Leading by example in a public goods experiment with benefit heterogeneity

Abstract

Social dilemmas such as greenhouse gas emission reduction are often characterized by heterogeneity in benefits from solving the dilemma. How should leadership of group members be organized in such a setting? We implement a laboratory public goods experiment with heterogeneous marginal per capita returns from the public good and leading by example that is either implemented exogenously or by self-selection. Our results suggest that both ways of implementing leadership only have small effects on contributions to the public good. Self-selected leaders—in particular self-selected low-benefit leaders—tend to set better examples than imposed leaders, but they are also exploited more strongly by followers. Leaders seem to need additional instruments to be more effective when benefits are heterogeneous.

Full text

Vol.:(0123456789)
Social Choice and Welfare (2023) 61:685–712
https://doi.org/10.1007/s00355-023-01459-1
1 3
ORIGINAL PAPER
Leading byexample inapublic goods experiment
withbenefit heterogeneity
JingYu1,2· MartinG.Kocher3,4
Received: 8 July 2021 / Accepted: 10 April 2023 / Published online: 22 June 2023
© The Author(s) 2023
Abstract
Social dilemmas such as greenhouse gas emission reduction are often characterized
by heterogeneity in benefits from solving the dilemma. How should leadership of
group members be organized in such a setting? We implement a laboratory public
goods experiment with heterogeneous marginal per capita returns from the public
good and leading by example that is either implemented exogenously or by self-
selection. Our results suggest that both ways of implementing leadership only have
small effects on contributions to the public good. Self-selected leaders—in particu-
lar self-selected low-benefit leaders—tend to set better examples than imposed lead-
ers, but they are also exploited more strongly by followers. Leaders seem to need
additional instruments to be more effective when benefits are heterogeneous.
JEL Classification C91· D03· D64
Financial support from the Ideenfonds of the University of Munich (financed through the excellence
initiative) and the Economics Department of the University of Munich is gratefully acknowledged.
We are grateful for many comments and suggestions at seminars, workshops and conferences,
including very helpful remarks by Marie Claire Villeval in the context of a formal discussion of our
paper, as well as by Lata Gangadharan and Jingjing Zhang.
* Martin G. Kocher
martin.kocher@univie.ac.at
Jing Yu
yj0787@googlemail.com
1 Department ofManagement andEconomics, Beijing Institute ofTechnology, Beijing, China
2 Department ofEconomics, University ofMunich, Geschwister-Scholl-Platz 1, 80539Munich,
Germany
3 Department ofEconomics, University ofVienna, Oskar-Morgenstern-Platz 1, 1090Vienna,
Austria
4 Department ofEconomics, University ofGothenburg, Gothenburg, Sweden
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1 Introduction
Social dilemma situations in which the collective interest is at odds with private
interests are widespread. Cooperation among decision makers leads to the Pareto
optimum, but free riding is a dominant strategy and results in a Pareto inferior out-
come. In this paper we analyze a specific social dilemma that involves different ben-
efits from cooperation to different types of players (benefit heterogeneity) and that
introduces leadership (leading by example) either by appointment (exogenous lead-
ership) or by self-selection through volunteering or voting (endogenous leadership).
Our results have implications for public goods provision with heterogeneous ben-
efits. Team work is a relevant example, with a team output that is a public good, and
with sometimes different benefits from this public good by different team members,
depending on the contractual situation. Leading by example seems to be important
in many cases. Take, for instance, an academic project that leads to a paper. Some-
body whose tenure clock is ticking has different benefits from a joint project than
somebody who has just received tenure. On a more global scale, greenhouse gas
emission reduction as a global public good involves both heterogeneous benefits and
the necessity of leading by example. Countries clearly have different benefits from
CO2 abatement investments. Similarly, the global coordination problem will require
countries or specific regions to take first steps and “lead by example”, because all
countries will never be aligned in climate policies. Our results, in a nutshell, seem to
indicate that it requires additional instruments such as coercion power, sanctioning
institutions, or communication to make leading by example work under benefit het-
erogeneity, regardless of whether leaders are appointed or volunteer.
Economists have analyzed social dilemmas in the context of public goods pro-
vision. In the experimental laboratory, the simultaneous linear public goods game
(also known as the voluntary contribution mechanism) has been the main workhorse
to study cooperation empirically (Isaac etal. 1985; Ledyard 1995; Chaudhuri 2011).
A general finding from economic experiments on the simultaneous public goods
game is that decision makers are willing to cooperate, i.e. willing to contribute vol-
untarily to the public good, but that cooperation declines over time unless there is an
enforcement mechanism such as peer punishment.
Leading by example turns the simultaneous linear public goods game (partly)
into a sequential game, without changing incentives or enforcement possibilities.
The first-mover can set an example with her contribution, but has no other means
of coercion. Many existing experimental results indicate that leading by example
leads to higher levels of contributions (Dannenberg 2015; Güth etal. 2007; Moxnes
and van der Heijden 2003; Pogrebna etal. 2011; Rivas and Sutter 2011). However,
there are also several studies reporting weak and non-significant leadership effects
(Gächter and Renner 2018; Gürerk etal. 2018; Haigner and Wakolbinger 2010; Jack
and Recalde 2015; Potters etal. 2007; Sahin etal. 2015).1 Regardless of finding an
average effect on contributions or not, almost all studies show that there is a positive
correlation between leaders’ and followers’ contributions.
1 Cartwright etal. (2013) explore the effect of leading by example in a weakest-link game and report a
limited effect of both exogenous and endogenous leading by example in increasing coordination.
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Leading byexample inapublic goods experiment withbenefit…
Heterogeneity of group members—though common outside the experimental labo-
ratory—is often not considered explicitly in experiments. The general gist of the exist-
ing results is that heterogeneity tends to lead to less cooperation. If group members
have other-regarding or pro-social concerns, they have to coordinate on cooperating,
respectively on the level of cooperation; heterogeneity makes coordination more dif-
ficult. Existing studies finding negative effects of heterogeneity or null effects have,
for instance, looked at heterogeneity in endowments (Buckley and Croson 2006; Chan
et al. 1999; Charness et al. 2014; Cherry et al. 2005; Ostrom et al. 1994; Reuben
and Riedl 2013), heterogeneity in benefits through different returns from the public
good (Fischbacher etal. 2014; Fisher etal. 1994; Kube etal. 2015; Reuben and Riedl
2013), heterogeneity in the source of endowment (earned endowment versus allocated
endowment; Oxoby and Spraggon 2013), and heterogeneity from other observable
characteristics such as religion, ethnic affiliation, nationality, or other identities (e.g.,
Chen etal. 2014; Habyarimana etal. 2007).
