Directed Reciprocity in an Exogenous Social Network: An Experiment

Transcription

1 Directed Reciprocity in an Exogenous Social Network: An Experiment Yohanes E. Riyanto Tan Y.S. Cheryl Yeo X.W. Jonathan July, 2013 Abstract Trust is an integral part of any social relationship. It reflects the willingness to put oneself in a vulnerable position of not being reciprocated by the other party. Nonreciprocation may result in monetary- and (or) psychological costs. The level of trust one is willing to show to others depends on his (her) perceived likelihood of receiving reciprocation. An important factor influencing one s willingness to reciprocate is the degree of social interconnectedness among individuals. No man is an island; they are connected to others through some social links forming a social network where much of social interactions are conducted. This paper investigates the link between reciprocity and social ties in an exogenous social network. It blends social network analysis and experimental economics. The result shows that the degree of reciprocity varies with the strength of relationship as measured by the social distance in the network. Further, the degree of reciprocity also depends to some extent on the gap between the actual degree of trust shown by the sender and the receiver s expectation of it Keywords: Trust, Reciprocity, Exogenous Social Network, Social Distance, Friendship Degree, Centrality JEL Classification: C90, C92 This is a very preliminary draft, please do not quote without permission. This research benefitted from the research grant awarded by Nanyang Technological University. Division of Economics, School of Humanities and Social Siences, Nanyang Technological University, 14 Nanyang Drive HSS 04-83, Singapore , Ph: , yeriyanto@ntu.edu.sg. 1

2 1 Introduction Social capital, defined as informal cooperation-enhancing values or norms shared collectively by members of a group or a society (Fukuyama, 1997), plays a significant role in a wide array of social and economic outcomes. For instance, it has been shown in literature that social capital promotes economic growth (Knack and Keefer, 1997), influences political participation (DiPasquale and Glaeser, 1999), enhances children s welfare (Putnam, 2000), improves judicial effi ciency (LaPorta et. al., 1997), reduces crime rate (Akçomak and ter Weel, 2008), and is positively related to a nation s financial development (Guiso et.al., 2004). Two key sources of social capital are trust and reciprocity. The former refers to the willingness to believe that someone whom he (she) gave favors to earlier, is going to reciprocate the act. The decision to trust somebody is therefore equivalent to a decision to put oneself in a vulnerable state of not being reciprocated by the person receiving favors. Trustworthiness, on the other hand, points to one s willingness to reciprocate by returning favors. Both trust and reciprocity reduce relationship friction in any social and economic transaction and promote social cohesiveness. Measures of trust and trustworthiness can be obtained from surveys. An example of such a survey would be the World Values Survey (WVS) which is commonly used to derive the cross-country trust index. 1 This measure of trust is, however, a macroeconomic measure of trust. On the microeconomic side, individual trust values can be measured through the exhibited behavior of subjects playing an experimental trust game 2. It should be noted, however, that this behavior does not only capture trust, but possibly also the degree of individual altruism (Cox, 2004). In order to cleanly measure trust, one needs to control for altruism in the experiment, and one way of doing so is to equalize subjects initial endowments. While trust is obviously important, it is often trustworthiness that features prominently in social capital discourse. 3 For example, Robert Putnam, who is regarded as one of the world leading authorities on social capital, defines social capital in his influential 1 See 2 The trust or investment game was first established in Berg et.al. (1995). 3 In this paper, we do not distinguish between trustworthiness and reciprocity and instead use them interchangeably. 2

3 book (Putnam, 2000) as, "... connections among individuals social networks and the norms of reciprocity and trustworthiness that arise from them...(putnam (2000), p.19)" It is interesting to note that Putnam highlighted the significant role of social networks in determining trustworthiness. Indeed, social networks are important in life. People are non-solitary beings. They are not arranged randomly without any relationship patterns; instead they form connections with others through interpersonal links taking various shapes, structures, and lengths. People who are connected through these links vary with regard to their social distance from others and the centrality of their location within the network. These factors could crucially shape the degree of trustworthiness shown by network members. Trustworthiness might not solely depend on moral virtues and inherent personal traits, but also on the social context behind people s interpersonal relationships. Despite the importance of these social network factors, economics experiments to date have not focused much on behaviour exhibited within real-life exogenous networks, focusing instead on random and anonymous interactions between select participants. Although some papers like Glaeser et. al. (2000) do attempt to examine possible social network effects on trust and trustworthiness, an actual network structure is not elicited; the paper finds that the degree of social connection 4 generally predicts the levels of trust and trustworthiness in a two-person trust game context. Though informative, we believe that a clearer picture of the role played by network variables can be attained through examining social behaviour in real-life social networks. Examples of recent studies which have performed social experiments in an elicited real-life exogenous network are Brañas-Garza et. al. (2010), Goeree et. al. (2010) and Leider et. al. (2009). However, all of these studies focus on altruistic behaviour of individuals by conducting dictator games and their variants within real social networks. They find that altruism decreases with social distance as measured by the friendship degree; although they do differ in the extent to which they account for social distance. However the findings on the effects of centrality are mixed. Brañas-Garza et. al. (2010) finds that centrality measures such as the between-centrality and reciprocal degree of the dictator also affect 4 This is measured by the number of common friends and the duration of acquaintanceship of partners in the trust game. 3

