness into two complementary

concepts: conditional trustworthiness and unfairness. This may help explain a higher share of

variability in the amount returned. Ignoring fairness equates to an overestimation of non-

reciprocity and therefore deeply affects the results of the statistical analysis. We also show

that an unequal distribution of show-up fees may reduce the incentive to co-operate for both

players. This may explain the recent decline in Social Capital witnessed in some developed

countries. Finally, we argue that the standard version of the trust game is not reminiscent of

actual relations of trust, we propose a more appropriate version and we underline a number of

positive features of the new game.

Keywords: Trust; Trustworthiness; Reciprocity; Fairness; Justice, Inequality, Social Norms

and Social Capital; Games; Bargaining Theory.

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1. INTRODUCTION

In the last three decades an increasing attention has been devoted to research on trust and

co-operation. These appealing but still controversial concepts have been described as key non-

economic resources for socio-economic development. After the seminal works of Coleman

(1990), Putnam (1993) and Fukuyama (1995), other scholars have carried out in-depth

empirical analysis on the primitives of Social Capital.

La Porta et al. (1997) and Knack and Keefer (1997), relying on survey measures of social

capital, have treated it on a par with more tangible factors, namely physical and human

capital, to explain disparities in GDP growth across countries. Their contributions have

claimed to prove the thesis earlier put forward by Fukuyama (1995), namely that trust may be

a predictor of economic success. These applications represent the first ambitious attempt to

account for the economic impact of trust. However, if these studies undeniably deserve the

merit of exalting the importance of non-economic factors in the development process, they

underline, at the same time, the need to validate survey measures with economic experiments.

In fact, as it is clearly explained by Carpenter (2000), self-reported responses to survey

questions are often biased. In particular, attitudinal measures may be affected by the

“hypothetical bias”, by the “idealised persona bias” and by a “lack of incentive

compatibility”. These three different types of biases are indeed linked to the very same

feature characterising surveys, namely the fact that respondents may be inclined to

misperceive the abstract situation described by the interviewer and answer accordingly.

Hence, the focus has switched from self-reported measures of trust and co-operative

behaviour to behavioural measures. This is done via the design of games, reminiscent of real-

life situations, which are not affected by the above sources of bias and therefore allow

validating survey results and singling out possible determinants of the behaviour at stake.

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As a matter of fact, most of the empirical applications concerning trust rely on survey

questions, from the General Social Survey (GSS) or the World Value Survey (WVS). The

question used to obtain self-reported measures of trust is: “Generally speaking, would you say

that most people can be trusted or that you can’t be too careful in dealing with people?”.

Putnam (2000) has noted that, in the United States, the average percentage of people replying

positively to this question has halved between 1960 and 1995. Of course, the “past-

dependency” theory (i.e., the idea that “history matters”) put forward by Putnam, and shared

by other scholars (among others, see the work of J-P. Platteau, 2000), cannot explain this

decline.

Hence, other factors, such as the increased income, race and/or ethnic heterogeneity - as

found by Alesina and La Ferrara (2000) - could account for the decrease in the general level

of self-reported trust. Also, widening our viewpoint, globalisation forces could also be

thought to bring about changes capable of affecting the general level of trust. In principle,

globalisation occurs alongside greater specialisation and this, in turn, is associated with an

increase in the number of transactions between strangers or, which is the same, with a lower

frequency of each interaction. Mainstream economics and rational choice theory would

predict that, in an infinitely long horizon, this would diminish the incentive to co-operate.

Although there is a growing literature interpreting behavioural responses elicited in

economic experiments, these studies measure trust and co-operative behaviour within a

population (Berg et al.,1995, Glaeser et al., 2000) or between populations (Fershtman and

Gneezy, 2001, Bouckaert and Dhane, 2002, Buchan et al., 2003). That is, the unit of analysis

of most of these studies are constituted by local communities. Therefore, in order to capture

the potential impact of globalisation on behavioural measures of trust and co-operation, it is

necessary to widen the geographical and social context in which these experiments are carried

out. This implies reproducing an experimental setting in which the individuals being paired in

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the game do not necessarily belong to the same geographically delimited or socially closed

unit of analysis.

In other words, whereas Glaeser et al. (2000) implicitly adopt Granovetter’s idea,

according to which “[individual transactors] are less interested in general reputations than in

whether a particular other may be expected to deal honestly with them – mainly a function of

whether they or their own contacts have had satisfactory past dealings with the other”

(Granovetter, 1985), it would still seem plausible to investigate on the impact of general

reputation.1 This is particularly true with respect to policy decisions concerning the provision

of public goods the utility of which goes beyond local or national borders (these are the so-

called “global public goods”). The results by Alesina et al., 1999, though related to an

empirical study conducted at a local level, show that the share of public spending on

productive public goods (education, roads, sewers, etc.) is inversely related to the region’s

degree of ethnic fragmentation, even controlling for other socio-economic and demographic

determinants.

This finding suggests that, if we accept that ethnic differences tend to be larger across

nations than within nations, the national identity of individuals may play a crucial role when

interactions occurs in an international context. From this consideration stems the interest in

carrying out international experiments (Public Good Games, Voluntary Contribution

Mechanisms, Trust Games and others) aimed to observe individual behaviour in a

“controlled” environment and to analyse the link between individual choices and social

performance. In a sense, focusing on the effect of a different unit of analysis implies avoiding

the vagueness of the locution “most people” (typical of most surveys), and allows digging into

each individual’s perception of others, where “others” do not necessarily belong to the same

socio-geographical group.

