Does strategic kindness crowd out prosocial
behavior?∗
Åshild A. Johnsen and Ola Kvaløy†
Abstract
In repeated games, it is hard to distinguish true prosocial behavior from
strategic instrumental behavior. In particular, a player does not know whether
a reciprocal action is intrinsically or instrumentally motivated. In this paper, we experimentally investigate the relationship between intrinsic and instrumental reciprocity by running a two-period repeated trust game. In the
‘strategic treatment’ the subjects know that they will meet twice, while in
the ‘non-strategic treatment’ they do not know and hence the second period
comes as a surprise. We find that subjects anticipate instrumental reciprocity,
and that intrinsic reciprocity is rewarded. In fact, the total level of cooperation, in which trust is reciprocated, is higher in the non-strategic treatment.
This indicates that instrumental reciprocity crowds out intrinsic reciprocity:
If one takes the repeated game incentives out of the repeated game, one sees
more cooperation.
Key words: Reciprocity; repeated game; experiment.
∗
For valuable comments and suggestions, we would like to thank Jim Andreoni, Kjell Arne
Brekke, Alexander Cappelen, Gary Charness, Kristoffer Eriksen, Nicholas Feltovich, Stein Holden,
Terrance Odean, Trond Olsen, Mari Rege, Arno Riedl, Bettina Rockenbach, Joel Sobel, Sigrid
Suetens, Bertil Tungodden, Marie Claire Villeval, Joel Watson, Ro’i Zultan, and participants at the
2012 North-American ESA meeting, the 9th IMEBE meeting, the 6th M-BEES meeting, the 7th
Nordic Conference in Behavioral and Experimental Economics, the 3rd Xiamen University International Workshop, and the annual meeting of Norwegian economists. Financial support from the
Norwegian Research Council is greatly appreciated.
†
Johnsen: University of Stavanger, email: [email protected]. Kvaløy: University of Stavanger, email: [email protected]
1
1
Introduction
The proverb “You always meet twice in life” is a rule of conduct for the dependable
business person. The message is that honesty and trustworthiness always pay off in
the end. This payoff is expectably highest if you surprisingly meet again. If you act
trustworthy in your first meeting, and you surprisingly meet twice, your kindness
may be perceived as more credible and your partner will more likely regard you as
trustworthy. If, on the other hand, you know you will meet again, your kindness
may be perceived as strategic.
Strategic kindness is termed “instrumental reciprocity” in the literature and contrasts with non-strategic “intrinsic reciprocity” (see Sobel, 2005). Instrumental
reciprocity is part of a repeated game strategy where agents sacrifice short term
gains in order to sustain reputation and increase long-term payoff. Intrinsic reciprocity, on the other hand, implies a willingness to sacrifice material payoff, either
by rewarding a kind action or by punishing a mean action.
In this paper we investigate how instrumental reciprocity and intrinsic reciprocity
interact. The standard idea is that instrumental reciprocity and reputational concerns amplify the positive effects of intrinsic reciprocity (i.e. that they are complements). If some people in the distribution are “good types” with intrinsic reciprocal
preferences, then selfish types can imitate reciprocal types when playing a game
repeatedly. Kreps et al. (1982) show that the mere belief in the existence of reciprocal types may sustain cooperative play for a number of periods in the finitely
repeated prisoner’s dilemma. This has been supported experimentally by Andreoni
and Miller (1993). Also a number of trust games / gift exchange experiments with
labor market contexts indicate that reputational concerns amplify the efficiency enhancing effects of reciprocity, see e.g. Falk and Gächter (2002) and Fehr, Brown
and Zehnder (2009).
However, instrumental reciprocity may also crowd out or substitute for trust and intrinsic reciprocity. If the players know that their game is played repeatedly, they do
not know whether reciprocal behavior is instrumentally or intrinsically motivated.
Now, if the players care about the motives behind the actions, i.e. if they value
intrinsic reciprocity higher than instrumental reciprocity, then strategic repeated
game incentives may potentially undermine trust and intrinsic reciprocity.1
1
There is evidence that the motives and intentions behind actions matter. People are more prone
2
We investigate the relationship between instrumental and intrinsic reciprocity by
running a two period version of Berg et al’s (1995) well-known trust game, called
the investment game by the authors. In this game, the trustor, called the sender,
sends money to a trustee, called the responder. The money is tripled. The responder then decides how much money to return to the sender. We run two treatments.
In both treatments, senders and responders meet each other twice. In the strategic
treatment the players know they will meet twice, while in the non-strategic treatment they do not know - the second round comes as a surprise. Hence, in the
non-strategic treatment, we have a repeated game without repeated game incentives. This enables us to study how instrumental reciprocity interacts with intrinsic
reciprocity, or more precisely how strategic repeated game incentives affect the
repeated game.
In order to fix ideas, we analyze the two period investment game by using a standard reputation/reciprocity model that does not incorporate the idea that some
agents may value intrinsic reciprocity higher than instrumental reciprocity. In the
model there are two types of responders: good types who are always trustworthy,
i.e. who always reciprocate, and bad types who are always self-interested. The
responder knows his own type, but the sender only knows the chances that a responder is of either type. This model can account for the complementarity effect
discussed above; more trust and reciprocity in the first period of the strategic treatment than in the first period of the non-strategic treatment. The model can also account for lower rates of reciprocity in the second period of the strategic treatment,
since a sender may trust a bad type in period 2 who instrumentally reciprocated
in period 1. However, the total level of cooperation, in which a pair of subjects
trusts and reciprocates trust in both periods, is predicted to be (weakly) higher in
the strategic treatment.
The main results are as follows: First, as expected, repeated game incentives work
in the first period. There is more trust and trustworthiness in the first period of the
strategic treatment than in the first period of the non-strategic treatment. Second,
senders who are reciprocated in the first period, show significantly more trust in the
second period if they are in the non-strategic treatment. Hence, reciprocal behavior
to reciprocate good actions if they are confident about the motivation or intentions. See Gouldner
(1960) for an early analysis, and e.g. McCabe et al. (2003) and Charness and Levine (2007) for
more recent experimental evidence. However, the literature has not explicitly addressed potential
crowding out effects from instrumental reciprocity. The crowding out literature has mainly focused
on the negative effect of monetary incentives (Gneezy and Rustichini, 2000a,b; Bohnet et al. 2001;
Fehr and Rockenbach, 2003) and monitoring (Falk and Kosfeld, 2006; Dickinson and Villeval, 2008).
3
in the first period of the non-strategic treatment is perceived as more credible than
reciprocal behavior in the strategic treatment. Third, there are considerably higher
levels of trustworthiness in the second period of the non-strategic treatment than
in the second period of the strategic treatment. While the senders’ rate of return
is on average −22% in the strategic treatment, it is 28% in the non-strategic treatment. Fourth, and most interestingly, the total level of cooperation, in which trust
is reciprocated in both periods, is higher in the non-strategic treatment. This cannot be explained by the model, and indicates that strategic instrumental reciprocity
crowds out prosocial behavior: If the repeated game incentives are taken out of the
repeated game, more reciprocity is observed.
Our results can illuminate a more subtle research question that has been addressed
recently about the relationship between instrumental and intrinsic reciprocity. The
idea from Kreps et al. (1982), that more cooperation in finitely repeated games
is due to reciprocity imitation is, as mentioned above, supported by a number of
experiments, such as Andreoni and Miller (1993) and Falk and Gächter (2002).