4 altruistic behaviour while Goeree et. al. (2010) finds no significance of betweeness, closeness and power centrality. In contrast to the above papers, ours delves further into trustworthiness, which we define as the willingness to reciprocate a kind act imparted by others. Specifically, we focus our analysis on how trustworthiness is affected by the characteristics of the social network. We concentrate on two network characteristics; the degree of social distance separating an individual from someone else in the social network and the degree of centrality of an individual within the social network. We take the latter to capture the popularity of a person within the network. To the best of our knowledge, there has yet been any significant research on reciprocal behaviour in a trust game conducted within an exogenous real life social networks. In our paper, we adopt a laboratory controlled experimental approach and measure trust and trustworthiness using a trust game. We concentrate our analysis on trustworthiness behavior where we treat individual trust levels as a possible influencing factor. Further, we embed the trust game within an exogenous social network, building upon the procedure introduced by Leider et. al. (2009) in their study on directed altruism using a modified dictator game conducted within a real-life exogenous social network. In particular, our focus in this study centers on directed reciprocity within a modified trust game 5. For this purpose, we elicit a real-life exogenous friendship-network among student subjects. We incentivized subjects to collectively sign up for our experiment with their friends and also created a Facebook group for our experiment. As part of the registration process, we require subjects to add our Facebook group using their personal Facebook account. We then use Netvizz, a Facebook application, to extract social network information, and subsequently employ Gephi, a network visualization software, to construct the social graph representation of our subjects. Gephi in tandem with UCINET allows us to derive measures of network centrality and friendship degree. Subsequently, we conduct a modified repeated trust game. We find that reciprocity decreases with social distance as measured by their friendship degree, controlling for other factors. Further, both one s and one s partners eigenvector centrality or popularity in the network has no significant influence on one s reciprocal tendencies. Lastly, we also find that on average receviers would be more willing to reciprocate 5 Directed reciprocity in our case refers to the likely tendency of receivers to treat closer connected friends better than strangers by reciprocating more. 4

5 senders who sent an amount exceeding their expectations. The rest of our paper is organized as follows. In Section 2, we describe our experimental design. In Section 3, we discuss several predictions of our experiment. Subsequently, we present our findings in Section 4. Finally, we conclude in Section 5, discussing the implications of our results. 2 Experimental Design and Procedures Our experiment consists of two stages; a network elicitation stage and a controlled laboratory experiment stage. In the network elicitation stage, we conduct a basic survey among participants and elicit their friendship network structure, while in the lab experiment stage we conduct a repeated trust game within various sub-networks of the derived friendship network. We also elicit receivers first order beliefs about the expected trusting behaviour of their partners towards strangers through an incentivized mechanism. 2.1 Stage 1: Network Elicitation Using Web Interface Participants were invited via from the pool of year one and two undergraduate students at Nanyang Technological University (NTU). They came from various schools that include the School of Mechanical and Aerospace Engineering, the School of Physical and Mathematical Sciences, the School of Humanities and Social Sciences and the School of Communication and Information. They were encouraged to bring their friends and to register as a group. We provided a monetary incentive scheme for participants to register as a group. The larger their group size, the bigger the monetary incentive received by every group member. A minimum group size of two was put in place so as to avoid individual participation. The incentive scheme is as shown in Table 1. [INSERT TABLE 1 HERE] When registering for the experiment, subjects were also required to fill in a basic survey which elicited demographic variables and individual risk and time preferences. Each participant participated only once. Once participants registered for the experiment, they were then required to join a Facebook group that we specifically created for this experiment. Once all participants joined the group, we extracted their friendship-network data using a Facebook application, NetVizz. We then used the data to map their social 5

