doing good or doing harm_khadjavi & lange
TRANSCRIPT
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Doing Good or Doing Harm – Experimental Evidence on Giving and
Taking in Public Good Games
Menusch Khadjavi and Andreas Lange*
University of Hamburg
August, 2011
Abstract.
This paper explores motives and institutional factors that impact the voluntary provision of
public goods. We compare settings where players can only contribute with those where their
actions may also reduce the public good provision. While the ‘giving’ decision has received
substantial interest in the literature, e.g. on charitable giving, many real world applications
involve actions that may diminish public goods. Our results demonstrate that the option to
‘take’ significantly changes contribution decisions. Through a series of treatments that vary in
the action set and the initial stock of the public good, we show that fewer agents contribute to
the public good when their action set allows for taking. As a result, the provision level of the
public good is reduced. Extending the action set to the take domain thereby allows us to
provide a new interpretation of giving in (linear) public good games: giving positive amounts
in a standard public good game may just reflect a desire to avoid the most selfish option,
rather than a ‘warm glow’ from giving. As such, ‘doing good’ may just mean ‘not doing (too
much) harm’.
Keywords: public good, voluntary provision, experiments
JEL: H41, C91
* Correspondence: Department of Economics, University of Hamburg, Von Melle Park 5,
20146 Hamburg, Germany ([email protected],
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1 Introduction
A functioning society relies on a sufficient provision of public goods. These can be financed
through taxes or through voluntary individual contributions. Both provision channels have
received substantial attention in the literature. However, it is equally important that existing
public goods are not exploited by individuals to their own personal advantage.
Examples are widespread where individuals may both contribute to a public good or
reduce its provision level. They range from environmental pollution where agents can emit or
try to reduce overall pollution by investing in offsets (Kotchen 2009), legal vs. illegal
employment, illegal claim of social services and tax evasion, to managers whose actions may
enhance the performance of a firm or just exploit the work contribution of others.
While doing good has been explored in numerous laboratory and field experiments on the
economics of charities, the option of individuals doing harm to the public for their own
private benefit has received much less attention in the literature.1 In this paper we investigate
how individuals behave when their action space allows for giving and taking, i.e. contributing
to a public good or exploiting it. Our study lends new insights into the motives of individuals
in private-public interactions. To our knowledge, simultaneous giving and taking decisions
have not been addressed in the literature.
Andreoni (1995) examines the extreme settings where agents can either only take or only
give. Comparing giving (positive frame) and taking (negative frame) decisions, he finds that
public good provision levels are significantly lower in the negative frame compared to the
positive frame. As a possible explanation, Andreoni suggests that agents may receive a
relatively large ‘warm glow’ from giving, while only getting a relatively small ‘cold prickle’
from taking. These findings have been confirmed by Park (2000) for a linear public good
1 For an overview of earlier studies of public good games, see Ledyard (1995). Social dilemma games and public
good games often find that behavior of individuals differs from the standard game theoretic prediction. While the
prediction in standard linear public good games is that participants give nothing to the public good, studies
present robust evidence that group contributions to the public good are significantly greater than zero (often
around 50 to 60 percent of total possible contributions) in the first period, and – even though with a declining
trend – mostly remain significantly greater than zero in subsequent periods (see e.g. Isaac and Walker 1988,
Isaac et al. 1994, Gächter et al. 2008).
Positive giving decisions in public good games, dictator and ultimatum, and other games are in conflict with
the Nash prediction of payoff-maximization and have led to a series of theoretical explanations based on other-
regarding, social preferences. See Meier (2007) for a recent survey.
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game and Sonnemans et al. (1998) for a comparison of step-level public goods versus step-
level public bads. 2
In this paper, we explore the more general and realistic setting where the action space
allows agents to give and take. We perform a series of experimental treatments that differ
with respect to the initial allocation given to the private and the public accounts. Besides the
extreme cases of (i) a voluntary contribution mechanism (VCM) with no initial resources in
the public account where agents can solely give and (ii) an inverse public good treatment
where all resources are in the public account and subjects can only take,3 we consider two
additional treatments that start with a positive allocation in both the private and the public
account. In the first, the action space allows both giving and taking decisions. In the second,
the action set is again limited to the giving domain. Our experimental design allows us to
investigate how an extension of the action space changes the behavior in public good settings.
The importance of the taking domain has been demonstrated by List (2007) and Bardsley
(2008) who investigate the impact of the action set manipulation on subjects’ willingness to
transfer money in dictator games. They find that providing dictators with the opportunity to
take resources from recipients leads fewer dictators to give positive amounts, while mean
offers decrease significantly and even turn to be negative. We use our combination of
treatments to show new insights into the motives of giving to and taking from public goods.