People act strategically/ instrumentally by imitating reciprocal preferences in order to sustain cooperation. However, the existing evidence for reciprocity imitation
is not clean. More cooperation in finitely repeated games than in one shot games
may not be due to reciprocity imitation, or uncertainty about types, but to an inappropriate use of the infinitely repeated game logic (see Rueben and Suetens, 2011).
According to the theory, people play as if it were an infinitely repeated game, but
change strategy in the final round when they realize that the game will end. Hence,
they act instrumentally, but they do not necessarily imitate reciprocal preferences
or form beliefs about opponents’ types. Experiments that find no differences between one shot games and the last round of the finitely repeated game are also
supported by such a model of bounded rationality, and therefore cannot identify
reciprocity imitation. Our experimental design makes it possible to identify reciprocity imitation. The reason is that players in the non-strategic treatment have
received a more credible signal about the opponents’ type prior to the last period.
If they act on this signal in the last period, then reciprocity imitation is anticipated.
Related literature: A number of papers (including those cited above) experimentally investigate behavior in repeated games.2 But in most of these experiments
it is not possible to distinguish strategically from non-strategically motivated co2
For an early experimental investigation of a finitely repeated trust game, see Camerer and
Weigelt (1988). More recent papers are Anderhub et al. (2002), Engle-Warnick and Slonim (2004,
2006), and Schniter et al. (2013).
4
operation. Some recent papers aim to fill this gap. Ambrus and Pathak (2011)
identify strategic cooperation in a finitely repeated public good game. By using a
probabilistic continuation design, they show that selfish players do contribute to the
public good because it induces future contributions by others. Reuben and Suetens
(2012) investigate motives for cooperation in a repeated prisoner’s dilemma game
by using the strategy method.3 Subjects condition their decisions on whether the
period they are currently playing is the last period of the game or not. They find that
most of the cooperation is strategically motivated. Cabral et al. (2012) identifies
instrumental reciprocity by running an infinitely repeated veto game which admits
a unique efficient equilibrium for selfish rational players. Like Rueben and Suetens
they find that most of the cooperation is motivated by instrumental reciprocity.
The approach we use in this paper is related to a procedure called “surprise restart”,
an approach first reported by Andreoni (1988) which has been used in several papers since then.4 Closest to our paper are Ben-Ner et al. (2004) and Stanca et al.
(2009). Ben-Ner et al. run a two-part dictator game where the subjects are told
after they have played a conventional dictator game that they will play one more
time, with reversed roles. Those subjects who were treated nicely in the first part
tended to be more generous towards the former dictators. Stanca et al. use a similar approach with the difference being that money sent from the dictator is tripled.
Hence, when the roles are reversed, the game resembles the second stage of a standard gift exchange game. Treatments differ in whether or not the subjects are told
about the second stage before the experiment starts. They find that reciprocity is
stronger when strategic motivations can be ruled out. However, neither Ben-Ner et
al. nor Stanca et al. can follow the behavior of a given subject (with a given role)
over two periods, like we can. Hence, they do not study a repeated game, which is
the object of our investigation.
The rest of the paper is organized as follows: In Section 2 we present a formal
analysis of the two period investment game. In Section 3 we present the experimental design and procedure. In Section 4 we present the results, while Section 5
concludes.
3
In the strategy method for eliciting choices, subjects state their contingent choices for every
decision node they may face. They are then matched, and their choices are played out.
4
See Ambrus and Pathak (2011) and Rietz et al. (2013) for a recent application of the surprise
restart method. Our approach is less of a surprise since we explicitly state that the experiment will
consist of two parts, and that the instructions for the second part will come after the first part. On a
more general level, our methodology is in line with experiments in which subjects are not informed
about the content of all stages ex ante, since this might induce strategic behavior, see e.g. Dohmen
and Falk (2011) and Bartling et al. (2012).
5
2
The two period investment game
The investment game of Berg et. al (1995) is a trust game where the trustor (sender)
chooses the degree to which she trusts the trustee (responder). The sender and responder start out with endowments of Es and Er , respectively. The sender chooses
an amount x to send to the responder (0 ≤ x ≤ Es ). The investment x is then
multiplied by m > 1 and the responder receives mx. Subsequently, the responder chooses an amount y that he or she returns to the sender, with 0 ≤ y ≤ mx.
Afterwards, the game ends with the sender receiving a payoff Es − x + y and the
responder receiving Er + mx − y.
If x > 0 the sender (to some extent) trusts the responder. If y > x the responder
reciprocates, i.e. she is trustworthy. If both x > 0 and y > x we say that the parties
cooperate. The level of x indicates how much the sender trusts the responder, while
the level of y > x indicates how trustworthy the responder is.
Consider now the game played twice, with xi , yi , as choice variables and where i =
1, 2 denotes periods. With standard (selfish) preferences and common knowledge
about rationality, the Nash equilibrium profile is (x1 = x2 = 0, y1 = y2 = 0).
From a number of experiments on finitely repeated games, we know that this is not
a plausible outcome.
We thus make the following assumptions: There are two types of responders. Btypes (bad types) play y2 = 0. G-types (good types) play yi = kxi where k > 1.
(Hence k is a definition of what a good type is, and thus exogenous). The responder
knows his own type, but the sender only knows the chances that a responder is of
either type. The distribution of types is common knowledge.
We will now sketch the derivation of a sequential equilibrium in the two period
investment game.5 In subgames along the equilibrium path, players are assumed
to use Bayes’ rule to update their information about others based on observed play.
We solve by backwards induction:
In period 2, the sender knows that a b-type responder will play y2 = 0 while a gtype responder will play y2 = kx2 . Therefore, if the sender thinks the probability
that the responder is a g-type is p2 ,his expected payoff from sending a positive
5
See Camerer and Weigelt (1988) for a similar analysis of t period trust game.
6
amount x2 > 0 is p2 (Es − x2 + kx2 ) + (1 − p2 )(Es − x2 ). The payoff from
sending exceeds the sure payoff from not sending (Es ) iff
p2 >
1
k
(1)
In period 1 a b-type responder can play y1 = 0 and get Er + mx1 in period 1 and
Er in period 2. Alternatively, he can play a mixed strategy, choosing to reciprocate
with probability σ1 and not reciprocate with probability 1 − σ1 . The responder will
choose σ1 so that when the sender observes the responder reciprocate in period 1,
the sender updates his beliefs about the responder such that the updated posterior
probability p2 is above the threshold k1 . Then the responder’s total expected payoff
from periods 1 and 2 is:
σ1 (Er + mx1 − kx1 + Er + mx2 ) + (1 − σ1 )(Er + mx1 + Er )
(2)
Since this expected payoff is increasing in σ1 (as long as kx1 < mx2 ), the responder will choose σ1 as large as possible, provided σ1 makes the posterior probability
p2 above the sender’s threshold k1 . If the sender uses Bayes rule to update probabilities, the posterior probability p2 is given by
p2 =
p1
[p1 + σ1 (1 − p1 )]
(3)
Note that for σ1 = 1, i.e. a b-type always reciprocates in period 1, then p2 = p1 ,
i.e. from observing reciprocal behavior, the sender does not increase his probability
that he actually meets a good type. But for σ1 < 1 reciprocity is a positive signal.