1 Fershtman and Gneezy, 2001, find that general reputation is significantly correlated with trust. In particular, they observed that, in the Israeli Jewish Society, there is a systematic mistrust toward men of Eastern origin.

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In this paper, we deal with a particular type of experimental game, the trust game, designed

by Berg et al. (1995), with the aim of studying trust and reciprocity in an investment setting.

In ten years time there have been a number of applications of the trust game, each aimed at

testing one specific hypothesis such as gender differences, ethnic differences, the impact of

the national or the regional culture, the impact of cheap talk, communication and so on.

Although this growing literature provides interesting insights on the determinants of trust

and co-operative behaviour, we believe that some of the results are somewhat puzzling and

we explore the potential reasons that might explain them. For example, Glaeser et al. (1999)

find that there is no significant correlation between trusting attitudes and trusting behaviour,

that is between survey responses on trust and actual amount sent in the trust game. Besides,

they also observe that there are factors - such as the different nationality of each pair – that do

not exert a similar effect on trust and trustworthiness although they logically should.

In this paper, we critically analyse their approach and we show that the neglect of fairness

in the trust game might underestimate the respondents’ positive attitude towards co-operation

and, in particular, might play down the extent to which they do reciprocate. This, in turn,

might affect the reliability of the identification of the correlates of trustworthiness.

We first show some of the results obtained in the experiments above and give a brief

account of the usual interpretation, in the trust game, of the amount sent and the amount

received. Then, we provide a microeconomic analysis of the game at stake. From the analysis

of the extensive form of the trust game, we derive an additional condition for reciprocity. In

particular, we solve the final payoffs of trustor and trustee for equality and obtain a measure

of the recipient’s fairness or conditional trustworthiness, which is trustworthiness up to the

point of equality between final payoffs. In other words, we admit that reciprocity may occur

even when the amount sent back by the trustee is strictly smaller than half of the amount

received by the experimenter, as long as it satisfies the fairness constraint. Indeed, “inequality

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averse” trustees do not reciprocate by equally sharing the amount received by the

experimenter. Rather, in their decision to reciprocate, they take into account the amount kept

by the trustor. This weaker definition of reciprocity implies that the smaller the amount sent

forward by the trustor (and the higher the portion of the stake kept by the trustor), the smaller

is the “fair” amount that the trustee needs to send back.

Once introduced the new concept of conditional trustworthiness, we proceed with

considering the effect of incorporating it in the two experiments above. We notice that a

higher share of variability in the amount sent back might be explained by the introduction of

conditional trustworthiness. In addition, we provide a measure of the error made when the

results of the trust game are analysed ignoring this weaker form of trustworthiness. Finally, in

this paper, besides criticising the interpretation of the standard version of the trust game, we

express concerns on the design of the game itself. We claim that the standard version of the

trust game does not represent actual relations of trust, and we suggest the use of a new

experimental game aimed at obtaining reliable measures of behavioural trust and reciprocity.

Section 5 concludes.

2. THE TRUST GAME – THE STANDARD APPROACH

The experiment designed by Berg et al. (1995) reproduces an investment setting where

individual actual decisions can be compared to the theoretical prediction of neoclassical

economics. This allows gauging the extent of neoclassical economics “individualist bias”, that

is the degree to which, in practice, the postulates of rationality and self-interest do not explain

individual choices.

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In Figure 1 we draw the general extensive form of the experiment designed by Berg et al.

(1995). We will refer to it as the “Trust Game”. This game, in its original form, consisted of

four steps:

(1) Both the trustor and the trustee are given a 10$ show-up fee. For practical reasons,

we indicate these as α and δ, respectively for the trustor and the trustee;

(2) The trustor is then given the chance to send an integer portion, Sf ≡αx, of his/her 10$

to the trustee. Sending money to the recipient is obviously risky but, if the trustee

does not break the trust, the potential gain for the trustor is greater than $10;

(3) The experimenter triples whatever amount the trustor decides to send to the trustee.

This step is intended to create a social dilemma, that is a situation where individual

and group incentives differ.

(4) Finally, the trustee can choose to send back to the trustor an integer portion, Sb ≡

y*(kαx + δ), of the amount received by the experimenter. In making this choice, as

we will see later on, the trustee may or may not take into account his/her show-up

fee.

The trust game in Glaeser et al. (2000) slightly differs from the one just described. In fact:

(1) The game in Berg et al. (1995) is conducted in a double-blind procedure, where

anonymity is guaranteed with respect to the other player as well as with respect to

the experimenter. On the contrary, in Glaeser et al. (2000) sender and recipient do

meet up;

(2) The trustor receives $15 rather than $10;

(3) The trustee does not receive a show-up fee, hence δ=0;2

2 Indeed, both trustor and trustee receive a $10 show-up fee for taking part in two experimental games: the trust game and the envelope game. This is paid a posteriori and seems to be a fixed and equal reward for the time spent in playing the two games and replying to a survey. The difference is then that, in the specific framework of the trust game, only the trustor receives an initial stake.

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(4) Finally, the experimenter doubles, rather than triples, the amount sent by the trustor.

This limits the incentive to cooperate in a setting where anonymity is not guaranteed

and co-operation may be encouraged by a past relationship or fear of punishment.