Our results demonstrate that the option to ‘take’ significantly changes contribution
decisions. Fewer subjects contribute to the public good when their action set allows for
taking. The provision level is least in the inverse public good setting where subjects can only
take from an initially existing public account. In line with Andreoni (1995), more subjects
choose the most selfish action, i.e. transfer the maximal allowed amount to their private
account when taking is possible.
Importantly, the percentage of subjects who give positive amounts to the public good also
declines when taking options are introduced for identical initial allocations to public and
private accounts. That is, we find that not only those subjects who contribute zero when
limited to the giving domain will exploit a chance to take from the public good when this is
2 Cubitt et al. (2010) follow a similar approach in a one-shot setting with second-stage punishment option and
ex-post elicitation of emotions, but largely find insignificant results. For a broader comparison of framing effects
in public good experiments, see Cookson (2000). 3 This treatment is comparable to the take frame of Andreoni (1995) and Cubitt et al. (2010). Note that an inverse
framing of the public good game resembles, but does not correspond to a typical common pool resource game.
The inherent and the functional structures differ significantly. While some use of the common pool resource is
socially optimal, every unit of depletion of the public good lets the outcome diverge from the social optimum.
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possible. These results extend findings by List (2007) and Bardsley (2008) to the domain of
public goods.
Our findings suggest new insights into the motives of giving. They are not consistent with
standard impure altruism models (Andreoni 1990) which assume warm glow utility to stem
from the number of tokens a subject allocates to the public good. Rather, they suggest that
‘doing good’ (and potentially some feeling of warm glow) depends on the chosen action
relative to the set of available actions.4 In other words, if a subject could potentially diminish
or destroy the public good, ‘doing good’ may just mean ‘not doing (too much) harm’. Our
results also relate to the literature on crowding out of voluntary contributions through a tax-
financed provision of public goods (e.g., Andreoni 1993, Chan et al. 2002, Bergstrom et al.
1986). We confirm earlier results that crowding out of private contributions is incomplete
when agents are limited to positive contributions to the public good. However, for the case
where agents can also diminish the provision level of the public good, our findings suggest
that a tax-financed provision may backfire such that the final public good provision is
reduced.
The remainder of this paper is organized as follows. Section 2 presents the experimental
design of the study. Results are presented and discussed in section 3. Section 4 provides a
concluding discussion.
2 Experimental Design
Our experimental design consists of four treatments. They include the standard linear public
good game in which participants receive their endowments in a private account and are able to
contribute to the public good (VCM), i.e. to transfer part of their endowment from their
private to public account. The other treatments differ in the initial allocation to the public
good and in the action set that is available to agents. Players always interact in groups of four.
The payoff to an agent i in the respective treatments is given by
�� = �� − �� + ℎ�� +�� � �� �
where ℎ denotes the per capita return to the public good with 0 < ℎ < 1 < ℎ�, �� represents
the initial endowment of i in treatment t (and is the same for all n group members), �� denotes
4 A similar idea was introduced by Rabin (1993) when modeling a theory of reciprocity: the kindness of an
action is defined relative to the range of payoffs that the player could allocate to other persons.
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i’s transfer to the public good account, and �� is the initial allocation to the public good
account. In the experiment, we chose � = 4 and ℎ = 0.4.
The first three treatments vary the initial allocation to agents and the public good as well
as in the action space. Parameters in treatment t are given by: �� = 20 − Δ��� = �Δ��� ∈ [−Δ�, 20 − Δ�] First, the baseline (VCM) treatment has Δ� ! = 0, i.e. no initial allocation to the public good
exists, the agents can contribute any amount between 0 and 20 units to the public good
account.
Second, we consider an inverse of the standard game (INV) in which agents do not have
any initial private endowment (Δ"#� = 20), but instead all budget is allocated to the public
good (�"#� = 4 ∗ 20 = 80) and players are able to take their share from the public good, i.e.
transfer any amount between 0 and 20 units to their private account.5
Third, we study an intermediate situation in which 40 percent of the budget is initially
allocated to the public good while players receive 60 percent of the budget in their private
account and may either contribute to or take from the public good. We denote this treatment
by VGT – Voluntary Give or Take. That is, Δ�&' = 8 such that the initial endowment of each
player is 12, while the public good level initially is given by ��&' = 4 ∗ 8 = 32. Players are
able to take up to 8 units out of the public good (by choosing �� = −8) or to give up to 12
units to the public good (�� = 12).