For p2 to exceed the threshold k1 , we must have
σ1 ≤
p1
[p1 +σ1 (1−p1 )]
≥
1
k
i.e.
p1 (k − 1)
(1 − p1 )
A rational responder will choose σ1 so that (4) holds with equality.
7
(4)
Now, in period 1 the sender will send x1 > 0 iff
[p1 + σ1 (1 − p1 )] (Es − x1 + kx1 ) + (Es − x1 )(1 − σ1 )(1 − p1 ) > Es
(5)
Since the responder will choose σ1 to satisfy (4), we can combine (4) and (5) to
derive the threshold for p1 , which is
p1 >
1
k2
(6)
We assume that the game begins with a commonly known prior probability h that
the responder is a g-type. The sequential equilibrium is then for the sender to send
and for the responder to reciprocate as long as the prior h is above the threshold.
But if the responder sees in period 1 that the threshold for sending in period 2 (h >
1
k ) will be violated, the responder starts playing mixed strategies with probabilities
1 (k−1)
to reciprocate as given by σ1 = p(1−p
. Once mixed strategies begin, the respon1)
der’s choice of σ1 in equilibrium makes the sender indifferent between strategies
and vice versa.6
Assume now that the game is played twice, but that they are informed about period
2 after period 1 is played. In this situation, instrumental reciprocity plays no role.
In period 1 the sender knows that a b-type responder will play y1 = 0 while a g-type
responder will play y1 = kx1 . Therefore, if the sender thinks the probability that
the responder is a g-type is h, the payoff from sending exceeds the sure payoff from
not sending iff h > k1 . The g-types reciprocate, while b-types do not. In period 2
the sender knows the responder’s type (since there are no reputation building / no
mixed strategies). He sends if he met a g-type in period 1 and does not send if he
met a b-type. Hence, there is a probability h that he sends in period 2. Again, a
g-type reciprocates, while a b-type does not. If h < k1 , then there is no trust (and
hence no trustworthiness) in any of the two periods.
We can now compare the two situations. For convenience, let us call the standard
two period game ”the strategic game”, and the game where period 2 comes as a
6
The sender chooses to send with probability q, where q makes the responder indifferent between
values of σ1 in the following expression for his expected payoff: σ1 (Er + mx1 − kx1 + (Er +
k
mx2 )q + Er (1 − q)) + (1 − σ1 )(Er + mx1 + Er ).When q = m
, this expression is equal to the
responder’s expected payoff when the sender does not mix (2).
8
surprise ”the non-strategic game”. First, we see that the model can account for
complementarity between instrumental and intrinsic reciprocity: The possibility of
meeting good types makes it possible for bad types to imitate good types in period
1 in the strategic game. Hence, the level of trust and trustworthiness is weakly
higher in period 1 of the strategic game than in period 1 of the non-strategic game.
In period 2, the trust level is (weakly) higher in the strategic game, since if h > k1 ,
the sender sends in both periods in the strategic game, while he only sends with
probability h in period 2 of the non-strategic game. With respect to trustworthiness, only a sender that met a good type in period 1 of the non-strategic game will
subsequently trust in period 2. By contrast, in the strategic game, a sender may
meet a bad type in period 2 who instrumentally reciprocated in period 1. Hence,
the likelihood of being reciprocated, conditional on sending a positive amount, is
higher in period 2 of the non-strategic game. However, since the probability of
initially meeting a good type is equal in the two games, and the trust level is higher
in the strategic game, the total level of cooperation - in which a pair of subjects
trusts and reciprocates trust (respectively) in both periods - is (weakly) higher in
the strategic game.
3
Experimental design and procedure
We run an experiment in which subjects play the two period investment game analyzed in the previous section. In one treatment, which we denote the strategic
treatment, subjects knew they were going to meet twice. In the other treatment,
denoted non-strategic treatment, the second period came as a surprise.
The subjects play four one shot versions of the game each period. More specifically, we announced that the experiment consisted of two parts. In the first part
they were going to play the investment game four times, which we will refer to as
rounds, each round against a new opponent. In the second and last part, subjects
were going to play four rounds against the same four opponents they met in the
first part. Prior to each round of the second part, they got information about how
they played when they met each other in Part I.
The two treatments were identical except for when information was revealed. In
the strategic treatment all information was revealed prior to the first part. In the
non-strategic treatment we announced that the experiment consisted of two parts,
9
then explained only the first part and said that information about the second and
last part would be given after the first part was finished.7
In the beginning of the experiment subjects were assigned the role as a sender or
a responder, and they kept the same role throughout the experiment. Senders and
responders were randomly paired in each round of the first part. In the tth round
of the second part the sender met the same responder as in the tth round of the
first part. In each round subjects were endowed with 100 ECU each (100ECU =
20N OK ≈ $3.5). The sender was then given the opportunity to send an amount
x from her endowment to the responder. The amount of money sent by the sender
was tripled (m = 3) by the experimenter so that the responder received 3x. Then
the responder had the opportunity to send back to the sender an amount y. Hence,
in a given round, the sender’s payoff was 100 − x + y, while the responder’s payoff
was 100 + 3x − y.
The experiment was conducted in March 2012 at the University of Stavanger, Norway. In all 196 subjects participated, 102 in the strategic treatment and 94 subjects
in the non-strategic treatment. Average earning per subject was $43. All instructions were given both written and verbally. The experiment was conducted and
programmed with the software z-Tree (Fischbacher 2007).
4
Results
We start by investigating the average trust and trustworthiness levels, and the average sent and returned amounts. We then look into how the subjects’ behavior
is conditional on their opponents’ actions, and finally we study how cooperation
evolves.
Table 1 presents the average trust and trustworthiness rates for part I and part II.
First, we calculate the the individual’s average trust rate and trustworthiness rate.
We then calculate the average trust and trustworthiness rate for each part in each
treatment. The trust rate is defined as the fraction of individual senders who send
a positive amount. The trustworthiness rate is defined as the fraction of individual
7
In a pilot study the subjects only played one repeated game. As several subjects asked questions
about whether or not there would be another round in the non-strategic treatment, we decided to
include more rounds. In the current design the subjects did not ask about this.
10
responders who return more than what the senders sent to them - conditional on
the senders sending them anything.
Strategic
Non-strategic
Ind
51
47
Trust rate
Part I Part II
0.98
0.77
0.88
0.70
Trustworthiness rate
Part I
Part II
0.73
0.34
0.53
0.62
Table 1: Trust and trustworthiness rates (individual averages)
Results from Mann-Whitney tests between treatments.
Trust rate
Trustworthiness rate
Ind
Part I
Part II
Part I
Part II
Strategic versus z
51
2.491
1.191
2.799
-2.970
Non-strategic
p-value 47
0.0127 0.2335
0.0051
0.0030
Wilcoxon signed-rank test between part I and II within each treatment.
Trust rate
Trustworthiness rate
Strategic treatment
Non-strategic treatment
Part I and II
0.2335
0.0000
3.963
0.0001
z
p-value
z
p-value
Part I and II
4.744
0.0000
-0.949
0.3424
Table 2: Non-parametric tests for the results in Table 1.