The current paper combines benefit heterogeneity and leading by example. We
are particularly interested in populations with benefit heterogeneity, not only because
this type of heterogeneity is ubiquitous outside the experimental laboratory, but also
considering that the normative conflict associated with benefit heterogeneity is dif-
ficult to be resolved. Previous studies have shown that, when people obtain differ-
ent benefits from the public good, there is a normative conflict between contribu-
tion equality and payoff equality. Specifically, high-benefit group members consider
equal contributions of all group members as the social norm, whereas low-benefit
group members try to enforce the norm that all group members earn the same. Hith-
erto it is unclear, however, whether leading by example helps promoting cooperation
under normative conflict caused by benefit heterogeneity.
In our laboratory experiment, groups of four members can contribute to a linear
public good. Two group members have a higher return rate from the public goods
than the other two, but it is still a dominant strategy for all group members to con-
tribute nothing to the public good, i.e. to free-ride. Four treatments allow us to study
the effects of leadership by example. We implement two treatments in which either
one randomly selected low-benefit member or one randomly selected high-benefit
member contributes first, and her contribution level is communicated to the other
three members that then contribute simultaneously. A baseline treatment requires
all four members to contribute simultaneously. We introduce a fourth treatment that
allows all members to volunteer for leadership. It changes the exogenous assignment
of leadership by example to an endogenous assignment (choice) by self-selected
leaders.
We are the first to implement an experiment with leadership by example by group
members with benefit heterogeneity using a linear public goods setting. There is a
nascent literature in experimental economics that looks at heterogeneity, more gen-
erally, in social dilemmas with leaders. For instance, heterogeneity in endowments
(Levati etal. 2007; Neitzel and Sääksvuori 2013), heterogeneity from different iden-
tities (Drouvelis and Nosenzo 2013), heterogeneity in the length of group member-
ship (Angelova etal. 2019), heterogeneity in religions (Keuschnigg and Schikora
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2014), and heterogeneity in opportunity costs (Au and Chung 2007; Collins 2016;
Dasgupta and Orman 2013) have been considered in different studies.2
Levati etal. (2007) find that leading by example works effectively in heterogene-
ous endowment populations if all group members rotate in the leader’s role, whereas
Neitzel and Sääksvuori (2013) do not find such a positive effect with a fixed group
member being the leader in repeated interaction. Drouvelis and Nosenzo (2013)
show that group members having the same group identity fosters the effectiveness
of leading by example, whereas Keuschnigg and Schikora (2014) and Angelova
etal. (2019) find that leading by example is likely to reduce cooperation in cultur-
ally diverse populations and in communities with group members of different group
membership tenures, respectively. Au and Chung (2007), Collins (2016) and Das-
gupta and Orman (2013) investigate heterogeneous opportunity costs of contrib-
uting. They report evidence that contributions are higher when subjects with low
opportunity costs/higher efficacy contribute first compared to when subjects with
high opportunity costs/lower efficacy contribute first.3
Ananyev (2019) concurrently developed a similar setup for leading by example
with heterogeneous benefits. He finds that leading by example does not promote
cooperation with heterogeneous benefits, which is in line with our results. He also
implements a voting treatment, in which voters can determine the benefit level, i.e.
the type, of the leader, but not the leader herself, and most voters prefer the high
benefit type to become leader. In contrast, our endogenous treatment is based on
volunteering for leadership.
Our treatment with self-selected leaders also adds to the literature on endogenous
leadership (e.g., Arbak and Villeval 2013; Bruttel and Fischbacher 2013; Cappelen
etal. 2016; Dannenberg 2015; Haigner and Wakolbinger 2010; Préget etal. 2016;
Rivas and Sutter 2011). In general, there is a tendency that self-selected or endoge-
nous leadership works more effectively than assigned leadership, but details matter.4
Our study also contributes to the experimental work studying the effect of vari-
ous mechanisms on cooperation in groups with benefit heterogeneity. Punishment
or reward are found to be less effective in increasing contributions in heterogeneous
groups than in homogeneous groups, and have no or limited impact on group effi-
ciency in heterogeneous groups (Gangadharan etal. 2017; Kölle 2015; Nikiforakis
etal. 2012; Reuben and Riedl 2009, 2013). Among these studies, Gangadharan etal.
(2017) show that on top of the reward or punishment effect, communication has a
positive impact on contributions and group efficiency, but the effects are still smaller
than in a homogenous benefit environment. It seems that normative conflict has a
3 Notice that our setting of heterogeneous benefits is different from heterogeneous opportunity costs. In
our setting, the marginal costs of contributing are the same for all group members, but the benefits from
the group project varies.
4 Apart from leading by example, other implementations of sequential public good provisions have been
analyzed in the experimental laboratory (see, for instance, Gächter etal. 2010; Nosenzo etal. 2011; Pot-
ters etal. 2005).
2 The experiment in Glöckner etal. (2011) shows that followers respond to leaders more strongly when
contributing is not a dominant strategy for leaders. Similar evidence is provided by Cappelen et al.
(2016) and van der Heijden etal. (2013), who suggest that leaders’ influence on followers is weak when
leaders get a high compensation for leading or have no cost of setting good examples.
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Leading byexample inapublic goods experiment withbenefit…
negative impact on group efficiency and undermines the power of otherwise effec-
tive mechanisms in promoting cooperation.
The findings from our experiment suggest a limited effect of leadership by exam-
ple with heterogeneous benefits. With exogenously imposed leadership, we observe
a significantly slower decline in contributions relative to the baseline. However, our
baseline treatment and the two treatments with exogenous leadership do not differ
statistically in terms of average contribution levels, irrespective of whether a high-
benefit member or a low-benefit member is the leader. When subjects are given
the opportunity to self-select into the role of leader, contributions are significantly
higher with self-selected leadership than without. Self-selected leadership, in par-
ticular self-selected low-benefit leadership, can also raise contributions significantly
over the baseline level. However, we do not observe a high enough willingness to
lead for high-benefit members, and the willingness for low-benefit members to lead
is decreasing quickly over time. This trend, combined with the fact that contribu-
tions are at a low level when nobody in the group volunteers to be the leader, weak-
ens, on average over all groups, the positive effect otherwise brought about by self-
selected leadership. Consequently, there is only a slight increase in contributions, on
average, in the endogenous leadership treatment over the baseline level.