It is important to bear in mind that the unique Nash Equilibrium prediction for the Trust

Game is that the trustor should send nothing. Indeed, by backward induction, he knows that

the recipient, acting rationally, has no incentive to keep the trust and will not reciprocate.

Notwithstanding, the results of the two experiments above markedly differ from the

theoretical prediction of the game. Figure 2 and Figure 3 show that this prediction is

confirmed only 5 out of 60 times in Berg et al. (1995) and 4 out of 97 times in Glaeser et al.

(2000).

How should these results be interpreted? Let us briefly review, first of all, the analytical

framework and the definitions that have been adopted in the past. The definition of trust and

trustworthiness adopted by Berg et al. (1995), as well as by Glaeser et al. (2000), are similar

to Coleman’s. In his view, “if the trustee is trustworthy, the person who places trust is better

off than if trust were not placed, whereas is the trustee is not trustworthy, the trustor is worse

off than if trust were not placed” (Coleman, 1990, page 98). Analytically, the sender is said to

be “trusting” or “to place a trust on the recipient” if and only if Sf > 0. On the other hand, the

recipient is said to be “trustworthy” or “to keep the trust” if and only if Sb = Sf. In Figure 2

and Figure 3 we can see a graphical representation of these two concepts. Points to the right

of (0,0) denote “trusting” senders. On the other side, observations on the “trustworthiness”

line denote “trustworthy” trustees, while points above this line denote more than

“trustworthy” trustees, and vice versa below the line.

It should be borne in mind that senders and recipients, in both types of experiments, are

only allowed to send (or send back) integer amounts of money. This implies that, in Berg et

al. (1995) as well as in Glaeser et al. (2000), there are values of S for which an exactly f

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“trustworthy” recipient would send back Sb that is not an integer. For example, in Berg et al.

(1995), when the trustor sends $5 to the trustee, the latter has to choose the amount to send

back out of $15. In this case, Sb=$7 or Sb=$8 should both be considered as motivated by

“trustworthiness”. Now, taking this definition of trustworthiness as benchmark for a “non-

cheating” trustee, Table 1 shows a very simple classification of trustees’ responses. As it

would be logical to expect, the percentage of untrustworthy trustees in Berg et al. (1995) is

much higher than in Glaeser et al. (2000).3 However, we should ask ourselves whether, by

adopting Coleman’s definition of trustworthiness, we obtain a reliable measure of reciprocity

or, rather, whether the “trustworthiness condition” is so strong that we are indeed

underestimating trustees’ tendency to reciprocate. All too often, in the context of the trust

game (e.g. Bouckaert, J. and Dhaene G., 2002), reciprocity is assimilated to trustworthiness

and vice versa, ignoring the possibility that a reciprocal pattern may arise conditionally to a

fairness rule. This is the question that we will try to answer in the next section.

3. INTRODUCING FAIRNESS IN THE TRUST GAME

In recent years there have been several attempts to incorporate fairness into game theory

and to take into account the equity concern (Rabin, 1993; Fehr and Schmidt, 1999). Brosnan

and de Waal (2003) conduct an experiment with a nonhuman primate, the brown capuchin

monkey, and show that, in exchanges with a human experimenter, their subjects respond

negatively to unequal reward distribution. They justify their findings, and attempt to

generalise their validity, by claiming that “during the evolution of cooperation it may have

become critical for individuals to compare their own efforts and payoffs with those of others”.

We share this view and we try to introduce this “sense of fairness” in the interpretation of the

3 The double-blind procedure in Berg et al. (1995) excludes potential punishment threats and therefore should logically disincentive trustees to reciprocate.

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results of the trust game. In practice, we suggest that “equality of final payoffs”, and not

“trustworthiness”, should be considered as a minimal requirement for reciprocity.

In order to find a weaker condition for reciprocity, we impose the equality of payoffs in the

trust game,

(1) α*(1-x) + y*(kαx + δ) = (1-y)*(kαx + δ) s.t. x, y ∈ [0,1].

Solving for y, we obtain

(2) yf = ( )( ) 2

1δxαk*2

1x*α ++− s.t. x, yf ∈ [0,1].

In the above equation, yf represents the share of the amount received by the trustee that

he/she has to send back to the trustor such that their final payoffs are equalised. In other

words, yf is the maximum share of the received amount that an “inequity averter” trustee

would send back to the sender. We can see that, given that (x-1) is non-positive, yf is

increasing in x,

(3) =∂∂

xyf ( )

( )2δxαk*4αk2)1x(*αδxαk*2

+

−−+ s.t. x, yf ∈ [0,1].

Equation (2) above also implies that yf takes a maximum value of ½ when x is equal to 1,

that is when the sender fully trusts the recipient. Assuming that x and yf can take any values in

the interval [0,1], though this is not the case in practice, Figure 4 graphs a comparison

between the “trustworthiness” condition and the weaker “fairness” condition for the trust

game conducted in Glaeser et al. (2000). For each amount sent, the two lines represent the

return ratio (the ratio between the amount returned and the amount sent) that satisfies either

the “trustworthiness” condition or the “fairness” condition. The “trustworthy” return ratio is

equal to 1, regardless of the amount sent. On the contrary, the “fair” return ratio clearly

depends on the amount sent. The “fair” return ratio is equal to 0 for values of the amount sent

equal or below $5. Indeed, when a sender sends $5, he/she keeps $10. Hence an “inequality

averter” recipient receiving twice the amount sent (two times $5, in this case) would send $0

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to generate payoffs equality ($10, $10). For values above $5, the larger the amount sent the

larger is the “fair” return ratio, although the latter increases at a decreasing rate. Finally, when

the sender fully trusts the recipient (i.e., when the amount sent is equal to $15), the “fairness”

condition coincides with the “trustworthiness” condition.