6 network using a social network software, Gephi. 6 Figure 1 shows the map of the friendship network of our participants. The nodes represent participants, and the size of the nodes indicates the eigenvector centrality 7 of a participant. It can be seen from Figure 1 that there are two major social groups in our network represented by two densely connected friendship networks. In addition of these two major groups, there exist several other smaller groups of friends in the periphery of our friendship network. [INSERT FIGURE 1 HERE] From the gathered social network data, we extracted information on the social distance (the degree of friendship) 8 of participants in relation to one another and also their respective centrality value of participants within the network. In particular, we used the eigenvector centrality value as our centrality measure 9. It can be loosely interpreted as a measure of popularity of a particular (node) individual within a social network. It assigns relative scores to all individuals, such that connections to high scoring nodes contribute more to the score of a particular node than connections to low scoring nodes. A popular example of the eigenvector centrality measure is the Google page rank. The Gephi network file was first exported to a UCINET file format which we used to calculate the eigenvector centrality values of each individual The participants were then divided into groups which consisted of sub-networks of the original network so as to create more variation in types of partners when randomising play in the second stage. Their assignments also took into account their session preferences. This is as illustrated in Figure 2. Note that participants are not informed of which groups they belonged to; these were only for the purpose of randomisation. [INSERT FIGURE 2 HERE] 6 Please see for further information on using Gephi to conduct a social network analysis. 7 This was from the inbuilt eigenvector centrality function in Gephi which is roughly similar to that of UCINETs. 8 Friendship degrees higher than 3 were treated as strangers. 9 We use this measure instead of degree centrality or betweeness centrality as we believe that it more accurately measures one s popularity in the network. This takes into account that individuals connected to larger numbers of popular people tend to be more popular too. Degree centrality does not allow for comparisons between individuals with similar number of first degree friends while betweeness centrality might be biased in the case that a participant links two social groups together. 6

7 2.2 Stage 2: Repeated Trust Game Within The Network The second stage was conducted 2 days after the end of stage 1. In this stage, we conduct a repeated trust game 10 among participants in the groups determined from the first stage. Though random matchings are only made amongst members of each group (approximately size 10), participants are informed that they will be matched to a random sender/receiver within the entire lab, so as to reduce any feeling that may be playing repeatedly with others, thus further reducing any incentive for reputation building among senders and receivers. In addition, an asymmetric information structure was adopted. Senders play with a random anonymous receiver: no information on the receiver is provided to the sender. Hence in essence, given that he is playing with a majority of strangers, the sender should thus behave as though he were playing with one. 11 Also, senders are not notified of the amounts returned by their partner receivers till the end of the experiment; this is to prevent the information from affecting senders behaviour. In contrast, partial information on the sender is provided to participants during the receiver stage, allowing for it to affect the receivers behaviour. In particular, we provide information on his/her partner s centrality in the network and also the friendship degree with relation to him/her. The provision of only partial information and not the exact identities of partners, in addition to the instructions regarding the random matching within the network further deters any attempt at reputation building in the repeated game. The above experimental control hence restrict any impacts on trust and reciprocity to that from play as a receiver. Before the decision to send back, we also elicit receivers beliefs about the expected trusting behaviour of their partners towards strangers via the following question: How many points on average (on a scale from 0 to 100 ) would you expect a Sender with the above traits to send to a stranger in this game? We use an incentive compatible mechanism for this procedure: if their prediction is within 5 ECU of the actual amount sent, they will receive a reward of 20 ECU. This amount is set such that it is not large enough to cause disappointment in the event of a 10 The experiment was programmed and conducted with the software z-tree (Fischbacher, 2007). 11 We can ensure this by making sure that the lab does not contain too many of a participant s friends: the proportion of 1st degree in the lab for participants has a mean of with a maximum of Further, we also use this as a control variable. 7

8 wrong prediction, but big enough to provide an incentive for participants to make accurate predictions. Further, the endowment for every sender in this stage is set to be 100 ECU with amounts sent to the receiver being tripled. Matching between players in each group is randomised for each period of play. The exchange rate used is 1 S$ : 100 ECU. Before the start of the playing periods, there is a set of questions which participants have to answer correctly before proceeding. This is to test their understanding of the instructions and the trust game. This is followed by a trial period that will not affect participants payoff. Following this, a total of 25 periods are played for this repeated trust game treatment. In particular, 1 period of play consists of each participant first playing as a sender, then as a receiver. Hence in total, each participant has 75 (25 3) decisions to make, where each period has a sending, expectation and receiving decision for each subject. At the end, 5 out of these 25 periods are randomly selected to make up the payoff of each participant so as to counter any income effects. A show up fee of 3 Singapore dollars is given to all participants. Participants earned 13.7 Singapore dollars on average, the lowest being 6 and the highest, 24. The standard deviation of payoffs is approximately 3.65 Singapore dollars. 3 Experimental Predictions The above experimental procedure has several testable implications. Firstly, providing partial information on senders to receivers allows for it to affect the amounts which they send back. This enables us to test whether the network factors provided affect the reciprocal behaviour of receivers. Besides, since we also elicit receivers expectations on the trusting behaviour of their partner given the information provided, we are thus also able to examine how receviers first order beliefs may affect their behaviour: i.e. how positive and negative deviations from their expectations may be treated differently. If receivers reward good behaviour (punish bad behaviour), then they should send back more (less) controlling for the amount received. Following the findings of other papers and some logical reasoning, we have the following propositions: 8