Our data reveal that imperfect conditional cooperation by followers, i.e. contrib-
uting less than leaders that set good examples, combined with conflicts about the
social norm regarding the “adequate” contribution level within heterogeneous group,
hampers the effectiveness of leading by example. The conflicts are reflected in the
conditional cooperation pattern of followers. Followers whose benefits are different
from the leader try to reciprocate according to their perceived contribution norm:
when led by high-benefit leaders, low-benefit followers reciprocate on a lower level
than high-benefit followers; when led by low-benefit leaders, high-benefit follow-
ers reciprocate similarly as low-benefit followers. As a consequence, setting good
examples does not yield higher profits for low-benefit leaders, but rather makes them
suffer from a larger income inequality to their disadvantage; they thereby quickly
decrease their contributions when in the role of leaders or refrain from becoming
leaders in later periods. For high-benefit leaders, even though, on average, it pays for
them to contribute more, we do not observe high enough leader contributions or a
widespread willingness to become leader. Apart from the influence of social prefer-
ence, pessimistic beliefs and the fear of losing out because of insufficient follower
contributions seem to constitute major reasons for low contributions and the missing
willingness to volunteer for leadership.
Our design also allows us to compare self-selected leadership with imposed
leadership. The findings show that self-selected leaders—in particular low-benefit
leaders—indeed set better examples than imposed leaders. However, compared to
imposed leaders, self-selected leaders are exploited more strongly by followers—
particularly by those whose benefit type is different from the leader. In consequence,
we only observe a slight increase in average contributions of early periods when
low-benefit leaders go from being imposed to being self-selected. Moreover, we
do not find evidence that high-benefit leadership is more effective than low-benefit
leadership. If anything, contributions with self-selected low-benefit leaders are on
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J.Yu, M.G.Kocher
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average higher than contributions with self-selected high-benefit leaders in the short
run.
The remainder of the paper is organized as follows. Section2 describes the design
and procedures of the experiment. Section3 presents the main results, and Sect.4
provides concluding remarks.
2 Experimental design, procedures, andtheoretical expectations
2.1 Experimental design andprocedures
Our basic game is a four-person linear public goods game that is repeated for ten
periods in fixed groups. In each period, each of the four group members receives an
endowment of 20 tokens and is asked to decide about how many tokens to contrib-
ute to a group account. The tokens not contributed remain in one’s private account.
Each group member’s contribution to the group account in period t,
Cit
, must satisfy
0 ≤
Cit
≤ 20. The payoff function for an individual i in period t is
Among the four group members, two subjects are randomly selected to be of type
A (low-benefit members) and two of type B (high-benefit members).5 The marginal
per-capita return from the public account (
𝛽i
) is set at 0.4 for members of type A and
0.8 for members of type B. That is, each token a subject keeps in her private account
is worth 1 point to her, regardless of her type; in addition, she earns 0.4 points for
each token all group members (including herself) contribute to the group account
if she is of type A, while she earns 0.8 points for each token she or any other group
member contributes to the group account if she is of type B. At the beginning of
the first period, each group member is randomly assigned an ID from 1 to 4. They
learn their own types and IDs (that remain the same throughout the experiment).
Design details are described in the experimental instructions, and by reading them
aloud at the beginning of the experiment they are made common knowledge to all
participants.
We implement the following four treatments in a between-subject design: (1)
Baseline (BASE): All 4 group members make private contribution decisions simul-
taneously. (2) Exogenous high-benefit leader (HBL): One high-benefit member is
randomly selected in each period as the leader. The leader contributes first, and the
other three members contribute simultaneously, after receiving information about
the leader’s contribution. (3) Exogenous low-benefit leader (LBL): Similar as HBL,
except that the leader is randomly chosen from the two low-benefit members in
each period. (4) Endogenous leader (EN): In each period, all members could choose
𝜋
it =20 −Cit +𝛽i×
∑4
i=1
C
it
5 We use neutral language in the experimental instructions so as not to bias decisions. For convenience,
players of type A are referred to as low-benefit members, and players of type B are referred to as high-
benefit members in this paper.
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whether they want to become leader or not. If none of the four members chooses
to become leader in a given period, the four group members contribute simultane-
ously and privately in that period, just like in BASE; if there is only one member
who chooses to become leader in a period, this member makes her contribution
decision before the other three group members, just as in HBL or LBL (depending
on the type of the volunteer); if there are at least two members who are willing to
become leader, a random draw determines the actual first mover in that period. After
their choice regarding contributing first, those subjects who have volunteered learn
whether they are leader for the given period. For those who have volunteered but are
not chosen as leader, they obviously learn implicitly that they are not the only group
member to volunteer.
We follow Gächter and Renner (2010) in how beliefs are elicited. Beliefs are elic-
ited in each period of the game, after subjects have made their contribution deci-
sions. Specifically, in the baseline treatment, we ask participants to estimate the
average of the other players’ contributions within their group, for each type sepa-
rately. In the leadership treatments, we ask the leader about her estimate of how
many tokens the two different-type followers would contribute on average, and how
many tokens the other same-type follower would contribute; each follower needs to
submit her estimate of the other followers’ average contribution, for each type sepa-
rately, after having seen the leader’s contribution. For subjects who are requested to
submit two estimates in a period, one estimate is randomly selected to count for their
earning. If the belief is correct, the subject receives an additional 3 points; if the
belief differs by 1(2) points, the subject receives 2(1) points; in all other cases, the
subject receives nothing from the estimate.
At the end of each period, subjects get feedback including each group member’s
type, contribution to the group account, income (excluding earnings from estimates)
and identity within the group in leadership treatments (i.e. whether one is first mover
or not). They are also informed about their own income from the estimates. Every
period of play counts towards final earnings.
After the ten periods, all treatments are followed by a monetarily incentivized
social value orientation questionnaire, known as the ring test (Liebrand 1984;
Liebrand and McClintock 1988). Subjects have to make binary choices in 24 dif-
ferent allocation tasks. In each task, a subject has to choose among two allocations
that allocate money to herself and another anonymous recipient. All 24 decisions are
paid and the pairing is fixed throughout this part. By adding up the subject’s 24 deci-
sions, we obtain the total sum of money allocated to herself (x-amount) and to the
recipient (y-amount). The subject’s social value orientation is calculated as the angle
of the vector
θ
that results from the ratio x/y. Based on the ratio x/y, one can assign
each subject to one of eight categories of social orientation (individualism, altruism,
cooperation, competition, martyrdom, masochism, sadomasochism, and aggression).
A more accurate measure of social value orientation is the exact angle
θ
, positive in
the first quadrant and negative in the fourth quadrant. Almost all subject ratios lie in
these two quadrants: thus, the larger this angle, the more pro-social the subject. We
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J.Yu, M.G.Kocher
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will use this measure in our analysis.6 From the 24 decisions, one can also measure
a subject’s consistency in making allocation choices. The length of the vector can
serve as the consistency measure: it is equal to 30 if a subject makes 24 consistent
choices and 0 if the choices are perfectly random. The longer the vector, the more
consistent are a subject’s decisions. When using the data from the social value orien-
tation test, we consider only subjects with a consistency measure of at least 50%.7 At
the end of the experiment, subjects learn their total income from the main part of the
experiment and from the ring test.