In monetary terms, condition (2) implies that the “fair” amount returned would be equal to

ARf = yf * (kαx + δ), that is:

(4) ARf = ( )[ δαxα1k21 +−∗+ ], ARf ≥0, s.t. x, y ∈ [0,1].

For values of AR larger than 0, ARf has a slope equal to 3/2 in the game of Glaeser et al.

(2000) and equal to 2 in the game of Berg et al. (1995), because of k being equal to 2 and 3,

respectively. Moreover, as recipients cannot send back negative values (i.e., cannot punish

untrusting senders), we will assume that the amount returned is equal to zero whenever

ARf<0.

A simple graphical representation of our hypothesis is done in Figure 5 where, aiming at a

more precise classification of trustees’ responses, we add the “fairness line” derived above

(i.e., ARf) alongside the “trustworthiness line”. It seems that the “fairness line” strikingly fits

a number of observations in the region below the “trustworthiness line”. In particular,

ignoring the four observations falling on the point ($0, $0), and bearing in mind the

considerations made above regarding the constraint to send integer amounts of money, we

find 12 observations in the region on and above the “fairness line” and below the

“trustworthiness line”.4 This corresponds to 12.9% (12 out of 93) of the whole sample.

Furthermore, and given that the two conditions are equivalent at the point ($15, $15), if we

admit that half of the trustees’ replies falling on this point (hence 22 out of 44) are motivated

by fairness, the percentage of trustees’ responses justified by a “fairness concern” rises to

36.6% (34 out of 93). Finally, when we only look at the region of the graph below the

4 When the trustor sends $0 to the trustee, the latter cannot make any decision at all.

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“trustworthiness line”, we find that 46% of the “untrustworthy” trustees’ responses are “fair”.

These findings have significant implications. In effect, if we accept the idea that individuals

do care about equity and might take it into account in their decision to reciprocate, ignoring

the “fairness concern” in the analysis of the trust game results would constitute a serious flaw.

In fact, if rather than adopting the “fairness line” as lower bound for trustees’ “reciprocity”,

we exclude this possibility limiting it to trustworthy responses (on and above the

trustworthiness line), we would overestimate non-reciprocity by 86%.5 This very fact may

substantially compromise, as it appears to be the case in Glaeser et al. (2000), the

identification of the socio-demographic determinants of trustworthiness.6

Figure 6 shows the incorporation of the “fairness constraint” in the experiment conducted

by Berg et al. (1995). The only difference with respect to the above analysis is that, in this

case, we have two possible “fairness constraints”, depending on whether the recipient takes

into account his/her own show-up fee in the decision to send back a share of the tripled

amount received. Following the classification approach of Andreoni and Vesterlund (2001),

we look at the variation in recipients’ responses with the aim of identifying possible

behavioural clusters, consistent with individual behavioural rules such as egoism, fairness,

trustworthiness and altruism. First, some recipients express selfishness, choose not to

reciprocate and send back no money; therefore it seems likely that their objective function is

of the form Ue(πs, πr) = πr, where πs and πr are the final payoffs of the sender and the recipient,

5 In fact, we would erroneously include in the objectively “non-reciprocating” trustees’ responses (14), 12 additional replies that do indeed meet a weaker constraint of reciprocity. Therefore, we would overestimate 14 by 12/14 (i.e., by 86%). 6 Incidentally, in the experiment conducted by Glaeser et al., biased results may also be the effect of the inclusion of 6 influential observations ($15, $30) in which the sender is fully trusting and the recipient is fully altruistic. It appears to us that this is the result of a non-random pairing procedure. Our opinion is that those 6 recipients are indeed people that, because of the special relationship tying them up (e.g., they might be partners, brothers, cousins, very close friends, etc.), might have decided to send everything (forward, for the sender, and back for the recipient). This choice, in turn, may allow the recipient to show up his or her spirit of abnegation (readiness to forgo everything for friendship or love, for example) though it does not necessarily have any actual financial consequences. Indeed, just because of the assumed relationship linking each of these pairs, sender and recipient might decide to spend the total payoff to go for diner or bowling together. In this way, sender and recipient would evenly share the total payoff, though this would occur after the game. Therefore, we think that Glaeser’s analysis should be conducted excluding these influential observations that clearly bias the results.

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respectively. Second, others are concerned with fairness and choose to send back an amount

that generates equal final payoffs. This choice implies behaviour consistent with that of a

Leontief, or perfect complement, utility function, Ul(πs, πr) = min{πs, πr}. Third, another

group of subjects manifest no concern about the relative size of final payoffs and follow the

simple “trustworthiness” rule imposing to send back half the amount received. Among this

group, there are some that immediately pocket their show-up fee and do not take it into

account in their choice, implying a utility function of the form Ut(AR, kαx) = min{AR-

½(kαx)}². Others, instead, might be particularly concerned with trustworthiness, include their

show-up fee in their sharing decision, implying Ut(AR, kαx) = min{AR-½(kαx+δ)}². Finally,

there are recipients following altruistic behavioural rules and sending back the whole amount

received, implying a utility function of the form Ua(πs, πr) = πs.