9 Proposition 1 Reciprocity decreases with increasing social distance as measured by friendship degree. Following the results of Brañas-Garza et. al. (2010), Goeree et. al. (2010) and Leider et. al. (2009) which have examined the effects of social distance on altrusitic tendencies in the dictator game, we propose that similar to the aforementioned concept of directed altruism, directed reciprocity also exists: individuals reciprocate more to closer connected people. Proposition 2 Reciprocity is positively correlated with with one s own increasing eigenvector centrality. In Brañas-Garza et. al. (2010), they find a significant positive correlation between centrality (reciprocal degree and betweeness centrality) and displayed altruism in individuals. However, the causal relationship between the two is not yet clear. In contrast, when eigenvector centrality(which we use) was used as a meaure of individual centrality, they find that is not a significant factor in their regressions. Nevertheless, we suppose that an individual with higher eigenvector centrality and popularity might be more inclined to reciprocrate more 12 due to a possible greater willingness to help. On the other hand, such reciprocal tendencies may have resulted in their prior strong position/popularity in the experimental network 13 in the first place. Proposition 3 The eff ect of partners eigenvector centrality on reciprocity is ambiguous. Firstly, since we have controlled for reputation building in our experiment, the partners centrality should not be expected to have any effect on receivers reciprocity: there is no logical reason for receivers to send back a larger amount to a more central partner for example to curry favour if no information is provided to that partner until the end of the experiment and has no chance of finding out his/her identity or even the amount returned. Furthermore, even if the above assumption does not hold, there are still two possible opposing effects. Reciprocity may be positively affected if individuals tend to return higher amounts based on increasing popularity. In contrast, reciprocity may also be negatively affected: knowing that one s partner is more popular might lead to the 12 This link follows from Ashraf et.al. (2006) where they find that unconditional kindness or altruism is a strong determinant of altruism. 13 This assumes that the social network links which have formed include a reciprocal dimension; i.e. friendships are formed because of reciprocal (and possible other) relationships between individuals. 9

10 (mis)conception that others will reciprocate more to him/her and hence the justification that one need not reciprocate as much. Proposition 4 An amount which exceeds one s expectations will result in greater reciprocity and vice versa. Taking into account first order beliefs of receivers, we suggest that for a similar amount received by a receiver, one will send back a greater amount if one s expectations was exceeded compared to if it was below or just met one s expectations. This follows because individuals may judge others based on their expectations of them, adjusting their reciprocity accordingly. Higher or lower reciprocity may then be due to effects of pleasant surprise or disappointment in their respective cases. This is somewhat similar to prospect theory where in this case the reference point of each receiver is their expectation of trust. 4 Experimental Results A total of 55 participants signed up for the study, of which 46 of them turned up. Attrition rate was 16%. The study was conducted in two sessions on Monday 18 March 2013 at the TIL and CATI computer labs of School of Humanities and Social Sciences, NTU. The experiment took under two hours to complete. Firstly, we describe some general observations on trust and trustworthiness in our experiment in two figures. [INSERT FIGURE 3] Figure 3 shows how average baseline trust as a proportion of endowment varies across periods as well where frequencies 14 are plotted in bins of 0.2 for each period. As can be seen, baseline trust varies across periods about the mean of It starts slightly higher than mean giving in past conducted trust games 15 but eventually ends lower at around Nevertheless, this does not deviate much from behaviour in previously conducted trust games. However, there is a high degree of polarisation in trust: the amounts sent are concentrated in the highest and lowest bins. 14 Frequency is proportional to the size and colour of the circle. 15 In Johnson and Mislin (2011), the average amount sent as a proportion of endowment in 161 trust game experiments is

11 [INSERT FIGURE 4] Figure 4 shows trustworthy behaviour with frequencies plotted in bins of 0.2 for each period. Note that trustworthy behaviour is only defined when a positive amount is received from one s partner. In contrast with the mean sending rate, trustworthy behaviour seems to be on a lower scale. Compared to the overall mean of 0.37 in past trust games, the mean trustworthy behaviour in our experiment is only , which is only slightly higher than the lowest ever recorded of 0.11; trustors earn negative returns on their investments on average! Further, mean trustworthy behaviour drops over time in our experiment. This is surprising: since there are regular random interactions with friends (remember that receviers have partial information on sender s behaviour), one would expect trustworthy behaviour to not decrease on average. It could possibly be that part of trustworthiness or reciprocity is a strategic act to build reputation and that individuals want recognition for their reciprocal acts; however, since we have controlled for reputation building, individuals feel increasingly "unrewarded" and hence reciprocate less. [INSERT FIGURE 5] In Figure 5, we examine roughly how trustworthiness varies with social distance on average across all periods and individuals. We see that there is a general decreasing trend with increasing social distance though trustworthiness to strangers is higher on average than to 3rd degree friends. This anomaly however disappears when properly controlling for other factors later on. Since senders do not know the identity of their partners, receiver behaviour should hence be void of any reputation building effects. Following this, we assume that the reciprocal behaviour of each individual follows the same mechanism for each period and only depends on ones personal variables, social network variables provided in the same period and the deviation from one s expectation; hence we pool data across all periods for each individual in our regressions. Also, we assume that any interpersonal information which is not provided to the receivers does not serve as explanatory variables of their behaviour. Furthermore, we control for any time effects by adding a period variable and also a variable indicating the number of times one has been paired before with that particular partner. 11