The experiment was conducted in the MELESSA laboratory at the University of
Munich in May 2014 and September 2015. A total of 236 subjects were recruited via
ORSEE (Greiner 2015). Subjects remained anonymous throughout the experiment,
and cash payments were made privately. The experiment was programmed and con-
ducted with the software z-Tree (Fischbacher 2007). We conducted two sessions
for each of the treatments BASE, HBL and LBL, and four sessions for treatment
EN, with 24 subjects in each session.8 At the beginning of each session, subjects
received the instructions for the public goods game. The instructions for the ring test
were handed out to subjects after the end of the main part. However, subjects knew
that there would be a second part after the ten periods of the main part and that it
would be unrelated to the first part. Instructions were written in neutral language,
avoiding terms such as “leader”, “follower”, etc. In order to test the understanding
of the rules and the incentive structure subjects were asked to answer control ques-
tions after reading the instructions aloud. The experiment did not proceed until all
subjects had answered all questions correctly. Sessions lasted, on average, for about
75min, and subjects earned approximately €13.7, on average.
2.2 Theoretical expectations
Obviously, leadership does not change the standard prediction of zero contribu-
tions based on dominant strategies in the public goods games. We know, however,
that decision makers contribute voluntarily to the public good, and that leading by
7 There is no standard with regard to the threshold for the consistency measure. While van Dijk etal.
(2002) uses a threshold of 60%, Brosig (2002) classifies all subjects with a consistency measure of at
least 25%. Following Sutter etal. (2010), we use an intermediate threshold of 50%. In our data, only
seven subjects do not meet this threshold. Note that relaxing this restriction by shifting the threshold
downwards (even including all subjects into the analysis, irrespective of their consistency score) or
upwards to 60% does not change any of the results.
8 There are 20 subjects in the second session of treatment HBL due to an insufficient number of subjects
showing up.
6 One may wonder whether subjects’ decisions in the social value orientation test are affected by their
experience in the public goods game. However, we believe this should not be a concern for our data
analysis. First, the recipient is randomly chosen from all other subjects in the session and is thus not
necessarily one of the former group members from the public goods game. Second, there is evidence that
experiencing a public goods game does not significantly affect subjects’ social/cooperative preferences
(Ackermann etal. 2019; Fischbacher and Gächter 2010). Third, the ratio from the social value orienta-
tion test is anyway only an auxiliary variable in our analysis.
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Leading byexample inapublic goods experiment withbenefit…
example has the potential of increasing contribution levels in comparison to simulta-
neous contribution decisions, although the observed effects depend on details of the
setup.
Our first set of research question pertains to leadership effects. Does leader-
ship increase overall contribution levels even in presence of heterogeneous ben-
efits from the public good? Does the effectiveness of leadership depend on the
leader type, i.e. whether a low-benefit member becomes the leader or whether it
is a high-benefit member? On the one hand, heterogeneity might make signaling
by leaders and coordination among group members more difficult. On the other
hand, the leadership signal might be stronger, particularly when it comes from the
low-benefit member.
Our second set of research questions pertains to the process of how leadership
is determined. We compare exogenously assigned leadership and self-selected lead-
ership. Do self-selected leaders contribute more than leaders that are exogenously
assigned? Are high-benefit members or low-benefit members more likely to volun-
teer as leaders? We know from previous research that self-selected leadership has
the potential to be more effective than assigned leadership. Whether there are differ-
ent inclinations to volunteer for different benefit types, is an exploratory question.
It could well be that groups realize that high-benefit leaders are more effective and
thus self-select more often; however, a similar argument could be made for low-
benefit members, whose signaling leverage is perhaps larger.
Given that standard models with other-regarding preferences or reciprocal con-
cerns do not yield unambiguous predictions for our setup, we think that it is best to
formulate theoretical expectations based on the tendencies in related existing stud-
ies. Our main hypotheses are:
H.1: Leadership—regardless of whether by low-benefit or high-benefit mem-
bers—increases contribution levels, even in the presence of benefit heterogeneity,
compared to simultaneous contributions decisions.
H.2: Endogenous (self-selected) leadership increases contribution levels over
exogenously assigned leadership, regardless of whether by low-benefit or high-ben-
efit members.
H.3: High-benefit members have more ressources for effective leadership and are
thus more effective than low-benefit members in fostering cooperation and raising
average contribution levels.
3 Experimental results
We organize the presentation of our results in the following way. Section3.1 com-
pares average contributions across the treatments and situations. It provides tests of
the three hypotheses in Sect.2.2. The remaining analysis is more exploratory. In
Sect.3.2, we investigate the structure and determinants of self-selected leadership.
Section3.3 studies contribution behavior of leaders and followers. Unless specified
differently, the non-parametric tests are two-sided Mann–Whitney rank sum tests,
with each group as a statistically strictly independent observation.
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694
J.Yu, M.G.Kocher
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3.1 Treatment differences
The upper panel of Table1 and the left panel of Fig.1 give an overview of the aver-
age contributions by treatment over time.9 Contributions start out at about 50% of
the total endowment in all treatments and decrease over time in varying degrees.
We first compare contributions in the two exogenous leadership treatments with
those in the baseline treatment. Subjects in BASE contribute, on average, 7.2 points,
which corresponds to 36% of their endowment. Average contributions are slightly
higher in HBL (9.17) and in LBL (8.21), but the differences are not significant (both
p > 0.35).10
As the right panel of Fig.1 indicates, there are three possible states of the world
in EN: (1) the actual leader is a high-benefit member (which we will refer to as
EN_HBL), (2) the actual leader is a low-benefit member (EN_LBL), and (3) nobody
volunteers, hence the group has no leader (EN_NL). Using a two-sided Wilcoxon
signed-rank test by including only those groups that experienced at least two of
these states, we find that, relative to the situation without self-selected leaders, aver-
age contributions are significantly higher with self-selected leaders, irrespective of
the leader type (4.61 in EN_NL vs. 9.24 in EN_HBL, p < 0.001, N = 21; 4.83 in
EN_NL vs. 11.43 in EN_LBL, p < 0.001, N = 18).