The results from non-parametric tests on the results in Table 1 are presented in Table 2. We test whether the trust and trustworthiness rates differ between treatments
using the Mann-Whitney test, and we compare whether trust rates/ trustworthiness
rates change significantly from part I to part II within each treatment using the
Wilcoxon signed-rank test. We see in Table 1 that both the trust rate and the trustworthiness rate are highest in part I of the strategic treatment. Table 2 confirms that
the trust rate and the trustworthiness rate differ significantly between the two treatments (in part I). In Table 1 we also see that both the trust and the trustworthiness
rates are significantly reduced from part I to II in the strategic treatment, and Table
2 confirms that these differences are significant. These results are all predicted by
the model.8
Result 1: The rates of trust and trustworthiness are highest in part I of the strategic
treatment.
Next consider part II. We see a slightly higher trust rate in the strategic treatment,
but it is not significant (p=0.23). With respect to trustworthiness, we see, as ex8
These results are also confirmed in regression Table 9 in the appendix.
11
pected, a higher rate of trustworthiness in the non-strategic treatment. If there are
subjects who act instrumentally and imitate reciprocal preferences, then the likelihood of not being reciprocated is lower in part II of the strategic game.
Result 2: There are higher rates of trustworthiness in part II of the non-strategic
treatment than in part II of the strategic treatment.
We now turn to the levels of trust and trustworthiness. Before considering the
regressions, it is useful to look at the summary statistics. Table 3 presents the
average amount sent and returned, in addition to rate of return (RoR)9 , for those
senders (responders) who chose to trust (were trusted).10
Strategic
Non-strategic
Ind
51
44
Part I
Sent
Ret
60.9 96.1
71.2 80.0
RoR
0.48
0.05
Ind
49
43
Part II
Sent
Ret
57.9 51.2
73.8 90.3
RoR
-0.22
0.28
Table 3: Average sent, returned amounts, and rate of return for senders and responders who showed and was shown trust.
The results from non-parametric tests on the results in Table 3 are presented in
Table 4. We calculate the average sent amount, average returned amount, and
average rate of return for each individual, for those subjects who showed and was
shown trust. We then test whether there are any differences between the treatments
using the Mann-Whitney test. We also compare how these amounts change from
part I to part II within each treatment using the Wilcoxon signed-rank test.
9
Rate of return is a simple measure indicating the payoff from trusting for the senders, and it is
the difference between sent and returned amount over sent amount.
10
Summary statistics for all decisions can be found in the appendix.
12
Results from Mann-Whitney tests between treatments.
Part I
Part II
Ind
Sent
Ret
RoR
Ind
Sent
Ret
RoR
Strategic versus z
51
-1.373
1.390
5.240
49
-2.549 -3.456
-4.998
Non-strategic
p-value 44
0.1696 0.1644 0.0000
43
0.0108 0.0005 0.0000
Wilcoxon signed-rank test between part I and II within each treatment.
Sent part I and II Returned part I and II RoR part I and II
Strategic treatment
Non-strategic treatment
z
p-value
z
p-value
1.017
0.3090
-1.463
0.1435
5.904
0.0000
-1.263
0.2067
5.240
0.0000
-3.055
0.0023
Table 4: Non-parametric tests for the results in Table 3.
The senders who chose to trust in the strategic treatment send on average about 60
percent of their endowment, while the senders in the non-strategic treatment send
about 70 percent in both part I and part II. This difference is only statistically different in part II, as we can see in Table 4. We can see from Table 3 that the responders
in the strategic treatment return more in part I, and less in part II - compared to
the non-strategic treatment. These differences are statistically significant, as can
be seen in Table 4. Furthermore, we can see that the responders in the strategic
treatment reduce how much they return significantly, while there is no difference
between amount returned in the first and the second part for the non-strategic treatment. This is reflected in the senders’ rates of return. In the strategic treatment,
the senders initially experience a significantly higher rate of return (0.48), which
is reduced dramatically and significantly in part II, and actually turns out negative
(-0.22). In the non-strategic treatment we observe the opposite pattern: from an
initial low but positive rate of return, the senders’ payoff from sending increases
significantly in the final part.
We now look closer at how trust, trustworthiness and cooperation in part II depend on previous behavior. First, we investigate how the senders’ trust levels in
part II are conditional on the level of trustworthiness experienced in part I. Table 5
presents the results from three regressions, where sent amount in part II is regressed
on a dummy variable for being in the non-strategic treatment, amount returned in
part I, and an interaction between the non-strategic treatment and amount returned
in part I. In addition we control for the senders’ age, gender, faculty background,
and possible round effects (we report robust clustered standard errors for individuals).
We see that regressions (a) imply no net treatment effect. When we control for how
13
Table 5: Sent in part II.
(c)
1.66
(5.544)
Returned amount part I
0.34***
(0.043)
Returned*treatment
0.13**
(0.054)
Dummy: male
19.55***
5.79
5.38
(7.286)
(5.074)
(5.056)
Age
0.97
0.65
0.59
(0.664)
(0.478)
(0.507)
Science and technology
4.95
2.06
1.66
(8.490)
(5.915)
(6.165)
Social sciences
2.84
-0.07
0.03
(8.242)
(5.452)
(5.619)
Round 2
-4.85
-9.58**
-9.15**
(4.483)
(4.065)
(3.983)
Round 3
-13.83*** -18.26*** -17.46***
(4.848)
(4.043)
(3.917)
Round 4
-12.59*** -15.50*** -14.69***
(4.214)
(3.972)
(3.884)
Constant
22.20
2.93
8.98
(16.624)
(11.279)
(12.306)
Adjusted R2
0.076
0.459
0.468
Observations
392
392
392
Note: OLS with robust clustered standard errors (individuals), * p<0.10, ** p<0.05, *** p<0.01.
Non-strategic treatment
(a)
-0.29
(6.120)
(b)
11.56***
(4.010)
0.39***
(0.033)
much the responders return in part I in regression (b), we see that the senders in the
non-strategic treatment seem to trust more than the senders in the strategic treatment in part II. In order to investigate whether experiencing trustworthy behavior
in part I has a stronger effect on trust in part II for the subjects in the non-strategic
treatment, we include an interaction term between returned amount in part I and
being in the non-strategic treatment in (c). We see that trust that is rewarded, i.e.
reciprocated, has a stronger effect in the non-strategic treatment. We have:
Result 3: Senders who are reciprocated in part I show more trust in part II if they
are in the non-strategic treatment.
Result 3 implies that reciprocal behavior in the first part of the non-strategic treatment is perceived as more credible than reciprocal behavior in the strategic treatment. This shows that subjects anticipate instrumental reciprocity in the strategic
treatment. Result 3 holds also after controlling for round effects, wealth effects,
and experiences with previous partners. See, respectively, Table 10, Table 11 and
14
Table 12 in the appendix.
Let us now look closer at the responders. We have seen that on average there are
higher rates of trustworthiness in part II of the non-strategic treatment than in part II
of the strategic treatment. From Table 6 we also see that responders return a larger
share in part II when we control for senders’ behavior and background variables.
This result also holds after controlling for wealth and round effects (Table 13).
Table 6: Percentage returned by responders in part II.