Table 2 provides, for the two types of games conducted by Berg et al. (1995), a

classification of recipients’ decisions, according to four behavioural rules that might have

influenced their choices.7 Since we focus on the recipients’ decisions we ignore the five

observations falling on the point ($0, $0) as, in that case, the recipient does not play. Looking

at the totals for the two games, out of 55 observations, 10 observations fall on the

“trustworthiness constraint”, 18 fall on either of the two “fairness constraints” and only 5 in

the area between the “fairness lines” (excluding the 10 observations above). Besides, only 3

recipients have shown some degree of altruism (sending back more than they had received),

while the choice of 19 recipients was affected by different degrees of selfishness. In

percentage terms, “fairness” appears to be by far the norm most affecting trustees’ replies.

More than four recipients out of ten conform to it. On the other side, more than 1/3 of the

trustees show some degree of selfishness, while trustworthiness accounts for 18.2% of

trustees’ choices.

7 We have included at least half of the observations falling on the point ($10, $15) under “Trustworthiness” as, in this point, “trustworthiness” and “fairness” conditions coincide.

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The implications of incorporating “fairness” into the trust game are twofold. First of all, as

we have just seen, fairness seems to explain more than 40% of trustees’ decisions and, by

result, expands the room for reciprocity behind the stronger trustworthiness constraint.

Secondly, if we accept that “fairness” plays such a relevant role in determining trustees’

choices, than it is clear that the relative size of show-up fees plays an equally important one.

To see it more clearly, we express equation (2) in terms of (α/δ), that is in terms of the ratio

between the sender’s and the recipient’s show-up fees:

(5) ( )δαyf = ( )( )( ) 2

1αδkx*2

1x ++− s.t. x, y ∈ [0,1].

Given that (x-1) is non-positive, the larger is (α/δ) - or, which is the same, the smaller (δ/α)

- the larger would be the negative effect on yf (and, hence on “fair reciprocity”) of an unequal

initial allocation. Vice versa, an increase in (δ/α) will have a non-negative effect on yf:

(6) ( )αδyf

∂∂ = ( )

( )( )αδkx*41x*2

+−− ≥ 0 s.t. x, y ∈ [0,1].

This implies that the larger α compared to δ, the lower is the share of the amount received

that an “equity concerned” trustee would be willing to send back. With reference to equation

(4), it is evident that the slope of the “fairness” condition (above ARf=0) is determined by k,

for every value of αx. On the other hand, the intercept, (-α+δ)/2, negatively depends on α and

positively on δ.

In figure 7 we made a graphical representation of trustees’ replies and, with reference to

the experiment of Glaeser et al. (2000), we subdivided the feasibility space of the trust game

into three areas: the “area of altruism”, the “area of fairness” and the “area of unfairness”,

depending on the minimum constraint satisfied by the recipient’s choice. This representation

is also useful to understand the result obtained in equation (6). An increase in (α/δ), that is a

distribution of show-up fees more in favour of the sender, corresponds to a downward shift of

the “fairness line”, ARf. This, in turn, will increase the probability of a lower response by the

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trustee, for each amount sent. Therefore, there seems to be two factors running in opposite

directions, one spurring co-operation and the other discouraging it, while it is not clear which

one prevails. In fact, when α increases with respect to δ, it implies that:

1. The sender has a higher amount to send forward to the recipient;

2. The recipient, however, has a lower show-up fee, hence (s)he might be more

concerned about equality of final payoffs;

3. The sender, by backward induction, might anticipate the higher fairness concern and

might decide to trust the recipient even less;

4. Finally, the recipient, receiving a lower amount of trust, would probably be even less

prone to reciprocate with respect to a situation characterised by equal show-up fees.

This result may contribute to renew the debate on the link between Social Capital and

egalitarian policies. The path-dependency theories put forward by Putnam (1993) could

certainly explain the relative backwardness of certain regions or countries with respect to

others. However, the same theory could not account for the recent decline in Social Capital

(and, more specifically, in the general level of trust) that arguably occurred in the United

States and other developed countries during the last 40 years. Our result, along with the

observation that some of the countries with the highest average level of self-reported trust –

Norway, Sweden, Finland, Canada - are characterised by progressive policies and a relatively

even distribution of wealth, may shed light on the temporal dynamics of social capital. As a

matter of fact, in the “Why” section of his most recent work, Putnam (2000) devotes only 2

pages out of one hundred to “pressure of money” and he does so only referring to the financial

vulnerability of each individual family. He accounts for the social changes taking place in the

USA by mentioning a number of factors (pressures of time and money, mobility and sprawl,

technology and mass media) but no room is given to wealth inequality and the progressive

abandon of egalitarian policies.

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In this section, we have tried to provide analytical and empirical arguments for the

inclusion of fairness in the interpretation of the trust game. In the next one, we look into detail

at the design of the standard version of the trust game and we argue that it does not replicate

the peculiarities of a real-life interaction of trust, where co-operative behaviour allows

attaining the social optimum.

4. A NEW VERSION OF THE TRUST GAME

The paper provides a second major contribution that originates from the rejection of the

standard version of the trust game, on the grounds that it does not represent actual relations of

trust. The trust game has been designed to reproduce a situation in which co-operation

enhance efficiency. Hence, in figure 1, k∈{2,3,...} implies that the experimenter should

double (or triple, etc.) the amount sent by the sender so as to create a higher total outcome

than if trust and reciprocity did not occur. However, nobody has ever noticed that the

experimenter does so regardless of whether reciprocity occurs. This equates with saying that,

if the trustor places full trust on the trustee, the social outcome of the transaction is

maximised, regardless of the trustee’s actual behaviour.