We next compare contributions in the three states of EN (as shown in the lower
panel of Table 1), to contributions in BASE. It turns out that average contribu-
tions with self-selected leadership (EN_HBL + EN_LBL) are significantly higher
than those in BASE (9.73 vs. 7.20, p < 0.05, N = 36).11 However, average contribu-
tions in EN_NL are significantly lower than those in BASE (4.61 vs. 7.20, p < 0.01,
N = 33).12 As we will analyze in greater detail in Sect. 3.2, the state of no self-
selected leadership occurs 26% of the time. The negative effect on contributions
without self-selected leadership countervails the positive effect brought by self-
selected leadership, leading to an insignificant difference in contributions between
the endogenous treatment (aggregating over the periods with and without self-
selected leaders) and the baseline treatment (8.38 vs. 7.2, p = 0.5).13
9 FiguresA1–A4 present the evolution of contributions by group for each treatment.
10 Only when we pool the two exogenous leadership treatments, we observe a marginally significant dif-
ference in average contributions with the baseline treatment in the last five periods (p < 0.1, N = 35).
11 Contributions are significantly higher in EN_LBL than in BASE (p < 0.01). They are also higher in
EN_HBL than in BASE, but the difference is not significant at conventional levels (p = 0.12).
12 This result is in line with previous studies showing that the failure to endogenously implement an
institution has a negative effect on voluntary contributions (see the survey by Dannenberg and Gallier
2020).
13 We have set our sample size such that it is comparable to related papers in the literature. Nonetheless,
it is helpful to give an indication of the statistical power that we operate with. Knowing that this is not
the perfect way to do it,an ex-post power calculation using a two-sided Mann–Whitney rank sum test
shows that if power is set to 80% and the significance level is set to 5%, we would need a much larger
sample size to detect significant difference between treatments (for instance, 63 groups per treatment for
HBL vs. BASE; for other non-significant comparisons of main treatment effects, the numbers are even
much higher). In other words, the economic magnitudes of the insignificant treatment differences that we
detect are small.
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Does the benefit type of the leader matter for contributions? In contrast to our
prediction, there is no significant difference in contributions between the two exog-
enous leadership treatments (p = 0.71). This is in contrast to existing findings that
groups are more cooperative when assigning the advantageous types (e.g., more pro-
ductive) as first movers (Au and Chung 2007; Collins 2016; Dasgupta and Orman
2013). In our case, when leadership is assigned endogenously, low-benefit leader-
ship seems to be more effective than high-benefit leadership, at least in the early
periods (12.49 in EN_LBL vs. 10.22 in EN_HBL in the first five periods, p < 0.01,
N = 18; 7.89 in EN_LBL vs. 7.63 in EN_HBL in the final five periods, p = 0.68,
N = 10).
Table 1 Average contributions
by treatment and by state in EN
Standard deviations based on group averages in parentheses
Periods 1–10 Periods 1–5 Periods 6–10
BASE 7.2 (1.91) 8.89 (1.49) 5.5 (2.7)
HBL 9.17 (4.76) 10.01 (4.74) 8.32 (5.08)
LBL 8.21 (3.28) 9.0 (2.71) 7.42 (4.45)
EN 8.38 (3.16) 9.71 (3.62) 7.04 (3.55)
EN_NL 4.61 (3.33) 6.99 (4.43) 3.87 (3.28)
EN_HBL 9.12 (3.48) 9.99 (3.67) 7.42 (3.69)
EN_LBL 11.18 (3.32) 11.64 (4.10) 9.62 (4.97)
Fig. 1 Average contributions by treatment (left) and by state in EN (right) over time
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Does self-selected leadership yield higher contributions than imposed leadership?
This does not seem to be case under high-benefit leadership (9.12 in EN_HBL vs.
9.17 in HBL, p = 0.72, N = 35). Relative to imposed low-benefit leadership, self-
selected low-benefit leadership seems to be more effective, yet, the difference is sig-
nificant only in the early periods (11.64 in EN_LBL vs. 9.0 in LBL in the first five
periods, p = 0.05, N = 33; 9.62 in EN_LBL vs. 7.42 in LBL in the final five periods,
p = 0.22, N = 26).
Table2 reports results for a random effects regression of individual contributions
across treatments (and states). Model (1) only includes the four treatment dummies
as independent variables, and it confirms the non-parametric results from above. In
Model (2), we further split the treatment dummy “EN” into three state dummies.
Both the coefficients of “EN_HBL” and “EN_LBL” are positive and significant,
indicating that contributions with self-selected leaders are significantly higher than
the baseline level, regardless of the leader type. The significantly negative coeffi-
cient of “EN_NL” clearly reflects the drawback in EN: when nobody is willing to
take the lead and all group members contribute simultaneously, contributions are
significantly lower than in BASE.14
Models (3) to (6) add controls for individual social preference using subjects’
ring test scores, which allow us to identify—at least tentatively—whether some of
the significant effects found in the non-parametric analysis, i.e. those that compare
exogenous with self-selected roles, are due to pure self-selection effects. The time
trend is also included. In Model (3) the coefficient of the treatment dummy “EN”
becomes significant at the 5%-level. There is no significant difference in contribu-
tions between “HBL” and “LBL” (p = 0.73, Wald test). We thus pool the two exog-
enous leadership treatments in Model (4). In line with the non-parametric results,
there is a significant increase in contributions in the pooled exogenous leadership
treatments as compared to the baseline treatment.15 However, given the small mag-
nitude of the coefficients “EXO_L (HBL/LBL)” and “EN”, both ways of imple-
menting leading by example seem to have only a limited effect in promoting con-
tributions. Model (5) further shows that the small effect of the pooled exogenous
leadership treatments is mainly driven by a significantly slower decay in contribu-
tions.16 Model (6), where we add control variables on top of Model (2), shows that
our main results are robust. We summarize ourmain findings so far:
Result 1a: (RELATED TO H.1) When leaders are assigned exogenously, neither
type of leadership has a significant influence on contributions, albeit we observe a
14 Further comparisons between the three state dummies confirm that self-selected leadership sig-
nificantly increases contributions relative to EN_NL (p < 0.0001, Wald test). Self-selected low-benefit
leaders are more effective in raising contributions than high-benefit members in the first five periods
(p = 0.01, Wald test). Moreover, we confirm that self-selected low-benefit leadership generates higher
contribution levels than imposed low-benefit leadership in the first five periods (p = 0.05, Wald test),
whereas self-selected high-benefit leadership is similarly effective as imposed high-benefit leadership
(p = 0.98, Wald test).
15 Note that with some other consistency thresholds for the ring test scores, the significance levels of
both the treatment EN and the pooled exogenous leadership treatments is reduced to 10%.
16 The slower decay is observed in both HBL and LBL, although the difference in LBL is not significant
at conventional levels (p < 0.05 for HBL vs. BASE; p < 0.12 for LBL vs. BASE).
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significantly slower decay in contributions in the exogenous leadership treatments
than in BASE.
Result 1b: (RELATED TO H.1) When subjects are given the choice to self-select
into leadership, contributions are significantly higher with self-selected leaders than
when nobody volunteers. Contributions with self-selected leaders, in particular self-
selected low-benefit leaders, are also significantly higher than those in BASE; how-
ever, total contributions are only slightly higher in EN than in BASE, due to the cost
of failed leadership implementation in terms of low contributions in such cases.