Fourth, we limited the VGT treatment to the giving domain, so that we get a second
VCM, called VCM*. Its parameters are calibrated so that �� !∗ = ��&' and �� !∗ =�� !∗. Like in the VGT treatment, 32 units are initially allocated to the public account, while
12 units are allocated to each of the four private accounts. The action set is however limited to �� ∈ [0, 20 − Δ�&']. That is, players may now contribute between 0 and 12 units to the public
account.
The standard game theoretic prediction for all treatments is that agents will contribute no
units of their endowments to the public good and – if taking is possible – transfer the maximal
allowable amount to their private account. We therefore would predict �� ! = 0, �"#� =−20, ��&' = −8, and �� !∗ = 0. In order to compare decisions across treatments, we
discuss the person’s effective contribution level �� + Δ� in the results section.
5 In our experiment, this treatment asked agents to decide on the transfer to their public account, i.e. their
decision was on −�� ∈ [0,20].
6
Contrary to the equilibrium prediction of zero contributions, many experiments have
demonstrated positive contributions by (at least some) players in the first period as well as
subsequent periods of a session (Ledyard 1995). Social preferences, bounded-rationality and
strategic considerations might explain such departures from the standard game theoretic
prediction (Meier 2007) or warm-glow (Andreoni 1990).
With our experimental design, we contribute to the understanding of motives of giving.
Our combination of treatments that vary both the action set and the initial endowment of the
public good is novel in several respects. While VCM, VCM*, and INV either allow for taking
or for giving, our VGT treatment provides players with both the option to give and to take.
Thereby, we are able to directly test for impure altruism. Based on the warm glow theory of
giving, the share of players deciding to give positive amounts from their endowment in the
VGT treatment should not be significantly different from the share in VCM* as the initial
income of players is identical. Comparing VGT and VCM* therefore directly allows to study
the effect of extending the action set to the taking domain.
The treatments can further provide useful information on crowding out behavior. Relative
to VCM, VCM* resembles a situation where agents’ income is reduced in order to provide the
public good. Agents are then able to further add to the public good. This comparison
corresponds to the literature on crowding out of voluntary contributions through public
provision of public goods (e.g. Bergstrom et al. 1986). Here, we are able to measure the
magnitude of crowding out in our public good game where taxation is inconspicuous rather
than explicit. This situation resembles what Eckel et al. (2005) analyze in their experiments
on the crowding out hypothesis with respect to charitable giving and refer to as fiscal illusion.
Note again that in case players take from the public good in the VGT, this is not motivated by
explicit taxation. By comparing VCM and VGT, we can further study how this crowding
effect changes when agents can not only add to a publicly provided public good, but also
diminish it by selfish actions.
All experimental sessions were conducted in the computer laboratory of the Faculty of
Economic and Social Sciences, University of Hamburg, Germany in January and April 2011.
Each session lasted approximately one hour. We used z-Tree (Fischbacher 2007) to program
and ORSEE (Greiner 2004) for recruiting. In total, 160 subjects participated in the
experiment. All were students with different academic backgrounds, including economics.
Each of our 8 sessions consisted of 10 periods. Once the participants were seated and
logged into the terminals, a set of instructions was handed out and read out loud by the
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experimenter.6 In order to ensure that subjects understood the respective game, experimental
instructions included several numerical examples and participants had to answer nontrivial
control questions via their computer terminals.7 At the beginning of the experiment subjects
were randomly assigned to groups of four. The subjects were not aware of whom they were
grouped with, but they did know that they remained within the same group of players for all
periods.
At the end of each period, participants received information about their earnings, the
cumulative group contribution to or extraction from of the group account and the final amount
of units in the group account. Subjects were never able to identify individual behavior of
group members. At the end of the experiment, one of the periods was randomly selected as
the period that determined earnings with an exchange rate between Euro and token of 3 EUR
= 10 tokens. Including a show-up fee of 4 EUR, the average payment over all treatments was
11.70 EUR. Table 1 summarizes the information for all 8 sessions.
3 Results
We craft the results summary by both pooling the data across all periods and reporting
treatment differences for the first period. We later explore the effects of time on contribution
schedules in more detail.
Since the action space and therefore the decisions differed across the treatments, Table 2
reports the decisions along with the corresponding public good contribution level per player
relative to the Nash equilibrium prediction in INV, VCM, VCM* and VGT. As stated in the
section 2, this is given by �� + �. At the group level, this normalized contribution coincides
with the provision level of the public good.