In reality, when placing trust on the trustee, the trustor risks a certain amount of resources,

be them temporal, physical or monetary resources. If the trustee is untrustworthy, (s)he cheats

and benefits from the trustor’s resources. If cheating occurs, the trustor is worse off and the

trustee better off. This coincides with no Pareto improvement. However, in this case (where

trust is placed but not reciprocated), the overall outcome should not be higher than if trust

were not placed; the only difference should be that it is the trustee that benefits from the

trustor’ resources.

16

In experimental settings of the trust game, on the other hand, a cheating trustee would earn

much more than what the trustor risks. The effect is twofold:

1. The total outcome, for each amount sent, is the same no matter the extent of

reciprocity. Given a certain amount sent, if a trustee keeps the trust the total outcome

(the sender’s plus the recipient’s) will be exactly the same as if (s)he had broken it.

This implies that, in the standard trust game, the total outcome does not depend on

both x and y, but just on x. However, reciprocity is crucial for any relation of trust to

persist. Therefore, we argue that the trust game, even if it is a one-off game, should

incorporate the dynamic aspect of any relation of trust. This would imply designing

the game in such a way as to make the additional outcome, brought about by co-

operation, dependent on both x and y;

2. The standard version of the trust game also introduces a perverse effect because, when

the experimenter multiplies by k the amount sent by the trustor, the trustee has indeed

a higher incentive to defect as (s)he would earn k times the amount sent. In actual

relations of trust, the cheating trustee only earns exactly the amount of resources

committed by the trustor. This is not a negligible effect as people’s stance towards

fairness and reciprocity seems to depend on the overall stake. Rabin (1993) argues that

“people will not be as willing to sacrifice a great amount of money to maintain

fairness as they would be with small amounts of money.” This suggests that, when the

profitability of defecting is high (as in the standard version of the game), people are

more tempted to pursue their self-interest at the expense of reciprocity. Hence, this is a

second reason why the “trust game” (in its standard version) is not representative of

actual relations of trust.

To avoid the above twofold effect, we propose an alternative trust game in Figure 8.

17

We ran a simulation (with k=1.5, α=€10 and δ=€10) and we noticed the following (see

tables 3-5):

1. The total outcome depends on both x and y. For example, if trust=1 and reciprocity=0,

the total outcome will be just equal to the sum of the initial endowments resources

(€20), whereas in the standard version would be higher (€25). Also, the highest total

outcome will occur when both x and y equal 1;

2. The contributions of x and y to the total outcome are not symmetric as the recipient,

when allowed to act, has more resources available than the sender had at the

beginning;

3. The recipient has an incentive to defect representative of actual relations of trust. That

is, by defecting, the recipient receives her endowment plus what the sender sent to her;

4. When the trustor shows low trust (x=0.1), the recipient’s wealth when defecting (y=0)

is smaller than if (s)he decided to reciprocate (y=1); in this case the recipient would

respectively obtain €11 and €15. Will (s)he be willing to reciprocate knowing that the

sender (who had previously not trusted her) will also benefit from it? Or will (s)he

rather decide not to reciprocate (and gain €11 < €15)?

5. When fully trusted (x=1), recipients have an incentive to defect. An experimental

game could indeed test whether they will defect or, whether they will be morally

obliged to reciprocate. So, the game will still be of interest to measure the inclination

to reciprocate.

6. There is no need to introduce the fairness concern in this trust game. This is especially

true if sender and recipient receive the same show-up fees, given that the experimenter

shares the additional payoff from co-operation, in proportion of x and y;

7. This game cannot capture recipient’s altruism as the experimenter shares the final

offers.

18

In summary, there are several features, in this version of the trust game, to be preferred to

the standard version. In particular, we think that this modified version of the game allows an

experimental study of trust and reciprocity while excluding, by design, a role for fairness and

altruism. Moreover, this comes at the cost of very little additional complexity.

5. CONCLUSIONS

Conventional economic theory has by and large ignored the possibility that people might

follow behavioural rules other than pure self-interest. However, there is a steadily increasing

bulk of experimental evidence showing that economic agents’ choices are somewhat affected

by additional behavioural rules. Hence, experimental economics is providing an invaluable

contribution in filling the gap between the assumptions of neoclassical theory and the actual

motives affecting the behaviour of many people. At the same time, leading economic scholars

are trying to identify a common pattern in the disjoint and somewhat conflicting wealth of

empirical evidence (see, among others, the works of Rabin, 1993, Fehr and Schmidt, 1999,

Bolton and Ockenfels, 2000). The final aim is obviously to incorporate different motives in a

unique model of individual behaviour. Notwithstanding these important results, our

impression is that the ideas developed in economic theory have not always filtered down to

the interpretation of empirical games results.

In particular, with reference to the trust game, we believe that neglecting fairness, in the

statistical analysis of the amount returned by the recipient, leads to an overestimation of non-

reciprocity. From the analysis of the extensive form of the trust game, we solve the final

payoffs of trustor and trustee for equality and obtain a measure of the recipient’s fairness or

conditional trustworthiness. This constitutes a weaker condition of reciprocity and assumes

that reciprocity may occur even when the amount sent back by the trustee is strictly smaller

19

than half of the amount received by the experimenter, as long as it satisfies the fairness

constraint.