Result 2: (RELATED TO H.2) While contributions with self-selected and
imposed high-benefit leaders are similar, contributions with self-selected low-benefit
leaders are slightly higher than those with imposed low-benefit leaders, particularly
in early periods.
Result 3: (RELATED TO H.3) When leadership is randomly imposed, the lead-
er’s benefit type has no significant influence on contributions. When leadership is
self-selected, low-benefit leaders contribute more than high-benefit leaders, particu-
larly in early periods.
3.2 Structure anddeterminants ofself‑selected leadership
So far, our results have indicated the positive effect of self-selected leadership and
the cost of failed leadership implementation. Under benefit heterogeneity, does self-
selected leadership become more frequent over time? Are high-benefit members or
low-benefit members more likely to volunteer as leaders? What determines subjects’
volunteering decisions? In this section, we analyze the structure and determinants of
self-selected leadership in treatment EN.
Overall, leadership is implemented 74% of the time. Broken down, 46% of the
time the group has a self-selected high-benefit leader and 28% of the time a self-
selected low-benefit leader. The left panel of Fig.2 plots the frequencies of the three
possible states in EN over time.17 We observe that each type of self-selected leader-
ship occurs over 40% of the time in the first period. While the instances of EN_HBL
remain fairly stable over time, the instances of EN_LBL decrease (Spearman’s
ρ
=
−0.21, p < 0.01 for EN_LBL, and Spearman’s
ρ
= −0.02, p = 0.74 for EN_HBL).18
Towards the end, EN_NL takes up about 50% of the cases. Apparently, self-selected
leadership occurs less frequently in our heterogenous groups than in homogenous
groups in previous studies (Rivas and Sutter 2011; Préget etal. 2016).19
The dynamics of states is consistent with subjects’ volunteering patterns. As
shown in the right panel of Fig.2, 33% of low-benefit members want to be the first
mover in the first period, and this proportion is decreasing over time (Spearman’s
ρ
= − 0.25, p < 0.001), whereas the proportion of high-benefit volunteers fluctu-
ates around 40% over the entire experiment. High-benefit members, on average,
17 TableA1 in the appendix reports the number of observations in each possible state of EN by period.
18 All Spearman tests, using the time trend as one of the variables are based on group-level averages per
period; other Spearman tests are based on group-level averages over all periods.
19 Similar to our study, group membership remains fixed over time in both Rivas and Sutter (2011) and
Préget etal. (2016).
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volunteer to be the leader more often than low-benefit members (39.4% vs 22.7%,
p = 0.01, two-sided Wilcoxon signed-rank test; p < 0.01, chi-square test). A ran-
dom effects probit regression on subjects’ willingness to be the leader (as shown
in Models (1) to (3) of Table3) confirms that the non-parametric results hold
when controlling for individual social preferences. Importantly, the regressions
reveal that social preferences are an important determinant of volunteering for
Table 2 Random effects regression of individual contributions
The reference category in the regression is the baseline treatment. The variables “HBL”, “LBL”, “EN”,
“EXO_L”, “EN_NL”, “EN_HBL” and “EN_LBL” are dummy variables indicating the treatments or
states. SVO is the angle of the vector elicited in the social value orientation task: the larger this value is,
the more pro-social the subject. “High-benefit type” is a dummy variable that is 1 if the subject is of the
high-benefit type. Clustered robust standard errors in parentheses (clustered on group level). *p < 0.1,
**p < 0.05, ***p < 0.01
Dependent variable:
individual contributions
(1) (2) (3) (4) (5) (6)
High-benefit type 5.314*** 5.314*** 5.414*** 5.416*** 5.416*** 5.418***
(0.608) (0.608) (0.631) (0.631) (0.631) (0.629)
HBL 1.970 1.970 2.176 2.171
(1.480) (1.481) (1.376) (1.380)
LBL 1.012 1.013 1.618 1.600
(1.061) (1.061) (1.117) (1.114)
EN 1.182 1.548** 1.897** 0.591
(0.832) (0.778) (0.961) (1.147)
EXO_L (HBL/LBL) 1.552** −0.308
(0.777) (1.128)
EXO_L*Period 0.401**
(0.166)
EN*Period 0.175
(0.175)
EN_NL −2.692*** −1.760**
(0.872) (0.849)
EN_HBL 1.927** 2.268***
(0.886) (0.822)
EN_LBL 3.533*** 3.312***
(0.926) (0.955)
Period −0.530*** −0.530*** −0.758*** −0.456***
(0.071) (0.071) (0.129) (0.065)
SVO 3.461*** 3.503*** 3.503*** 3.299***
(0.868) (0.877) (0.877) (0.837)
Constant −0.775 1.809 0.888 0.874 2.125*0.523
(1.099) (1.146) (1.143) (1.143) (1.208) (1.095)
R2 overall 0.14 0.19 0.22 0.22 0.22 0.25
N 2360 2360 2290 2290 2290 2290
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leadership: the more pro-social a subject, the more likely she is willing to be the
first mover.
To understand why the simultaneous move structure becomes more frequent over
time, we go on to investigate whether being leader pays off, on average, for the two
benefit types.20 For low-benefit members, on average, they end up better off when
being followers than when being leaders (29.64 vs. 23.36, p < 0.0001, two-sided
Wilcoxon signed-rank test). Surprisingly, being leader is, on average, not more prof-
itable than being in a state without a leader (23.36 vs. 24.48, p = 0.51, two-sided
Wilcoxon signed-rank test). Rather, when being a leader, one bears an earning disad-
vantage within the group: low-benefit leaders’ average earnings are 25% lower than
low-benefit followers’ and 47% lower than high-benefit followers’ earnings. This can
explain why low-benefit members’ willingness to volunteer decreases over time.
High-benefit leaders earn more, on average, than when there is no leader (34.78
vs. 28.43, p < 0.01, two-sided Wilcoxon signed-rank test). Furthermore, there is no
statistically significant difference in earnings relative to low-benefit followers (5.22
vs. 3.85, p = 0.52, two-sided Wilcoxon signed-rank test). This may explain why
high-benefit members are more often willing to become the leader than low-benefit
members.
Fig. 2 Evolution of the three states and volunteering in EN. “HB” and”LB” represent high- and low-
benefit members in EN
20 Figure A5 in the appendix displays average payoffs of group members by player type in each state of
EN.