Table 2 provides summary statistics for decisions in all treatments and the corresponding
contribution levels in VCM, VCM*, VGT, and INV. Across all periods, in VCM, each player
contributed 7.71 tokens on average, resulting in a public good provision level of
4*7.71=30.84 tokens. In VCM* the average contribution was 12.84 tokens.8 In VGT, the
average contribution was 7.23, while it is substantially smaller in INV with 4.44. For the first
6 We mainly followed the instructions of Fehr and Gächter (2000), but slightly changed the wording. For
instance, instead of ‘contributions to a project’, instructions asked participants to divide tokens between a private
and a group account. Instructions can be found in Appendix B. 7 In case a participant did not answer the questions correctly, she was given a help screen that explained the
correct sample answers in detail. We believe this might further reduce experimenter demand effects compared to
individual talks with subjects. See Zizzo (2010) for more information on experimenter demand effects. 8 Note that the minimum contribution in the VCM* was 8 tokens, because the public account contained 8 tokens
per person already and ‘taking’ was no option.
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period, the mean contributions are 11.75 tokens for the VCM, 14.25 tokens for the VCM*,
8.61 tokens for the INV, and 11.53 tokens for the VGT treatment. Figure 1 depicts
contribution levels by period.
The differences between the treatments are confirmed by a series of tests. Based on
Mann-Whitney tests with the average contribution by one group across all periods as the unit
of observation, INV results in smaller contributions than VGT (5% level) and VCM* (1%
level). While Mann-Whitney does not show a significant difference between INV and VCM,
this difference is confirmed by a Welch’s t-test (10% level).9 Contributions are greater in
VCM* compared to all other treatments. Of course, this is also due to the minimum
contribution of 8 tokens. There is no significant difference in contributions between VCM and
VGT. Table 3 summarizes these test results.
Using the individual contributions in the first period as the unit of observation, Mann
Whitney tests again confirm the difference between INV and VGT, VCM (both differences
significant at 10%), and VCM* (1% level).
We can therefore formulate the following results:
Result 1. Average provision of the public good in the inverse public good game
(INV) is less than in VCM, VCM* and VGT.
Result 2. Average provision of the public good in the VCM* is greater than in
VCM, INV and VGT.
Result 3. There is no significant difference in the provision of the public good
between VCM and VGT.
Further evidence for these results can be found through a series of linear regression models as
illustrated in Table 4. The regressions predict the contribution to the public good (in tokens)
as a result of the different treatments. We test the INV against the VCM, VCM* and VGT.
Averaged across all periods, the INV treatment leads to less contributions than VCM (3.3
tokens, statistically significant at the 10% level), VCM* (8.4 tokens 1% level), and VGT (2.8
9 The reason for using the Welch t-test is as follows: In order to be allowed to use a Mann-Whitney test, the
variances of the samples need to be equal (see, e.g., Zimmerman 1992, Fay and Proschan 2010 and Ruxton
2006). A Levene’s test leads to no significant difference in variances for the VCM and VGT such that a Mann-
Whitney test is valid. In contrast, a Levene’s test shows that the variances of the samples of VCM and INV are
not equal (p = 0.014) such that a Welch’s t test for unequal variances can be used (a Shapiro-Wilk W test cannot
reject the hypothesis of normality for both distributions).
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tokens, 5% level). Table 4 also separates the effects between the first five and last five
periods. It should be noted that our regressions indicate a declining trend in contributions over
the periods that also reduces the difference between the treatments.
Result 1 suggests an interesting effect of allowing agents to take from the public good.
Contrary to ideas of status quo bias, a larger initial endowment of the public good account
does not lead to an increased provision. Rather, reversing the public good to a taking game in
INV diminishes the contribution levels. We thereby confirm findings by Andreoni (1995) and
Park (2000). Importantly, this effect is large enough for INV to be inferior to VGT where
agents can give and take.
However, the effect appears to be primarily driven by the fact that INV does not allow for
giving. Comparing VCM and VGT, we do not find any significant differences. In fact, Figure
1 shows almost identical contribution rates. While this suggests that – without changing the
range of possible contributions – introducing a taking domain has no significant on average
contributions impact as long as giving remains possible, we will later see important
differences between the underlying distributions. When taking options are introduced that
extend the range of possible contribution levels (VGT vs. VCM*), contributions not
surprisingly go down. This is particularly driven by the fact that the most selfish option in
VCM* still corresponds to a positive contribution level.