(2)
12.32***
(4.472)
Sent part I
0.09
(0.052)
Sent part II
0.09
(0.067)
Dummy: male
-3.34
-3.45
(5.235)
(5.107)
Age
-0.04
-0.08
(0.434)
(0.414)
Science and technology
-2.72
-4.16
(6.342)
(6.100)
Social sciences
5.50
4.51
(6.218)
(5.967)
Round 2
-3.43
-4.12
(2.829)
(2.806)
Round 3
-1.17
-2.04
(3.066)
(3.421)
Round 4
1.25
0.21
(3.110)
(3.243)
Constant
30.19***
21.93**
(10.003)
(9.421)
Adjusted R2
0.093
0.133
Observations
289
289
Note: OLS with robust clustered standard errors (individuals), * p<0.10, ** p<0.05, *** p<0.01.
Non-strategic treatment
(1)
14.11***
(4.527)
The linear probability models in Table 7 further illuminate the cooperative behavior
in part II. Cooperation means that the sender chooses to trust, and the responder
reciprocates. The dependent variable is whether the subjects chose to cooperate or
not in part II - cooperation is a dummy variable equal to one for each pair where
trust was reciprocated. In (I) we regress the probability of cooperation in part II on
a dummy for being in the non-strategic treatment, with the same controls as before.
The treatment dummy shows that it is more likely that a pair cooperates in the
second part of the non-strategic treatment. Controlling for how much the sender
sent in part I and how much the responder returned in part I, we see from (II) that
15
Table 7: Cooperation in part II.
(IV)
(V)
0.09
0.11**
(0.064)
(0.054)
Cooperation part I
0.20**
0.28***
(0.078)
(0.055)
Cooperation part I*treatment
0.29*** 0.27***
(0.087)
(0.083)
Sent part I
-0.00**
0.00
0.00
(0.001)
(0.001)
(0.001)
Returned amount part I
0.00***
0.00
0.00
(0.001)
(0.001)
(0.001)
Dummy: male
0.05
-0.01
-0.03
-0.04
-0.01
(0.053)
(0.056)
(0.054)
(0.054)
(0.048)
Age
0.01
0.01
0.01
0.01
0.00
(0.006)
(0.006)
(0.005)
(0.005)
(0.005)
Science and technology
0.03
0.02
0.04
0.03
0.05
(0.068)
(0.067)
(0.064)
(0.063)
(0.060)
Social sciences
0.06
0.06
0.06
0.06
0.05
(0.069)
(0.069)
(0.066)
(0.065)
(0.062)
Round 2
-0.08
-0.10
-0.10
-0.10
-0.08
(0.069)
(0.069)
(0.066)
(0.065)
(0.061)
Round 3
-0.07
-0.08
-0.08
-0.07
-0.04
(0.068)
(0.068)
(0.066)
(0.065)
(0.062)
Round 4
-0.05
-0.05
-0.07
-0.06
-0.03
(0.069)
(0.068)
(0.067)
(0.066)
(0.063)
Constant
0.12
0.00
-0.17
-0.06
-0.01
(0.158)
(0.155)
(0.153)
(0.157)
(0.147)
Adjusted R2
0.025
0.141
0.194
0.211
0.208
Observations
392
364
364
364
392
Note: OLS with robust standard errors, * p<0.10, ** p<0.05, *** p<0.01. The number of
Non-strategic treatment
(I)
0.15***
(0.050)
(II)
0.27***
(0.051)
(III)
0.28***
(0.049)
0.34***
(0.072)
observations is reduced from 392 to 364 when we control for returned amount, as responders who
did not receive anything are missing values.
the point estimate suggests an even higher probability of cooperation in the nonstrategic treatment. In (III) we add a dummy for whether or not they cooperated
the first time they met, and this dummy captures the effects from sent and returned
amounts. The treatment effect remains strong and significant. In (IV) we add an
interaction term between cooperation in part I and being in the non-strategic treatment, and we see that the probability of cooperation - in which trust is reciprocated
- is higher in the non-strategic treatment for those subjects who have experienced
cooperation in part II. The result is robust to excluding sent and returned amount
in (V), and including an interaction term between treatment and rounds (Table 14
in the appendix). We have:
Result 4: The probability of cooperation in part II of the non-strategic treatment
16
is higher than in part II of the strategic treatment.
Finally, we are interested in the total level of cooperation during the repeated game.
Figure 1 compares the rate of pairs cooperating between parts and treatments.
Figure 1: Rate of pairs cooperating.
In the strategic treatment, 72 percent (146 of 204 observations) of the pairs cooperate in the first part. This is significantly higher than the first part of the non-strategic
treatment. 26 percent of the pairs cooperate in both part I and part II of the experiment, which is significantly less than in part I. In the non-strategic treatment 47
percent (88 of 188) cooperate in part one, and 35 percent cooperate in both part
I and part II. So while the initial cooperation rates are significantly larger in the
first part of the strategic treatment (72 versus 47), the rate of pairs who cooperate
throughout both parts is significantly larger than that of the strategic treatment (26
versus 35).11 This is also confirmed by the simple robust linear regression Table
15 in the appendix. We have:
11
We compare the cooperation rates for each pair. Mann-Whitney tests (two-tailed) between treatments: p for part 1, p=0.05 for part II. Wilcoxon signed-rank test comparing parts I and II for the
non-strategic and strategic treatments, respectively: p<0.01, p<0.01.
17
Result 5: The total level of cooperation, in which trust is reciprocated in both
parts, is higher in the non-strategic treatment.
This result cannot be explained by the standard reputation/reciprocity model outlined in Section 2, and shows that instrumental reciprocity can crowd out true
prosocial behavior.
5
Concluding remarks
In repeated games it is hard to distinguish intrinsic reciprocity from strategic instrumental reciprocity. As a result, the latter can substitute for the former. We
investigate this by running a two period version of Berg et al’s (1995) well-known
trust game, also called the investment game. We run two treatments. In the strategic treatment the players know they will meet twice, while in the non-strategic
treatment they do not know - the second period comes as a surprise. Hence, in
the non-strategic treatment we have a repeated game without repeated game incentives. This enables us to study how instrumental reciprocity interacts with intrinsic
reciprocity, or more precisely how strategic repeated game incentives affect the
repeated game.
We find that subjects who are reciprocated in the first period (part), show significantly more trust in the second period if the second period comes as a surprise. This
implies that subjects anticipate instrumental reciprocity in the strategic treatment.
Moreover, we find that the total level of cooperation, in which trust is reciprocated
in both periods, is higher in the non-strategic treatment. Hence, if one takes the
repeated game incentives out of the repeated game, one sees more cooperation.
Our paper thus provides evidence that instrumental reciprocity may, under given
conditions, crowd out intrinsic reciprocity. However, we cannot identify the exact mechanism behind the crowding out result. The problem with the strategic
treatment is that subjects can neither reward intrinsic reciprocity (relevant for the
senders), nor signal intrinsic reciprocity (relevant for the responders). Future research should try to disentangle these two potential sources for the crowding out
result.
18
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21
6
Appendice
6.1
Summary statistics
Part I
Sent
Ret
60.7 93.5
63.8 70.1
Decisions
204
188
Strategic
Non-strategic
RoR
0.49
0.07
Part II
Sent
Ret
46.3 41.9
50.7 66.1
Decisions
204
188
RoR
-0.16
0.19
Table 8: Average sent, returned amounts, and rate of return, all observations.