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Table 3 Determinants of the decision to lead in EN (random effects probit)
Marginal effects shown. “High-benefit type” is a dummy which is 1 if the subject is of the high-benefit type. “SVO” is the angle of the vector elicited in the social value
orientation task: the larger this value is, the more pro-social the subject is. Models (4) and (5) focus on subjects who were leaders in the previous period. “Lagged ratio of
follower (same-type)-to-own contribution” refers to the ratio of the same-type follower’s contribution to own contribution in the previous period; “Lagged ratio of follower
(different-type)-to-own contribution” refers to the ratio of the different-type followers’ average contribution to own contribution in the previous period. Clustered robust
standard errors in parentheses (clustered on group level). *p < 0.1, **p < 0.05, ***p < 0.01
Choose to lead in t Choose to re-volunteer for leadership in t, conditional on leading
in t − 1
ALL subjects High-benefit Low-benefit High-benefit Low-benefit
(1) (2) (3) (4) (5)
High-benefit type 0.181***
(0.065)
SVO 0.262*** 0.354*** 0.196** 0.227 0.256*
(0.076) (0.110) (0.090) (0.184) (0.139)
Period −0.019** −0.013 −0.023*** 0.025 0.030
(0.008) (0.013) (0.009) (0.022) (0.020)
Male 0.076 0.143 0.018 0.343*** 0.093
(0.053) (0.094) (0.060) (0.118) (0.102)
Lagged ratio of follower
(same-
0.285*** 0.589***
type)-to-own contribution (0.098) (0.080)
Lagged ratio of followers
(different-
0.229 0.298**
type)-to-own contribution (0.224) (0.126)
Lagged own contribution 0.031*** 0.005
(0.010) (0.009)
Wald
𝜒
224.84*** 9.17** 16.51*** 13.34** 19.52***
Pseudo log likelihood −515.43 −286.08 −227.27 −54.93 −23.44
N 940 470 470 96 59
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We are interested in the reasons why high-benefit members do not self-select into
leadership more often. One possible explanation is that they wait for others to vol-
unteer because leadership is still less profitable for high-benefit members than being
follower (34.78 vs. 40.37, p = 0.02, two-sided Wilcoxon signed-rank test). Another
potential reason could be disappointment with the lack of cooperativeness by other
members, in particular by the same-type member. In order to address the latter
aspect, we analyze how subjects’ willingness to remain the leader depends on events
in the previous period, as shown in Models (4) and (5) of Table3. Apparently, for
leaders the willingness to re-volunteer strongly depends on the responsiveness of
followers in the previous period: the less responsive followers are in terms of con-
tributions, the less likely the previous leader chooses to volunteer again. Differences
exist across different benefit types. While low-benefit leaders take the responsive-
ness of both types of followers into account, high-benefit leaders focus strongly on
the responsiveness of the high-benefit follower.21
Result 4: Low-benefit members exhibit a decreasing trend to volunteer for lead-
ership; high-benefit members are overall more likely to volunteer for leadership than
low-benefit members, yet the proportion never exceeds 50%. Social preferences and
other members’ responsiveness in terms of contributions are important determinants
of the willingness to become leader.
3.3 Leader andfollower contributions
The success of leadership relies on two factors: leaders setting good examples, and
followers responding to the leaders’ examples. To understand treatment effects in
more detail, in this section, we explore how leader and followers behave in different
leadership treatments and states.22 Figures3 and 4 present contribution dynamics
of leaders and followers under high- and low-benefit leadership, respectively: the
left panel shows exogenous leadership, and the right panel self-selected leadership.
For reasons of comparison, we add contribution dynamics of group members in the
baseline treatment, as illustrated by the two dashed lines.
We start the analysis by looking at leaders’ behavior. In the presence of norma-
tive conflicts, do leaders set good examples? Do self-selected leaders contribute
more than leaders that are exogenously assigned? As shown in Fig.3, contributions
of high-benefit members decline significantly over time in BASE (Spearman’s
ρ
=
− 0.49, p < 0.01). In contrast, high-benefit leaders’ contributions are fairly stable
(Spearman’s
ρ
= −0.02, p = 0.81 in HBL; Spearman’s
ρ
= −0.04, p = 0.69 in EN_
HBL). Over all periods, high-benefit leaders contribute more than their same-type
counterparts in BASE, but the difference is only significant in EN_HBL (p = 0.18
21 For high-benefit leaders, we obtain suggestive evidence of gender differences in re-volunteering: cet-
eris paribus, high-benefit males are significantly more likely to re-volunteer than females of the same
type; the coefficient of “lagged own contribution” is significant, but the magnitude is small.
22 TableA2 in the appendix displays average contributions of group members by type in each treatment
and state. FiguresA6–A8 show the evolution of members’ contributions by group in our baseline as well
as exogenous leadership treatments.
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for HBL; p = 0.01 for EN_HBL).23 Leaders’ contributions are higher in EN_HBL
than in HBL, though the difference is not significant (p = 0.51).
Low-benefit leaders’ behavior is shown in Fig.4. Leaders in LBL start out at a
medium contribution level that is only slightly smaller than the initial leader contri-
bution in HBL. However, contributions drop quickly to about half of the contribu-
tion of high-benefit leaders. There is an overall decreasing trend in leaders’ con-
tributions in LBL (Spearman’s
ρ
= −0.22, p = 0.02), while this is not the case in
EN_LBL with self-selected leaders (Spearman’s
ρ
= 0.07, p = 0.55).
Nonetheless, under both forms of low-benefit leadership, leaders’ contributions
are significantly higher than the same-type counterparts in BASE (p = 0.04 in LBL;
p < 0.01 in EN_LBL), and leaders’ contributions are significantly higher in EN_LBL
than in LBL (p < 0.01).
Table4 reports the results of a random effects regression comparing contributions
of leaders and their same-type counterparts in BASE. Models (1) to (3) compare
between high-benefit leaders and their high-benefit counterparts, while Models (4)
to (6) compare between low-benefit leaders and their low-benefit counterparts. The
coefficients of treatment/state dummies in both Models (1) and (4) are significantly
positive, indicating that high-benefit leader and low-benefit leader contributions are
significantly higher than their corresponding counterparts in BASE, regardless of
the way how leadership is generated. The magnitude of the effect, however, is larg-
est for EN_LBL. Wald tests further confirm that self-selected low-benefit leaders
contribute significantly more than imposed low-benefit leaders (p < 0.001), whereas
there is no significant difference between self-selected and imposed high-benefit
leaders (p = 0.55).24 We get qualitatively the same results when controlling for the
time trend and leaders’ social preferences, as shown in Model (2) and (5), indicating
that leadership behavior cannot simply be attributed to time or pure self-selection
effects.25
In Models (3) and (6), we add the interaction terms between the time and treat-
ment/state dummies. Model (3) shows that high-benefit leaders’ contributions have
a completely different time trend than their counterparts. An F-test further confirms
the stable trend of high-benefit leaders’ contributions by failing to reject the null
24 According to Gächter etal. (2012), leaders’ contributions in a one-shot public goods game are influ-
enced by both their cooperative attitude and their belief towards others’ cooperativeness. Could we
attribute high contributions of self-selected low-benefit leaders to their social preferences and optimistic
beliefs towards others’ cooperativeness? Indeed, self-selected low-benefit leaders are found to be more
other-regarding than imposed low-benefit leaders, as the mean SVO angle is higher for self-selected low-
benefit leaders (0.29 vs. 0.12), yet, the difference is not significant at conventional levels (p = 0.18). More
importantly, self-selected low-benefit leaders seem to be more optimistic about followers’ cooperative-
ness than imposed low-benefit leaders (p < 0.001 for the same-type follower; p < 0.05 for different-type
followers, with the treatment dummy, lagged contributions of both types of followers, and the time trend
as independent variables; random effects regression clustered for matching groups).