Our results also shed some new light on the extent to which private contributions to a
public good are crowded out by government contributions that are financed through taxes
(e.g., Andreoni 1993, Chan et al. 2002, Bergstrom et al. 1986). The payoff structure of VCM*
relative to VCM can be reinterpreted as having private income of agents reduced (taxed)
while simultaneously providing a public good at the corresponding level (tax-based financing
of public good). This public finance literature suggests that crowding out is incomplete, i.e.
tax-financed provision may increase the total provision level of a public good. We find
evidence for this incomplete crowding out even in our linear public good setting by
comparing contributions in VCM vs. VCM*. However, Result 3 indicates that this finding is
driven by the assumption of non-negative contributions. When extending the action set to the
taking domain, i.e. when agents have options to diminish the public good to their own private
advantage, we find complete crowding out (VGT vs. VCM). Note that we find this result even
though the reduced allocation to the private account in VGT and VCM* was not framed as ex
ante taxation. The setting thereby resembles fiscal illusion (Eckel et al. 2005). It might not be
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unreasonable to speculate that crowding out will even be larger when taking options exist in
settings without fiscal illusion.
After this discussion of average contribution levels, we now have a closer look at the
individual decisions and how they are affected by the option to take. In Table 5, we report the
percentage of the respective most selfish action, i.e. where players maximize the units in their
private account (MaxSelf), that is, give 0 in VCM and VCM*, take 8 in VGT or take 20 in
INV. We further report the percentage of actions that correspond to contributing the
maximum to the public good (MaxPubl), i.e. give 20 in VCM, give 12 in VCM* and VGT, or
take 0 in INV. Finally, we give the percentage of choices in VCM, VCM* and VGT that
transfer a positive amount to the public good.
Across all periods, 16.6% of the decisions in VCM involve a full allocation to the public
good. This statistic is 18.3% in VCM*. In VGT 11.3% of all individuals decide to contribute
all resources to the public good, while only 4.8% of choices are not withdrawing any tokens
from the public good in INV. Corresponding, while 52.7% of actions involve the maximal
transfer to the private account (MaxSelf) in INV, 45.3% in VGT, and 33.9% in VCM, only
25.3% of decisions involve zero giving in VCM*. In all treatments, there is a declining trend
in cooperation and an increase in fully selfish behavior.
In order to identify how taking options change the behavior of agents due to changed
intentions rather than due to reactions to behavioral changes of others, we now concentrate on
period 1 decisions. We use a series of Fisher’s exact tests to compare the distributions for the
different treatments. In INV, 36.4% of players take out the maximum amount. Less players
choose the corresponding selfish action in VGT (20.0%, difference significant at the 10%
level), VCM* (12.5%, at 5% level) and in VCM (11.1%, at 1% level). We can therefore
conclude that the action space in a public good setting matters for the display of selfish
behavior that maximizes the player’s own payoff while minimizing the contributions to the
public good.
Result 4. More players choose the most selfish action in INV than in VCM,
VCM* and VGT.
Result 4 indicates that extending the action set to the taking domain can lead to a substantial
change in behavior. Interestingly, the standard public good setting appears to reduce the
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number of agents who act fully selfishly compared to settings where agents take from an
initially existing public good account.
We now have a closer look at giving in VCM, VCM* and VGT. In all three treatments,
agents could add to the public good account. Considering first period decisions only, 89% of
players give a positive amount in VCM and 87.5% in VCM*, while only 65% give in VGT.
The differences between VCM and VGT as well as VCM* and VGT are both significant at
the 5% level. They remain stable over the periods.
Result 5. Fewer players give a positive amount if the action space allows for
giving and taking (VCM vs. VGT and VCM* vs. VGT).
A random effects probit regression for the probability of a positive giving in Table 6 confirms
this finding. The estimated coefficients for VCM and VCM* are positive and statistically
significant.
Taking jointly, Results 4 and 5 allow us to gain further insights into the motives of giving.
Giving in public good games is often interpreted as a sense for efficiency, conditional
cooperation or agents gaining a warm glow from giving (Andreoni 1990). Our results show
that introducing the option to take from the public good does not merely induce a smaller total
provision level because some agents will transfer tokens to their private accounts. Rather, the
percentage of players who contribute positive amounts to the public good declines. 10
Our findings are therefore neither consistent with some status quo bias, nor with a strict
version of warm glow. If an agent’s warm glow utility from contributing was driven by the
number of tokens she allocates to the public good, we would not expect to see the differences
between VGT and VCM* and VCM. Our results are, however, consistent with a modified
version in which an agent’s utility depends on the chosen action relative to the available set of
actions. In order to capture this idea, we posit a kindness measure for voluntary actions.
Inspired by Rabin (1993) who applied this idea in his theory of intention-based social
preferences, we define
Kindness of contribution = )*+,-./01+234,+301563137-.809934.:*01+234,+3016-;37-.809934.:*01+234,+301563137-.809934.:*01+234,+301
10
Note that this comparison could not have been made based on VCM and INV and therefore goes beyond the
existing literature.