We notice that although controlling for fairness, in the statistical analysis of the amount

returned by the recipient, seems to be both logical and in line with the theory of equity and

reciprocity, empirical analysis has not yet incorporated this practice. However, controlling for

fairness and for the amount sent, in the statistical analysis of the amount returned by the

recipient, is not straightforward as the fairness rule is likely to be a linear function of the

amount sent.

An alternative possibility to skirt around the problem of final wealth comparison is to

adopt a slightly more complicated game. In this new version of trust game, the experimenter

would only intervene once the recipient has played and, moreover, would share the additional

payoff in proportion to the co-operative behaviour shown by each player.

In our view, this modified version of the trust game presents several advantages with

respect to the standard version. In particular, it seems to be more representative of actual

relations of trust and allows a statistical analysis of trust and reciprocity controlling, by

design, for fairness and altruism.

20

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approach, Quar. J. Econ. 116, 350-377.

21

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Glaeser E.L., Laibson D., Scheinkman J.A., Soutter C.L., 2000. Measuring Trust. Quart. J.

Econ. 65, 811-846.

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La Porta R., F. Lopez-De_Silanes, A. Shleifer and R. Vishny, 1997. Trust in Large

Organisations, AEA P. and P. 87, 333-338.

Platteau J-P., Institutions, Social Norms, and Economic Development, (Amsterdam, The

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Putnam, R. (with Robert Leonardi and Raffaella Y. Nanetti), 1993. Making Democracy Work.

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Rabin, M., 1993. Incorporating Fairness into Game Theory and Economics. Am. Econ. Rev.

83, 1281-1302.

22

FIGURES

Figure 1: Extensive form of the Trust Game

x*α k*(αx)

y*[(k*αx) + δ]

[α*(1-x)+y*{(k*αx)+δ}; (1-y)*{(k*αx)+δ}]

Sender (who is given $ α and chooses to send “x” of α to the receiver, via the experimenter)

Experimenter (who multiplies αx by k)

Receiver (who chooses to send back “y” of the amount received)

Figure 2: Relationship between the Amount Sent and the Amount Returned

Trust Game, Berg et al. (1995), Whole sample

5 12

3111

21

12

22

31312

1

111

2

1

2

1

1

11

1 11

1

1

51

2

010

2030

Amou

nt R

etur

ned

0 2 4 6 8 10Amount Sent�����������������������������������������������������������������������������������������������������

���������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������

Total Available to ReturnTrustworthiness

23

Figure 3: Relationship between the Amount Sent and the Amount Returned

Trust Game, Glaeser et al. (2000)

411

1

5

3

1

12

1

11

1

1

1

11

1

1

63

3

443

11

1

6

010

2030

Amou

nt R

etur

ned

0 5 10 15Amount Sent����������������������������������������������������������������������������������������������

������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������

Total Available to ReturnTrustworthiness

Figure 4: Amount Sent and Fair Return Ratio, Glaeser et al. (2000)

0 5 10 15

0

0.2

0.4

0.6

0.8

1

Amount Sent

Ret

urn

Rat

io =

Am

ount

Ret

urne

d / A

mou

nt S

ent

Fairness Trustworthiness

24

Figure 5: Trust Game results, including “Fairness”, Glaeser et al. (2000)

Trust Game, Glaeser et al. (2000)

411

1

5

3

1

12

1

11

1

1

1

11

1

1

63

3

443

11

1

6

05

1015

2025

30Am

ount

Ret

urne

d

0 5 10 15Amount Sent��������������������������������������������������������������������������

������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������

TrustworthinessFairness

Figure 6: Trust Game results, including “Fairness”

Berg et al. (1995), Whole Sample

5 12

3111

21

12

22

31312

1

111

2

1

2

1

1

11

1 11

1

1

51

2

05

1015

2025

30Am

ount

Ret

urne

d

0 2 4 6 8 10Amount Sent��������������������������������������������������������������������������������������������������������������������������������������

������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������

Fairness, incl. show-up fee FairnessTrustworthiness

25

Figure 7: Trust Game, classification of trustees’ response

30 Amount Returned

15 0 5 10 15

Amount Sent

B

Area of « Altruism »

Area of « Unfairness »

« Trustworthiness » line

Area of « Fairness » or of « Conditional Trustworthiness »

Line of « Sheer Altruism »

« Fairness » line

C

A

Figure 8: Extensive form the new version of the Trust Game

x*α

y*(αx+δ)

k*[y(αx+δ)]

( ) ( )( ) ( )

+∗+++−+∗++− )δxα(ykyx

y)δxα(y1;)δxα(ykyxxαx1

kept by the distributed by the kept by the distributed by the trustor experimenter to trustee experimenter to

trustor trustee

Sender (who is given $ α and chooses to send “x” of α to the receiver, via the experimenter)

Experimenter (who multiplies [y(αx+δ)] by k, and shares it between the two parts, in proportion of the shown willingness to co-operate (respectively, y and x).