12 [INSERT TABLES 2-8 HERE] To examine how reciprocal behaviour differs depending on network variables and the difference of the amount received from one s expectations, we include them as explanatory variables on top of several control variables in a random effects regression of the amount sent back. In particular we include the amount received as one of the control variables. Furthermore, we also exclude cases where an individual does not receive anything. This is because in that case, receivers are restricted to sending back nothing, no matter what are the values of the explanatory variables: there is no allowed variation in response to the explanatory variables which biases coeffi cients to non-significance. Similarly, we also conduct similar regressions of trustworthiness 16 for the same defined cases. For the trustworthiness regressions, we do not include the amount received as a control variable since the trustworthiness measure already controls for it. Tables 2-8 provide an explanation of the used variables and their descriptive statistics. [INSERT TABLE 9 HERE] Examining Table 9, Models B and C, there seems to be a significant negative time trend for the amount sent back. Thus, in our experiment, there is evidence of reciprocal behaviour decaying over time. This was described earlier on in Figure 4. One possible explanation for this may be due to our experimental procedure not notifying senders of amounts returned by receivers till the end. Given that sendback behaviour may be an attempt to show one s reciprocal/altruistic tendencies, delaying the announcement of amounts returned may nullify warm glow effects from such behaviour, hence resulting in falls in trustworthy behaviour over time 17. The amount received as expected, is a highly significant factor which corroborates the finding that reciprocity is indeed a motivation for sending back positive amounts. Further, for each additional ECU received, the amount sent back increases by 0.55 on average. Tripling the ECU received, this means that out of each 3 additional ECU, 0.55 is returned, which gives ratio of about This generally low value coincides with the overall average trustworthiness value of which was mentioned earlier to be only slightly higher than the lowest recorded value of 0.11 in Johnson and Mislin (2011). 16 The standard measure of trustworthiness is the proportion of the amount sent back out of 3* the amount received. 17 Put simply, receivers whom were repeatedly trustworthy might feel increasingly unrewarded as the period of play increases. 12

13 Also, baseline trust is a significant factor influencing the amount sent back: we find that an individual whom was more trusting was more likely to reciprocate more in the same period, controlling for the amount received. Further, our results are also consistent with that of Ashraf et.al. (2006) which focused on elucidating the motivations of people to be trustworthy in that personal control variables like gender and risk preferences do not affect levels of trustworthiness. Also, the network variables 1st degree and 2nd degree friend are both positive and significant. Furthermore, the magnitude of their coeffi cients decreases with friendship degree; on average, receivers send back 15 ECU and 11.8 ECU more to 1st and 2nd degree friends respectively than to strangers, controlling for the amount received. This shows that directed reciprocity is indeed present: individuals do tend to treat closer friends better than further connected ones as defined by the friendship degree in the network. This is in line with the results from the studies on altruism mentioned earlier: a 1/d law of reciprocity seems to exist too. In fact, our results might be stronger in that this effect is present even without notifying individuals of the actual identities of their partners. Furthermore, it seems that 3rd degree friends are treated almost similarly to strangers as seen from its non significant coeffi cient. The significance of the former 2 variables is robust to the inclusion of other control variables in models B and C. In contrast, it seems that individuals indeed do not take centrality factors of one s partner into account when sending back: the coeffi cient on partner s centrality is not significant in any of the models in Table 9. This might be expected in our experiment because there should be no chance for reputation building due to the experimental design as mentioned earlier. Alternatively, the lack of any significant effect of partner s centrality may be due to two different kinds of reputational effects (if actually present) as mentioned earlier. Also, the idea of popularity being measured by a centrality value may be too abstract an idea to affect one s reciprocal decisions; perhaps individuals require a tangible identity to associate with a person s popularity. Furthermore, one s own centrality also does not seem to play any role in amounts sent back: i.e popular individuals do not have any tendency to reciprocate more than less popular ones as measured by eigenvector centrality. This corroborates to some extent with Brañas-Garza et. al. (2010) who finds that eigenvector centrality has an insignificant correlation with altruism. However, they do find that the reciprocal degree and betweeness centrality are significant in determining one s altruistic tendencies: a more 13