12
In terms of our notation, this measure is defined by (�� −min�)/(max� − min�). The
distribution of this kindness measure for first period actions (i.e. when decisions are not yet
blended with information about previous periods and group member behavior) are depicted in
Figure 2. While we demonstrated differences between INV and other treatments for the most
selfish and the most publicly oriented action, pairwise (nonparametric) two-sample exact
Kolmogorov-Smirnov tests of the distributions of the kindness measures cannot not reject the
null hypothesis of equality of the respective distributions.
The idea that actions has to be seen relative to the available action set is also consistent
with List (2007) and Bardsley (2008) who observe that ‘giving’ in dictator games is not the
same as ‘doing good’. Correspondingly, ‘taking’ (from a public good or directly from other
subjects) may not be readily interpreted as ‘doing harm’.11
Rather, when subjects compare
their actions to all feasible actions in situations that allow for taking, ‘doing good’ may simply
mean ‘not doing (too much) harm’.
4 Conclusion
The last decades have seen an enormous interest of economists in providing insights why
people give to public goods. A diverse and insightful public good game literature has emerged
that studies voluntary contributions to public goods. By mainly focusing on the giving
decision, the public good game literature has largely ignored a simple and obvious twist to
how individual actions may affect the provision of public goods: agents may not only engage
in giving, but may also choose actions that diminish the public good. Environmental amenities
serve as a prominent, yet not exclusive example.
In this paper we report findings from experiments that allow a direct comparison of the
impact of allowing takings to the provision of public goods. We study modifications of a
standard linear public good game that vary the initial provision level of the public good and
the degree to which agents may contribute to or degrade the public good.
We provide a number of interesting and important insights. First, if the action set only
allows for taking from an initially provided public good, the resulting provision level of the
public good is smaller than in any situation where agents can (also) contribute positive
amounts. Additionally, the share of agents who engage in the most selfish action is larger.
Secondly, fewer agents give positive amounts to the public good if they also hold the
11
This is at least true if there are no implicitly or explicitly defined formal or informal norms and rules.
13
opportunity to take from it. Extending the action space to taking from the public good
therefore has an important impact on its provision level.
Our findings add insights to the motives of agents to give. Our findings suggest that
explanations of giving based on warm glow theories may have to take the action space into
account as well: ‘doing good’ (and potentially generating a feeling of warm glow) depends on
the chosen action relative to the set of available actions. When agents can diminish or destroy
the public good, ‘doing good’ may just mean ‘not doing too much harm’.
Naturally, this paper can only provide initial insights into how and why individuals
contribute to or diminish the provision of public goods. It provides an interesting avenue for
future research. For a better understanding how to overcome social dilemmas, it is necessary
to both explore which institutions induce agents to provide public goods and which ones
discipline agents to refrain from exploiting them.
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16
Appendix A – Figures and Tables
Figure 1. Average contributions in INV, VCM, VCM* and VGT for all groups over all
periods.
Figure 2. Contributions relative to maxima in INV, VCM, VCM* and VGT, period 1 only.
0
2
4
6
8
10
12
14
16
18
20
1 2 3 4 5 6 7 8 9 10
Co
ntr
ibu
tio
n
Period
INV VGT VCM VCM*
010
20
30
40
010
20
30
40
0 .5 1 0 .5 1
INV VCM
VCM* VGT
Perc
ent
contribution_ratioGraphs by treatment
17
Table 1. Summary of experimental sessions.
Session Number of groups Number of participants Treatment
1 5 20 INV
2 6 24 VGT
3 5 20 VCM
4 6 24 INV
5 4 16 VGT
6 4 16 VCM
7 5 20 VCM*
8 5 20 VCM*
Note: Numbers of groups across treatments are not perfectly equal due to some registered subjects not showing
up.
Table 2. Summary statistics of VCM, VCM*, INV and VGT.
Statistic
First period All 10 periods (means)
VCM VCM* INV VGT VCM VCM* INV VGT
Mean
decision
11.75
(7.52)
6.25
(4.18)
-11.39
(7.80)
3.53
(7.55)
7.71
(7.69)
4.84
(4.42)
-15.56
(6.19)
-0.77
(7.87)
Mean
contribution
11.75
(7.52)
14.25
(4.18)
8.61
(7.80)
11.53
(7.55)
7.71
(7.69)
12.84
(4.42)
4.44
(6.19)
7.23
(7.87)
% of positive
contribution
88.89
100.00
63.64
80.00
66.11
100.00
47.27
54.75
Mean
contribution
conditional
on > 0
13.22
(6.62)
14.25
(4.18)
13.54
(5.28)
14.41
(5.36)
11.66
(6.59)
12.84
(4.42)
9.39
(5.89)
13.21
(5.83)
Note: Standard deviations for individual level data in parentheses.