Recipient (who receives $ δ and chooses to cooperate with “y” of the amount received, αx+δ)

26

TABLES

Table 1: Analysis of recipients’ responses

OBSERVATIONS PERCENTAGES Berg et al. Glaeser et al. Berg et al. Glaeser et al. Trustworthy (+/- 1) 12 51 21,8% 54,8% More than Trustworthy 12 16 21,8% 17,2% Less than Trustworthy 31 26 56,4% 28,0% TOTAL 55 93 100,0% 100,0%

Table 2: Norms explaining the “Amount Returned”, in Berg et al. (1995)

OBSERVATIONS PERCENTAGES

No History Soc History TOTAL No History Soc History TOTAL

Trustworthiness (+/- 1) 4 6 10 13,3% 24,0% 18,2%

Fairness (excl. Show-up fee) 6 4 10 20,0% 16,0% 18,2%

Fairness (incl. Show-up fee) 4 4 8 13,3% 16,0% 14,5%

Intermediate Fairness 1 4 5 3,3% 16,0% 9,1%

Total Fairness 11 12 23 36,7% 48,0% 41,8%

Egoism 4 3 7 13,3% 12,0% 12,7%

Moderate Egoism 9 3 12 30,0% 12,0% 21,8%

Total Egoism 13 6 19 43,3% 24,0% 34,5%

Altruism 2 1 3 6,7% 4,0% 5,5%

TOTAL 30 25 55 100,0% 100,0% 100,0% 1Egoism is defined by trustees’ replies equal to $ 0 even when the lowest of the “reciprocity constraint” would impose a positive amount to be returned. 2 Moderate Egoism is defined by trustees’ replies larger than $ 0 but smaller than minimum amount to be returned imposed by the lowest of the “reciprocity constraints”.

Table 3: Sender’s Final Payoff, New Trust Game

y x 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 0 10,00 10,00 10,00 10,00 10,00 10,00 10,00 10,00 10,00 10,00 10,00

0,1 9,00 9,83 10,10 10,24 10,32 10,38 10,41 10,44 10,47 10,49 10,50 0,2 8,00 9,20 9,80 10,16 10,40 10,57 10,70 10,80 10,88 10,95 11,00 0,3 7,00 8,46 9,34 9,93 10,34 10,66 10,90 11,10 11,25 11,39 11,50 0,4 6,00 7,68 8,80 9,60 10,20 10,67 11,04 11,35 11,60 11,82 12,00 0,5 5,00 6,88 8,21 9,22 10,00 10,63 11,14 11,56 11,92 12,23 12,50 0,6 4,00 6,06 7,60 8,80 9,76 10,55 11,20 11,75 12,23 12,64 13,00 0,7 3,00 5,23 6,97 8,36 9,49 10,44 11,24 11,93 12,52 13,04 13,50 0,8 2,00 4,40 6,32 7,89 9,20 10,31 11,26 12,08 12,80 13,44 14,00 0,9 1,00 3,57 5,66 7,41 8,89 10,16 11,26 12,22 13,07 13,83 14,50 1 0,00 2,73 5,00 6,92 8,57 10,00 11,25 12,35 13,33 14,21 15,00

27

Table 4: Recipient’s Final Payoff, New Trust Game

y x 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 0 10,00 10,00 10,00 10,00 10,00 10,00 10,00 10,00 10,00 10,00 10,00

0,1 11,00 10,73 11,00 11,41 11,88 12,38 12,89 13,41 13,93 14,47 15,00 0,2 12,00 11,40 11,40 11,64 12,00 12,43 12,90 13,40 13,92 14,45 15,00 0,3 13,00 12,19 11,96 12,03 12,26 12,59 13,00 13,46 13,95 14,46 15,00 0,4 14,00 13,02 12,60 12,50 12,60 12,83 13,16 13,55 14,00 14,48 15,00 0,5 15,00 13,88 13,29 13,03 13,00 13,13 13,36 13,69 14,08 14,52 15,00 0,6 16,00 14,74 14,00 13,60 13,44 13,45 13,60 13,85 14,17 14,56 15,00 0,7 17,00 15,62 14,73 14,20 13,91 13,81 13,86 14,03 14,28 14,61 15,00 0,8 18,00 16,50 15,48 14,81 14,40 14,19 14,14 14,22 14,40 14,66 15,00 0,9 19,00 17,39 16,24 15,44 14,91 14,59 14,44 14,43 14,53 14,73 15,00 1 20,00 18,27 17,00 16,08 15,43 15,00 14,75 14,65 14,67 14,79 15,00

Table 5: Total Final Payoff, New Trust Game

y x 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 0 20,00 20,00 20,00 20,00 20,00 20,00 20,00 20,00 20,00 20,00 20,00

0,1 20,00 20,55 21,10 21,65 22,20 22,75 23,30 23,85 24,40 24,95 25,50 0,2 20,00 20,60 21,20 21,80 22,40 23,00 23,60 24,20 24,80 25,40 26,00 0,3 20,00 20,65 21,30 21,95 22,60 23,25 23,90 24,55 25,20 25,85 26,50 0,4 20,00 20,70 21,40 22,10 22,80 23,50 24,20 24,90 25,60 26,30 27,00 0,5 20,00 20,75 21,50 22,25 23,00 23,75 24,50 25,25 26,00 26,75 27,50 0,6 20,00 20,80 21,60 22,40 23,20 24,00 24,80 25,60 26,40 27,20 28,00 0,7 20,00 20,85 21,70 22,55 23,40 24,25 25,10 25,95 26,80 27,65 28,50 0,8 20,00 20,90 21,80 22,70 23,60 24,50 25,40 26,30 27,20 28,10 29,00 0,9 20,00 20,95 21,90 22,85 23,80 24,75 25,70 26,65 27,60 28,55 29,50 1 20,00 21,00 22,00 23,00 24,00 25,00 26,00 27,00 28,00 29,00 30,00

28