14 central individual tends to be more altruistic 18. Nevertheless, interpreting our regression results with a pinch of salt, the negative coeffi cient indicates that there may be a small negative impact of one s own centrality on the amount sent back. This suggests that popular individuals may regard the amount received from one s partner as a given/(their own privilege) and hence send back smaller amounts on average. Note that this possible negative result is opposite to that of the findings in altruism and implies that reciprocity and altruism may have some underlying differences in how they are determined. Alternatively, the social network elicited might be defined on various dimensions which do not emphasise reciprocity in particular; hence it is not related to centrality. Also, it is likely that centrality measures in general are not very accurate since participation is voluntary and only restricted to the university: what we are eliciting are only measures of the social network of students participating within the experiment. Given a small sample size, it is highly unlikely that we are able to obtain centrality estimates of each individual which reflect their true measures within a full social network. This is one major drawback of using centrality measures in a social experiment. Examining the deviation from one s expectations, D, we can see that most if not all the dummy variables are significant. This shows that the extent by which the amount received exceeds one s expectations does seem to have an effect on receivers sendback behaviour, controlling for the amount received. In particular, the significantly positive coeffi cient on D > 5 implies that compared to the baseline case of D < 5, individuals reciprocate more when the amount received exceeds one s expectations. However, assuming that reciprocity increases monotonically with the deviation from one s expectations, then the coeffi cients should also follow this trend. Contrary to this, we find that the magnitude of the coeffi cients on the other dummy variables seem to outweigh that of D > 5. For example, the effect of 5 D < 0 is greater even though the deviation from one s expectation is negative. We postulate that this has something to do with the incentive for predicting the amount received correctly (i.e. when 5 D 5): our incentive may have been too large and hence affected participants. In response to the observations from the regression, we list 4 possible ways that D may affect one s sendback decisions. 18 The centrality measure, reciprocal degree is somewhat analogous to our control variable: proportion of first degree friends in the lab. In our case, this variable is insignificant. 14

15 1. Negative deviation from one s expectation (varies with magnitude) 2. Positive deviation from one s expectation (varies with magnitude) 3. Acquiring the incentive for a correct prediction (constant) 4. Being spot on (constant) [INSERT TABLE 10 & 11 HERE] By comparing the coeffi cients for the different subgroups and the various effects present as in Table 10 in conjunction with the descriptive statistics for each group in Table 11, we can have a rough idea of how the effects from the various sources contrast with each other. Firstly, comparing (1) and (5), we see that positive deviations from one s expectation seem to increase the amount sent back on average, controlling for the amount received as compared to negative deviations. Further, from cases (2), (3), (4) and (5) of regression 1, the deviation from one s expectation seems to have a relatively small impact on reciprocal behaviour compared to obtaining the incentive 19 even though obtaining the incentive does not actually increase the amount available for sending back; the incentive may have changed the reference point from which receivers make their decisions. Lastly, being spot on in ones prediction also seems to have a sizeable impact even though there is no additional monetary gain when compared to being in the incentive interval; this can be seen from case (3) having the largest coeffi cient among the dummy variables. [INSERT TABLE 12 HERE] Moving on, we briefly examine analogous regressions of trustworthiness in Table 12. The main conclusions drawn from the regressions are similar to the ones we made for the send back regressions: i) trustworthy behaviour does decrease with friendship degree, ii) centrality factors do not play a major role in one s trustworthiness and iii) the difference between the amount received and one s expectation has a significant impact on one s trustworthiness. This shows that the 2 regressions are consistent with each other, supporting the validity of our results. Note that there are some minor differences in the inferences on the effects of D. For the trustworthiness case, D > 5 and 0 < D 5 have 19 The coeffi cients in cases (2), (3) and (4) where the incentive effect is present outweight that of case (5) even though there is a much larger average positive deviation from expectations in case (5). It might hence be implied that the incentive component is relatively larger in these cases. 15