18
Table 3. Results of test statistics for comparison of group contributions, all 10 periods.
(row vs. column comparison) Treatment
VCM VCM* INV
Treatment
VCM* >
(p = 0.0412)
INV <
(p = 0.0557)†
<
(p = 0.0001)
VGT = <
(p = 0.0012)
>
(p = 0.0411)
Note: All test statistics are (nonparametric) Mann Whitney tests except for INV vs. VCM. The table is to be read
row vs. column. For instance, group contributions are significantly greater in the VCM* compared to the VCM.
† The comparison of INV vs. VCM is done using a Welch t test because of unequal variances.
19
Table 4. Linear Regression of Contribution Levels of Treatments VCM, VCM*, INV and
VGT.
Dependent Variable: Contribution Level
Independent
Variables
(I)
All 10
periods
(II)
All 10
periods
(III)
All 10
periods
(IV)
Periods 1 to 5
(V)
Periods 6 to 10
VCM 3.270*
(1.813)
3.270*
(1.814)
3.745**
(1.842)
3.745**
(1.841)
2.795
(1.894)
VCM* 8.394***
(1.071)
8.394***
(1.072)
7.473***
(1.201)
7.473***
(1.200)
9.315***
(1.087)
VGT 2.789**
(1.236)
2.789**
(1.236)
3.193**
(1.513)
3.193**
(1.513)
2.385**
(1.145)
Period 6-10 -3.528***
(0.394)
-3.573***
(0.483)
Period 6-10_VCM -0.949
(0.884)
Period 6-10_VCM* 1.843**
(0.803)
Period 6-10_VGT -0.807
(1.039)
Constant 4.441***
(0.695)
6.205***
(0.745)
6.227***
(0.819)
6.227***
(0.819)
2.655***
(0.637)
Observations 1600 1600 1600 800 800
Individuals 160 160 160 160 160
Groups 40 40 40 40 40
Note: Random effects estimation clustered at group level; INV is the baseline. Standard errors in parentheses,
significance: *p < 0.10, **p < 0.05, ***p < 0.01.
20
Table 5. Percentage of decisions with (i) highest possible contribution (MaxPubl), (ii) the
least possible contribution (MaxSelf), (iii) transferring a positive amount to the public good in
VCM, VCM* and VGT, and percentage of groups with zero provision of the public good.
Statistic
First period All 10 periods (means)
VCM VCM* INV VGT VCM VCM* INV VGT
% of decisions
MaxPubl 33.33 25.00 20.45 25.00 16.66 18.25 4.77 11.25
% of decisions
MaxSelf 11.11 12.50 36.36 20.00 33.89 25.25 52.73 45.25
% of decisions with
positive giving 88.89 87.50 - 65.00 66.11 74.75 - 41.50
% of groups with
group account = 0 0.00 0.00 0.00 0.00 10.00 0.00 14.55 15.00
Table 6. Probit Regression of Giving a Positive Amount for Treatments VCM, VCM* and
VGT.
Dependent Variable:
Binary variable on whether a positive amount was given (yes = 1)
Independent Variables
(VI)
All 10 periods
(VII)
All 10 periods
VCM 1.005***
(0.305)
1.141***
(0.349)
VCM* 1.353***
(0.301)
1.537***
(0.345)
Period 6-10 -1.043***
(0.106)
Constant -0.319
(0.204)
0.162
(0.238)
Observations 1160 1160
Individuals 116 116
Groups 29 29
Note: Random effects estimation; VGT is the baseline. Standard errors in parentheses, significance: *p < 0.10,
**p < 0.05, ***p < 0.01.
21
Appendix B – Experimental Instructions
General Instructions for Participants
Welcome to the Experiment Laboratory!
You are now taking part in an economic experiment. You will be able to earn a considerable
amount of money, depending on your decisions and the decisions of others. It is therefore
important that you read these instructions carefully.
The instructions which we have distributed to you are solely for your private information. It is
prohibited to communicate with other participants during the experiment. Should you
have any questions please raise your hand and an experimenter will come to answer them. If
you violate this rule, we will have to exclude you from the experiment and from all payments.
During the experiment you will make decisions anonymously. Only the experimenter knows
your identity while your personal information is confidential and your decisions will not be
traceable to your identity.
In any case you will earn 4 Euros for participation in this experiment. The additional earnings
depend on your decisions. During the experiment your earnings will be calculated in tokens.
At the end of the experiment your earned tokens will be converted into Euros at the following
exchange rate:
1 Token = 0,30 €,
and they will be paid to you in cash.