6.2
Rounds
Average amount sent and returned each round
Responders
ECU
0
0
20
20
40
40
ECU
60
60
80
80
100
100
Senders
1
2
3
4
1
2
Rounds
3
4
Rounds
Strategic: part I
Strategic: part II
Strategic: part I
Strategic: part II
Non−strategic: part I
Non−strategic: part II
Non−strategic: part I
Non−strategic: part II
®
Figure 2: Average amount sent and returned in each round.
22
Instructions for the strategic treatment:
Welcome!
This experiment will last for about 30 minutes. Throughout the experiment you will
get the opportunity to earn money that will be paid out in cash and anonymously
after the experiment is over.
You will now be given time to read through the instructions for this experiment. If
you have any questions concerning these instructions, please raise your hand and
we will come to you. Talking or communicating with others is not allowed during
the experiment.
Throughout this experiment we will use experimental kroner (EK), and not Norwegian kroner (NOK). By the end of the experiment, the total amount of EK which
you have earned will be converted to NOK at the following rate:
5 EK = 1 NOK
6.2.1
Instructions
This experiment consists of two parts, Part I and Part II – and these parts are identical.
All subjects are divided into pairs, where one will be a sender and one will be
a responder. This means that half of you will get to be senders and half of you
responders. You will not get to know who will be your partner. Your partner is in
the room, but you will not get to know who this person is, neither during nor after
the experiment.
23
Each part consists of four rounds. In each round of Part I a sender meets a new
responder.
In Part II senders and responders meet again in the same order that they met in Part
I. In other words: the person you met in round 1 of Part I, you will meet again in
round 1 of Part II. The person you met in round 2 of Part I, you will meet again in
round 2 of Part II, and so on.
PART I:
ROUND 1: In the beginning of each round all participants receive 100 EC. The
sender can now choose to send everything, nothing or some of the 100 EC to the
responder. The money which is sent is then tripled. If the sender chooses to send
for instance 20 EC to the responder, the responder receives 60EC. If 90 EC is sent,
the responder receives EC 270.
The responder then decides how much he/ she wants to keep, and how much he/
she would like to return. The money which will be sent back will not be tripled.
When the sender chooses to send an amount x of the100 EC to the responder and
the responder returns y, the total income of the sender in each round then equals:
100-x+y
The responder receives three times the sent amount x, and returns y. In addition,
he/ she has the 100 EC he received in the start. The total income for the responder
in each round then equals:
100+3x-y
24
By the end of each round the income from that round is put into the participant’s
account, and the round ends.
ROUNDS 2, 3 AND 4:
Rounds 2, 3 and 4 are identical to round 1. Remember
that each sender meets a new responder in each round. By the end of each round
the money earned will be put into each participant’s account.
PART II: Rounds 1, 2, 3 and 4 are identical to rounds 1, 2, 3 and 4 in Part I. It
means that the sender meets the same responder in each round who he met in Part
I. Before each round in Part II you will be reminded of the choices you made when
you met in Part I.
Please follow the messages which appear on the screen. In the end you will be
asked to fill out a short questionnaire, and you will be informed about your total
earnings converted into NOK.
On the pc cabinet you can see a white sticker with the logo of the university, and
a number, for instance D10136. Please write down this number and your total
income on the receipt when the experiment is over. When we tell you that the
experiment is over, you can leave the room with the receipt. Bring this to the EAL
building, office H-161, to collect your total earnings.
25
Instructions for the non-strategic treatment:
Welcome!
This experiment will last for about 30 minutes. Throughout the experiment you will
get the opportunity to earn money that will be paid out in cash and anonymously
after the experiment is over.
You will now be given time to read through the instructions for this experiment. If
you have any questions concerning these instructions, please raise your hand and
we will come to you. Talking or communicating with others is not allowed during
the experiment.
Throughout this experiment we will use experimental kroner (EK), and not Norwegian kroner (NOK). By the end of the experiment, the total amount of EK which
you have earned will be converted to NOK at the following rate:
5 EK = 1 NOK
Instructions
This experiment consists of two parts, and you will now receive the instructions for
Part I of the experiment. Part II we will explain to you later.
All subjects are divided into pairs, where one will be a sender and one will be
a responder. This means that half of you will get to be senders and half of you
responders. You will not get to know who will be your partner. Your partner is in
the room, but you will not get to know who this person is, neither during nor after
the experiment.
26
Each part consists of four rounds. In each round of Part I a sender meets a new
responder.
PART I:
ROUND 1:
In the beginning of each round all participants receive 100 EC. The
sender can now choose to send everything, nothing or some of the 100 EC to the
responder. The money which is sent is then tripled. If the sender chooses to send
for instance 20 EC to the responder, the responder receives 60EC. If 90 EC is sent,
the responder receives EC 270.The responder then decides how much he/ she wants
to keep, and how much he/ she would like to return. The money which will be sent
back will not be tripled. When the sender chooses to send an amount x of the100
EC to the responder and the responder returns y, the total income of the sender in
each round the equals:
100-x+y
The responder receives three times the sent amount x, and returns y. In addition,
he/ she has the 100 EC he received in the start. The total income for the responder
in each round then equals:
100+3x-y
By the end of each round the income from that round is put into the participant’s
account and the round ends.
27
ROUNDS 2, 3 AND 4:
Rounds 2, 3 and 4 are identical to round 1. Remember
that each sender meets a new responder in each round. By the end of each round
the money earned will put into each participant’s account.
Please follow the messages which appear on the screen. In the end you will be
asked to fill out a short questionnaire, and you will be informed about your total
earnings converted into NOK. On the pc cabinet you can see a white sticker with the
logo of the university, and a number, for instance D10136. Please write down this
number and your total income on the receipt when the experiment is over. When
we tell you that the experiment is over, you can leave the room with the receipt.
Bring this to the EAL building, office H-161, to collect your total earnings.
7
The restart effect
In part II of the non-strategic game, subjects learn only at the beginning of the
second period that they will play again the same game with the same partner. In
our paper we argue that observing a higher level of trust and trustworthiness in
this context results from the full revelation of partner types in period 1. But one
could also argue that it is a result of a restart effect. In his paper from 1988, Andreoni studies cooperation in finite games. The starting point is an observation that
cooperation tends to decline throughout experiments. This can either be because
subjects are learning that cooperation is not an equilibrium, or it can be because
subjects are trying to influence their partners, as in the model of Kreps (1982). Andreoni investigates whether declining cooperation in a finite public good game is
due to subjects learning to play the free-riding equilibrium. His approach is to have
the subjects play a game of ten rounds. At the end of the ten rounds he announces
that there is just enough time to play another game of ten rounds. The learning
hypothesis then suggests that subjects should cooperate less in the surprise game.
Andreoni observes a strong restart effect in the partners treatment contributions
increase sharply from the last round of the original game to the first round of the
restart game. The restart effect has later been observed in many experimental studies, and there is no consensus on what drives the restart effect.