16 larger relative impacts, while 5 D < 0 has no significant difference from the baseline case where D < 5. Hence the trustworthiness regressions suggest that there is a relatively larger positive deviation impact rather than an incentive effect which contrasts with our previous explanation for the sendback regressions. 5 Conclusion With the little research done on the interplay between social networks and reciprocal behaviour, our paper aims to study the important effects present, emulating previous research on social networks and altruistic behaviour. We do so by comining social network analysis and experimental economics methods within a novel modified trust game. In doing so, we find that directed reciprocity indeed exists: individuals reciprocate more to 1st and 2nd degree friends than to strangers. Given that trust is inherently dependent on reciprocity/trustworthiness of one s partner, levels of trust and reciprocity: sources of social capital are very much affected by the friendship links within social networks. This reiterates the point that the social networks present within an economy are likely vital components to its smooth functioning and growth. Furthermore, one may also attribute racial tensions to the phenomenom of directed reciprocity; attrition between various groups of people could be due to the lack of real friendship links between these people. Putting individuals from different groups in an environment where they may interact may not be enough to ensure higher levels of trust and reciprocity between them. Rather, actual friendships have to be established between them for social capital to be built. This suggests that social policies which serve to create actual relationships between various people may be recommended as a stimulus to increase social capital.. Also, our results suggest that it may also be possible to influence people to be more trustworthy by first exceeding their expectations/ first order beliefs. However, this may have limited scope in the presence of adaptive expectations of individuals; i.e. it may become harder and harder to exceed someone s expectations. Lastly, with the inconclusiveness of centrality as a determining factor, it seems that current methods within social network experiments to elucidate participants centrality measures may be inadequate if one were to use random elicited social networks; i.e the experimental network does not actually consist of almost a complete picture of individuals social networks, but combinations of fragments of each individuals networks. If so, then 16

17 perhaps one way would be to create a central database of the links between all individuals in the university and hence a more complete picture of the actual networks and thus more accurate centrality measures. This could be implementable via the Facebook network elicitation method as used in this paper, albeit on a much larger scale and hence requiring more computational power. 17

18 References [1] Akçomak, S. and ter Weel, B The Impact of Social Capital on Crime: Evidence from the Netherlands. IZA Discussion Paper [2] Ashraf, N., Bohnet, I. and Piankov, N Decomposing Trust and Trustworthiness. Experimental Economics, 9 (3), [3] Berg, J., Dickhaut,J. and McCabe, K Trust, Reciprocity, and Social History. Games and Economic Behavior, 10 (1), [4] Brañas-Garza, P., Cobo-Reyes, R., Espinosa, M. P., Jiménez, N., Kovárík, J. and Ponti, G Altruism and Social Integration. Games and Economic Behavior, 69 (2), [5] Borgatti, S.P., Everett, M.G. and Freeman, L.C Ucinet for Windows: Software for Social Network Analysis. Harvard, MA: Analytic Technologies. [6] Cox, J How to Identify Trust and Reciprocity. Games and Economic Behavior, 46, [7] DiPasquale, D. and Glaeser, E. (1999). Incentives and social capital: do homeowners make better citizens?, Journal of Urban Economics, vol. 45, pp [8] Fischbacher, U z-tree: Zurich Toolbox for Ready-made Economic Experiments. Experimental Economics, 10 (2), [9] Fukuyama, F Trust : The Social Virtues and the Creation of Prosperity. London: Hamish Hamilton. [10] Glaeser, E. L., Laibson, D.I., Scheinkman, J. A. and Soutter, C. L Measuring Trust. Quarterly Journal of Economics, 115 (3), [11] Goeree, J., McConnell, M., Mitchell, T., Tromp, T. and Yariv, L The 1/d Law of Giving. American Economic Journal: Microeconomics, 2 (1), [12] Guiso, L., Sapienza, P. and Zingales, L The Role of Social Capital in Financial Development. American Economic Review, 94 (3), [13] Johnson, N.D. and Mislin, A. A Trust Games: A Meta-Analysis. Journal of Economic Psychology, 32 (5),

19 [14] Knack, S. and Keefer, P Does Social Capital have an Economic Pay-Off? A Cross-Country Investigation. Quarterly Journal of Economics, 112 (4), [15] La Porta, R., Lopez de Silanes, F., Shleifer, A. and Vishny, R. W Trust in Large Organizations. American Economic Review, 87 (2), [16] Leider, S., Möbius, M., Rosenblat, T. and Quoc-Anh, D Directed Altruism and Enforced Reciprocity in Social Networks. Quarterly Journal of Economics, 124 (4), [17] Leider, S., Möbius, M., Rosenblat, T. and Quoc-Anh, D What Do We Expect from Our Friends? Journal of the European Economic Association, 8 (1), [18] Putnam, R Bowling Alone. The Collapse and Revival of American Community. New York, Simon & Schuster. 19

20 APPENDIX TABLES AND FIGURES Number of members in group Incentive per person in the group 2 $0 3 4 $ $ $ $5.0 >10 $6.0 Table 1: Incentive Scheme for Participants Control Variables Male Gender; =1 if male, =0 if female Year of Study Year of study at university; integer values from 1 to 3 Risk Measure of how risk loving an individual is; integer values from 1 to 11 Times played before Number of times played with a particular sender before, including the current period; integer values Impatience Measure of how impatient an individual is; integer values from 1 to 11 Period Period; integer values from 1 to 25 Proportion of 1 st Degree Friends in Lab Number of 1 st degree friends participating out of the total number of participants in the same lab. Table 2: Description of Control Variables 20