The experiment consists of 10 periods in which you always play the same game. The
participants are divided into groups of 4. Hence, you will interact with 3 other participants.
The composition of the groups will remain the same for all 10 periods. Please mind that you
and all other participants decide anonymously. Therefore group members will not be
identifiable over the periods.
At the end of the experiments you will receive your earning from one out of the ten periods
converted in Euros (according to the exchange rate above) in addition to the 4 Euros for your
participation. The payout period will be determined randomly. You should therefore take the
decision in each period seriously, as it may be determined as the payout period.
The following pages describe the course of the experiment in detail.
22
Rules of the Game
Each player faces the same assignment. Your task (as well as the task of all others) is to
allocate tokens between your private account and a group account.
At the beginning of each period each participant receives 20 tokens in a private account. You
have to decide how many of these 20 tokens you transfer to a group account, and how many
you keep in your private account. Your transfer can be between 0 and 20 tokens (only whole
numbers).
[INV: At the beginning of each period there are 80 tokens in the group account and no
tokens in your private account. You have to decide how many of the 80 tokens you leave in
the group account and how many tokens you transfer to your private account. Your transfer
can be between 0 and 20 tokens (only whole numbers).]
[VGT: At the beginning of each period each participant receives 12 tokens in a private
account. There are 32 tokens in a group account. You have to decide how many of these 32
tokens you leave in the group account and how many of the 12 tokens you transfer from your
private account to the group account respectively. Your transfer input is related to the group
account, so that a negative input means a transfer from the group account to your private
account and positive inputs mean transfers from your private account to the group account.
Your transfer can be between -8 and 12 tokens (only whole numbers).]
[VCM*: At the beginning of each period each participant receives 12 tokens in a private
account. There are 32 tokens in a group account. You have to decide how many tokens you
transfer to the group account. Your transfer can be between 0 and 12 tokens (only whole
numbers).]
Your total income consists of two parts:
(1) the tokens which you have kept in your private account,
(2) the income from the group account. This income is calculated as follows:
[INV: (1) the tokens which you have transferred to your private account]
Your income from the group account =
0,4 times the total amount of tokens in the group account
Your income in tokens in a period hence amounts to
(20 - your transfer) + 0.4 *(total amount of tokens in the group account).
23
[INV: (transfer to the private account) + 0.4*(total amount of tokens in the group account)]
[VGT, VCM*: (12 – your transfer) + 0.4*(total amount of tokens in the group account)]
The income of each group member from the group account is calculated in the same way, this
means that each group member receives the same income from the group account. Suppose
the sum of transfers to the group account of all group members is 60 tokens. In this case each
member of the group receives an income from the group account of 0.4*60 = 24 tokens. If
you and your group members transfer a total amount of 9 tokens to the group account, then
you and all other group members receive an income of 0.4*9 = 3.6 tokens from the group
account. Every token that you keep in your private account yields 1 token of income to you.
[INV, VGT, VCM*: similar or same examples.]
24
Information on the Course of the Experiment
At the beginning of each period the following input screen is displayed:
The Input Screen:
The period number is displayed on the top left. The top right shows the time in seconds.
This is how much time is left to make a decision.
At the beginning of each period your endowment contains 20 tokens (as described above).
You decide about your transfer to the group account by typing a whole number between 0 and
20 into the input window. You can click on it by using the mouse.
[INV: At the beginning of each period the group account contains 80 tokens. You decide
about your transfer to your private account by typing a whole number between 0 and 20 into
the input window. You can click on it by using the mouse.]
[VGT: At the beginning of each period the group account contains 32 tokens. You decide
about your transfer to your private account or your transfer to the group account by typing a
whole number between -8 and 12 into the input window. You can click on it by using the
mouse.]
25
[VCM*: At the beginning of each period the group account contains 32 tokens. You decide
about your transfer to the group account by typing a whole number between 0 and 12 into the
input window. You can click on it by using the mouse.]
When you have decided about your transfer to the group account, you have also chosen how
many tokens you keep to yourself, that is (20 - your transfer) tokens [differs by treatment].
When you have typed in your decision, you need to press the Enter Button (by use of the
mouse). By pressing the Enter Button your decision for the period is final and you cannot go
back.
After all group members have made their decisions, your income from the period will be
displayed on the following income screen. You will see the sum of transfers to the group
account and your income from your private account. You will also see your total income in
that period.
The Income Screen:
As described above, your income is
(20 – your transfer) + 0,4*(total amount of tokens in the group account).
[INV: (transfer to the private account) + 0.4*(total amount of tokens in the group account)]
[VGT, VCM*: (12 – your transfer) + 0.4*(total amount of tokens in the group account)]
Good luck in the experiment!