In our design, we apply a version of the restart game. The restart effect implies
28
that there should be an increase in trust and trustworthiness when the subjects meet
again in part II. In the first round of part II, senders should send more, and responder should return more compared to part I. But this is not what we observe. Only
responders increase how much they return:
ECU
0 10 20 30 40 50 60 70 80 90 100
Restart effect? Amounts sent and returned
1
2
3
4
1
Part I and Part II: Rounds
2
3
Strategic: Sent
Strategic: Returned
Non-strategic: Sent
Non-strategic: Returned
4
Figure 3:
The restart effect could also imply a jump in trust and trustworthiness rates from
round 4 in part I to round 1 in part II. Again, we only observe this for the responders
in the non-strategic treatment.
Share
0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1
Trust and trustworthiness
1
2
3
4
1
Part I and Part II: Rounds
2
3
Strategic: Trust
Strategic: Trustworthy
Non-strategic: Trust
Non-strategic: Trustworthy
Figure 4:
29
4
If the restart effect explains the behavior of the responders in the non-strategic
treatment, we should expect it to explain the senders’ behavior as well. But we do
not observe a jump in sent amount, and hence we do not believe that the restart
effect can explain our findings.
8
Regressions
Table 9: The dependent variable in (1) is a dummy variable equal to one for a
sender who trusted. The dependent variable in (2) is a dummy variable equal to 1
if a responder reciprocated trust. We see that there is significantly more trust and
trustworthiness in part I of the strategic treatment.
Table 9: Higher trust and trustworthiness in part I of the strategic treatment.
(1)
(2)
Trust
TW
Non-strategic treatment -0.10** -0.19**
(0.045)
(0.078)
Dummy: male
0.01
-0.05
(0.056)
(0.082)
Age
-0.00
-0.00
(0.005)
(0.011)
Social sciences
0.01
0.11
(0.055)
(0.110)
Science and technology
0.02
0.18*
(0.055)
(0.103)
Rounds
-0.02**
0.00
(0.007)
(0.017)
Constant
1.07***
0.68**
(0.120)
(0.276)
Adjusted R2
0.030
0.048
Observations
392
364
Note: OLS with robust clustered standard errors (individuals), * p<0.10, ** p<0.05, *** p<0.01.
Table 10: The dependent variable is sent in part II. In addition to returned amount
and interaction, we here test for possible round effects. We see that controlling
for rounds and interacting rounds and the non-strategic treatment do not change
our results: Senders in the non-strategic treatment send significantly more to those
responders who rewarded their trust in part I.
Table 11: The dependent variable is sent amount in part II. In addition to returned
amount, interaction with returned amount, and round effects, we here test for possible wealth effects. We see that controlling for accumulated wealth in part I and
30
Table 10: Sent in part II and round effects.
(1)
Sent part II
-3.09
(8.420)
(2)
Sent part II
-0.48
(7.665)
0.39***
(0.033)
(3)
Sent part II
Non-strategic treatment
-10.09
(8.198)
Returned amount part I
0.34***
(0.043)
Returned*treatment
0.13**
(0.054)
Round
-5.21***
-7.83***
-7.48***
(1.825)
(1.989)
(1.904)
Round*treatment
1.12
4.82*
4.68*
(2.719)
(2.591)
(2.552)
Dummy: male
19.55***
5.77
5.35
(7.276)
(5.065)
(5.043)
Age
0.97
0.65
0.59
(0.663)
(0.477)
(0.507)
Science and technology
4.95
2.06
1.65
(8.479)
(5.906)
(6.156)
Social sciences
2.84
-0.07
0.03
(8.232)
(5.441)
(5.610)
Constant
27.42
11.63
17.37
(16.978)
(11.344)
(12.359)
Adjusted R2
0.076
0.458
0.467
Observations
392
392
392
Note: OLS with robust clustered standard errors (individuals), * p<0.10, ** p<0.05, *** p<0.01.
accumulated wealth in part II (up to the previous round) do not change our results:
Senders in the non-strategic treatment send significantly more to those responders
who rewarded their trust in part I.
Table 12: Our design consists of four repeated games. Hence, it is possible that the
player is influenced by the interaction with previous players in their current round.
Here we test whether including a measure of previous experience has any influence
on our results. Sender’s previous experience in part I is equal to the share of times
that the player experienced that trust was reciprocated (given that he/ she showed
trust). Sender’s previous experience in part II is equal to the share of times the
player experienced that trust was reciprocated (given that he/ she trusted) up to the
previous round. Hence, in the first round of part II this variable is equal to the the
sender’s previous experience in part I. We find that it does not change our result:
Senders who are reciprocated in part I still show more trust in part II if they are in
the non-strategic treatment.
Table 13: The dependent variable is percentage returned by responders in part II.
We test for possible round and wealth effects. First, we see that adding an interac31
Table 11: Sent in part II, wealth and round effects.
Non-strategic treatment
Returned amount part I
(1)
35.79*
(21.287)
(2)
7.63
(16.565)
0.38***
(0.039)
Returned*treatment
(3)
38.20*
(20.612)
0.25***
(0.060)
0.25***
(0.074)
(4)
18.63
(28.761)
(5)
-28.12
(21.811)
0.40***
(0.035)
Rounds
-19.96*** -23.13***
(6.203)
(5.212)
Rounds*treatment
12.74
23.86***
(11.082)
(8.697)
Dummy: male
9.74
5.74
5.69
10.22*
6.49
(6.073)
(5.249)
(5.226)
(5.994)
(5.270)
Age
0.58
0.63
0.63
0.69
0.78
(0.473)
(0.465)
(0.498)
(0.495)
(0.510)
Science and technology
5.73
2.26
2.60
4.83
1.28
(6.338)
(5.902)
(6.156)
(6.233)
(5.901)
Social sciences
-0.17
-0.32
1.24
0.70
0.78
(6.421)
(5.576)
(5.827)
(6.313)
(5.545)
Accumulated wealth part I
0.18***
0.03
0.09*
0.01
-0.17***
(0.047)
(0.044)
(0.052)
(0.081)
(0.065)
Accumulated wealthI*treatment
-0.01
0.00
-0.09
0.09
0.21**
(0.056)
(0.050)
(0.065)
(0.126)
(0.102)
Accumulated wealth part II
-0.01
-0.03*
-0.02
0.15**
0.16***
(0.020)
(0.017)
(0.017)
(0.060)
(0.049)
Accumulated wealthII*treatment
-0.02
0.00
-0.00
-0.13
-0.19**
(0.026)
(0.024)
(0.024)
(0.099)
(0.079)
Constant
-61.66***
-2.76
-24.87
-34.55
29.75
(21.227)
(18.336) (21.433)
(23.018)
(19.329)
Adjusted R2
0.236
0.437
0.458
0.265
0.476
Observations
392
392
392
392
392
Note: OLS with robust clustered standard errors (individuals), * p<0.10, ** p<0.05, *** p<0.01.
tion for round and treatment render the coefficient for the non-strategic treatment
insignificant. Second, we see that when we control for accumulated wealth in part
I and accumulated wealth in part II (up to the previous round) our results remain:
There are higher rates of trustworthiness in the non-strategic treatment.
32
(6)
-2.03
(24.422)
0.27***
(0.050)
0.24***
(0.065)
-22.29***
(5.280)
25.34***
(8.382)
6.48
(5.200)
0.79
(0.532)
1.67
(6.091)
2.24
(5.759)
-0.11
(0.070)
0.13
(0.108)
0.16***
(0.051)
-0.21***
(0.078)
7.83
(21.077)
0.494
392
Table 12: Sent in part II and experience with previous partners.