21 Network Variables Centrality Eigenvector centrality measure obtained using UCINET * 1000 Centrality of Partner Centrality of sender when playing as a receiver 1 st Degree Friend =1 if playing with a first degree friend, =0 if not 2 nd Degree Friend =1 if playing with a second degree friend, =0 if not 3 rd Degree Friend =1 if playing with a third degree friend, =0 if not Table 3: Description of Network Variables Experimental Data Variables Baseline Trust Integer values from 0 to 100 Amount Received Sendback D Amount received from sender when playing as a receiver Amount sent back when playing as a receiver Amount received Expectation; (Received Expectation) Table 4: Description of Trust Game Variables Gender Frequency Percentage Female Male Friendship degree of partner when playing as a receiver Stranger st Degree Friend nd Degree Friend rd Degree Friend Table 5: Descriptive statistics for dummy variables 21

22 Time Variant Variables Count Mean SD Min Max Baseline Trust Amount Received Sendback D Table 6: Descriptive Statistics for Time-Variant Variables Times Played Before Count Mean SD Min Max Period Period Period Period Period Period Period Period Period Period Period Period Period Period Period Period Period Period Period Period Period Period Period Period Period Descriptive statistics for Times Played Before by period. Time Invariant Variables Count Mean SD Min Max Risk Impatience Centrality Proportion of 1 st degree friends in lab Table 8: Descriptive Statistics for Time-Invariant Variables 22

23 Model A Model B Model C Amount Received (0.000) *** (0.000) *** (0.000) *** Baseline Trust (0.022) ** (0.055) * (0.052) * 5 D < (0.030) ** (0.014) ** (0.014) ** D = (0.026) ** (0.003) *** (0.003) *** 0 < D (0.015) ** (0.001) *** (0.001) *** D > (0.033) ** (0.017) ** (0.019) ** Centrality (0.379) (0.194) (0.157) Partner Centrality (0.683) (0.693) (0.729) Centrality Partner Centrality (0.831) 1 st Degree Friend (0.832) (0.819) (0.005) *** (0.004) *** (0.005) *** nd Degree Friend (0.061) * (0.099) * (0.100) * 3 rd Degree Friend (0.203) (0.202) (0.216) Male (0.741) (0.764) (0.826) Year of Study (0.482) (0.439) (0.687) Risk (0.512) (0.307) (0.271) Period (0.000) *** (0.000) *** Impatience (0.222) (0.084) * Times played before (0.809) (0.838) Proportion of 1st degree friends in lab (0.248) Constant (0.935) (0.564) (0.962) Observations Overall R squared Chi Model df p values in parentheses Heteroskedasticity robust standard errors used. D = (Amount received Expectation) * p < 0.10, ** p < 0.05, *** p < 0.01 Table 9: Random Effects Regressions of amount Sent Back ve Dev +ve Dev incentive spot on Coeff. Reg 1 Coeff. Reg 2 D < 5 O X X X 5 D < 0 O X O X D = 0 X X O O < D 5 X O O X D > 5 X O X X O: present X:not present Table 10: Comparison of various effects present. 23

24 Count Mean SD Min Max D < D < D = < D D > Table 11: Descriptive statistics for D in the 5 different cases where amount received > Model A Model B Model C Baseline Trust (0.064) * (0.152) (0.149) 5 D < (0.243) (0.110) (0.112) D = (0.000) *** (0.000) *** (0.000) *** 0 < D (0.000) *** (0.000) *** (0.000) *** D > (0.000) *** (0.000) *** (0.000) *** Centrality (0.375) Partner Centrality (0.937) Centrality Partner Centrality (0.533) (0.147) (0.911) (0.497) (0.198) (0.936) (0.491) 1 st Degree Friend (0.002) *** (0.001) *** (0.002) *** 2 nd Degree Friend (0.016) ** (0.025) ** (0.025) ** 3 rd Degree Friend (0.442) Male (0.665) Year of Study (0.427) Risk (0.486) (0.418) (0.692) (0.411) (0.265) (0.441) (0.937) (0.571) (0.249) Period (0.000) *** (0.000) *** Impatience (0.166) (0.062) * Times played before (0.563) (0.576) Proportion of 1st degree friends in lab (0.365) Constant (0.298) (0.135) (0.051) * Observations Overall R squared Chi Model df p values in parentheses Heteroskedasticity robust standard errors used. Diff=(Amount received Expectation) * p < 0.10, ** p < 0.05, *** p < 0.01 Table 12: Random Effects Regressions of Trustworthiness 24

25 Figure 1: Elicited Network 25

26 Figure 2: Groups by which play is randomised in the network Figure 3: Binned Plots of Baseline Trust over Time 26

27 Figure 4: Binned Plots of Trustworthiness over time (negative bin indicates zero received) Figure 5: Amount Sent back as proportion of 3* amount received when playing at various social distances 27