Non-strategic treatment
(1)
36.05***
(12.201)
(2)
22.41**
(10.199)
0.35***
(0.033)
14.49**
(6.815)
7.74
(5.244)
Returned amount part I
Returned*treatment
Dummy: male
(3)
22.73**
(10.184)
0.27***
(0.040)
0.19***
(0.060)
8.09
(5.272)
(4)
43.61***
(14.401)
(5)
18.65
(12.294)
0.35***
(0.035)
14.41**
7.58
(6.856)
(5.263)
Round
-0.94
-4.23*
(2.079)
(2.132)
Round*treatment
-3.21
1.16
(3.078)
(2.834)
Age
1.01*
0.88*
0.80
1.01*
0.86
(0.595)
(0.525)
(0.540)
(0.600)
(0.521)
Science and technology
8.67
2.80
2.69
8.70
2.74
(7.464)
(6.013)
(6.365)
(7.500)
(6.029)
Social sciences
6.31
3.57
4.27
6.24
3.26
(7.039)
(5.320)
(5.530)
(7.069)
(5.328)
Sender’s experienced TW part1
45.30***
-8.25
3.64
45.86***
-6.67
(13.231)
(11.361)
(11.794)
(13.246)
(11.490)
Sender’s experienced part1 TW*treatment
-6.38
15.12
-9.05
-8.47
12.02
(21.007)
(16.446)
(17.485)
(20.941)
(16.357)
Sender’s experienced TW part2
33.83***
29.97***
30.98***
32.82***
25.38***
(7.562)
(6.609)
(6.651)
(8.153)
(7.010)
Sender’s experienced part2 TW*treatment -40.77*** -39.45*** -41.44*** -37.72*** -33.40***
(13.932)
(10.763)
(10.148)
(14.136)
(10.838)
Constant
-35.18**
-19.01
-19.24
-32.68*
-7.25
(15.790)
(14.032)
(14.128)
(17.384)
(14.963)
Adjusted R2
0.210
0.442
0.458
0.212
0.448
Observations
358
358
358
358
358
Note: OLS with robust clustered standard errors (individuals), * p<0.10, ** p<0.05, *** p<0.01.
33
(6)
19.96
(12.430)
0.28***
(0.043)
0.18***
(0.062)
7.93
(5.288)
-3.53*
(2.101)
0.81
(2.818)
0.79
(0.536)
2.66
(6.362)
3.97
(5.521)
4.11
(11.989)
-9.97
(17.466)
27.07***
(7.206)
-36.16***
(10.416)
-9.40
(15.158)
0.462
358
Table 13: Returned in part II, round and wealth effects.
Non-strategic treatment
(1)
9.19
(6.308)
Sent part I
Sent part II
Dummy: male
-3.43
(5.222)
-0.04
(0.435)
-2.69
(6.322)
5.32
(6.215)
-0.47
(1.621)
2.11
(2.013)
(2)
6.77
(6.025)
0.09*
(0.052)
0.09
(0.067)
-3.54
(5.088)
-0.07
(0.415)
-4.12
(6.094)
4.32
(5.963)
-0.93
(1.669)
2.38
(1.974)
(3)
40.29**
(19.171)
-3.28
(4.905)
-0.01
(0.427)
-3.65
(6.232)
3.86
(6.174)
(4)
31.95*
(18.529)
0.16***
(0.055)
0.06
(0.068)
-3.19
(4.584)
-0.03
(0.394)
-5.40
(5.719)
2.58
(5.567)
(5)
42.55*
(22.426)
-3.63
(4.653)
Age
0.09
(0.417)
Science and technology
-1.86
(6.117)
Social sciences
4.72
(6.108)
Round
9.84**
(4.600)
Round*treatment
-3.87
(8.777)
Responder’s wealth part I
0.01
-0.00
0.05*
(0.020)
(0.020)
(0.026)
Responder’s wealth in I*treatment
-0.05**
-0.05*
-0.06
(0.025)
(0.023)
(0.050)
Responder’s accumulated wealth part II
-0.01*
-0.02** -0.05***
(0.006)
(0.007)
(0.018)
Accumulated wealthRII*treatment
0.01
0.02**
0.02
(0.010)
(0.009)
(0.041)
Constant
30.29*** 22.54**
32.56*
34.26**
16.55
(10.279)
(9.932)
(17.544) (16.563) (18.116)
Adjusted R2
0.094
0.134
0.121
0.184
0.137
Observations
289
289
289
289
289
Note: OLS, robust clustered standard errors (individuals) * p<0.10, ** p<0.05, *** p<0.01.
Table 14: The dependent variable is cooperation in part II. We test for possible
round effects. The results confirm the overall finding: The probability of cooperation in part II of the non-strategic treatment is higher.
Table 15: The dependent variable is the rate of pairs cooperating, the independent
variable is treatment.
34
(6)
39.52*
(22.075)
0.14**
(0.056)
0.09
(0.067)
-3.36
(4.279)
0.03
(0.386)
-3.57
(5.513)
3.66
(5.413)
11.37**
(4.631)
-8.00
(8.554)
0.04
(0.025)
-0.07
(0.047)
-0.06***
(0.018)
0.05
(0.039)
16.66
(17.287)
0.203
289
Table 14: Cooperation in part II and round effects.
(4)
(5)
-0.01
-0.01
(0.124)
(0.117)
Cooperation part I
0.21*** 0.28***
(0.078)
(0.055)
Cooperation part I*treatment
0.28*** 0.27***
(0.087)
(0.082)
Sent part I
-0.00**
0.00
0.00
(0.001)
(0.001)
(0.001)
Returned amount part I
0.00***
0.00
0.00
(0.001)
(0.001)
(0.001)
Dummy: male
0.05
-0.01
-0.02
-0.03
-0.01
(0.053) (0.056)
(0.054)
(0.053)
(0.048)
Age
0.01
0.01
0.01
0.01
0.00
(0.006) (0.006)
(0.005)
(0.005)
(0.005)
Science and technology
0.03
0.02
0.04
0.03
0.05
(0.068) (0.067)
(0.064)
(0.063)
(0.060)
Social sciences
0.06
0.05
0.06
0.05
0.05
(0.069) (0.069)
(0.066)
(0.065)
(0.062)
Round
-0.02
-0.03
-0.04
-0.04
-0.03
(0.029) (0.029)
(0.029)
(0.029)
(0.028)
Round*treatment
0.02
0.04
0.04
0.04
0.05
(0.044) (0.043)
(0.041)
(0.041)
(0.039)
Constant
0.12
0.02
-0.14
-0.03
0.02
(0.171) (0.165)
(0.165)
(0.169)
(0.163)
Adjusted R2
0.024
0.140
0.195
0.212
0.210
Observations
392
364
364
364
392
Note: OLS, robust standard errors, * p<0.10, ** p<0.05, *** p<0.01.
Non-strategic treatment
(1)
0.11
(0.121)
(2)
0.18
(0.120)
(3)
0.17
(0.115)
0.34***
(0.072)
Table 15: Rate of pairs cooperating
(1)
Non-strategic treatment
0.09*
(0.047)
Constant
0.26***
(0.031)
2
Adjusted R
0.007
Observations
392
OLS, robust standard errors, * p<0.10, ** p<0.05, *** p<0.01.
35