25 Inclusion of lagged contributions of other group members in the regressions that explore treatment
differences in leader’s/followers’ contributions, i.e., in Tables4 and 5, does not yield different results.
Note that the coefficient of “HBL” and “LBL” would turn marginally significant with some other consist-
ency thresholds of the ring test scores.
23 There is evidence that imposed high-benefit leaders contribute significantly more than their same-type
counterparts in BASE in the last five periods (p < 0.05).
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hypothesis that the combined effect of Period and Period*HBL (or Period*EN_
HBL) is equal to zero (p = 0.32 for HBL and p = 0.17 for EN_HBL). The picture
looks a bit different for low-benefit leaders. We only find a stable trend of low-ben-
efit leaders’ contributions in EN_LBL (p = 0.52 for the combined effect of Period
and Period*EN_LBL; p = 0.06 for the combined effect of Period and Period*LBL).
These results confirm the Spearman rank correlation analysis.
Result 5a: Over all periods, leaders, in particular self-selected leaders, contrib-
ute significantly more than their same-type counterparts in treatment BASE. The
magnitude of the effect is largest for self-selected low-benefit leaders.
Result 5b:Self-selected leaders tend to contribute more than imposed leaders,
yet, the difference is only significant for the low-benefit type.
Next, we turn to the behavior of followers. As shown in Fig.3 that considers
only the situation of high-benefit leadership, high-benefit followers exploit leaders
by undercutting leaders’ contributions by 13% in HBL, and 19% in EN_HBL (two-
sided Wilcoxon signed-ranks test: p = 0.04 in HBL and p = 0.01 in EN_HBL). Low-
benefit followers contribute about half of leader contributions in the first period and
further decrease contributions over time; on average, they undercut leaders’ contri-
butions by 55% in HBL and 64% in EN_HBL (two-sided Wilcoxon signed-ranks
test: p < 0.005 in HBL and p < 0.0001 in EN_HBL). Using data from all periods, we
do not observe a significant difference in contributions between followers and their
corresponding same-type counterparts in treatment BASE (p > 0.3).
Fig. 3 Average contributions of leaders and followers under high-benefit leadership(HBL). “HL” rep-
resents high-benefit leaders. “HF”/“LF” represents high- and low-benefit followers respectively, while
“HB”/“LB” represents high- and low-benefit members in BASE
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Figure4 shows that low-benefit followers undercut leaders’ contributions by 25%
in LBL and 52% in EN_LBL (two-sided Wilcoxon signed-ranks test: p < 0.005 in
LBL and p = 0.0001 in EN_LBL). Surprisingly, for high-benefit followers, despite
the fact that their MPCR is twice as high as that of leaders, their contributions are
only marginally significantly higher than those of leaders in LBL (two-sided Wil-
coxon signed-ranks test: p = 0.06), and even significantly lower than those of lead-
ers in EN_LBL (two-sided Wilcoxon signed-ranks test: p = 0.02). This is in sharp
contrast to the baseline treatment where high-benefit members contribute 146%
more than low-benefit members. Still, we find no significant difference in contri-
butions between followers and their corresponding counterparts in treatment BASE
(p > 0.3).
Table5 presents a random effects regression of followers’ contributions on treat-
ment/state dummies. Models (1) and (2) compare high-benefit followers with their
high-benefit counterparts in treatment BASE; Models (3) and (4) compare low-
benefit followers with their low-benefit counterparts in BASE. All coefficients on
treatment/state dummies are positive, indicating a positive effect on followers’ con-
tributions, yet, the only significant coefficient is the one for low-benefit followers in
EN_LBL. Note that this coefficient also becomes marginally significant in Model
(4) with some lower consistency thresholds of the ring test score.
Taken together, leadership has little effect in promoting follower contribu-
tions. Only under self-selected low-benefit leadership do we observe a marginally
Fig. 4 Average contributions of leaders and followers under low-benefit leadership(LBL). “LL” rep-
resents low-benefit leaders. “HF”/“LF” represents high- and low-benefit followers respectively, while
“HB”/“LB” represents high- and low-benefit members in BASE
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significant increase in low-benefit followers’ contributions. Interestingly, self-
selected leaders do not seem to have more impact than imposed leaders in our set-
ting. In contrast, followers tend to exploit self-selected leaders to a stronger extent
than imposed leaders, as the distance between leaders’ and followers’ average con-
tributions is larger with self-selected leaders than with randomly assigned leaders
(p = 0.11 for HBL vs. EN_HBL; p < 0.001 for LBL vs. EN_LBL).26 In consequence,
Table 4 Leaders’ contributions across treatments and states
The reference category is high-benefit members in BASE in Models (1) to (3) and low-benefit members
in BASE in Models (4) to (6). The variables “HBL”, “LBL” “EN_HBL”, “EN_LBL” are dummy vari-
ables indicating leaders in those treatments/states. “SVO” is the angle of the vector elicited in the social
value orientation task: the larger this value is, the more pro-social the subject. Clustered robust standard
errors in parentheses (clustered on group level). *p < 0.1, **p < 0.05, ***p < 0.01
Dependent variable:
leaders’ contributions
High-benefit Low-benefit
(1) (2) (3) (4) (5) (6)
HBL 3.118*3.319** − 0.857
(1.708) (1.623) (1.683)
EN_HBL 4.182*** 4.051*** 0.297
(1.155) (1.230) (1.570)
Period*HBL 0.762***
(0.221)
Period*EN_HBL 0.698***
(0.220)
Period −0.608*** −0.925*** −0.487*** −0.590***
(0.118) (0.147) (0.122) (0.164)
SVO 4.273*** 4.287*** −0.194 −0.179
(1.622) (1.614) (1.295) (1.312)
LBL 2.782** 3.222** 1.957
(1.410) (1.413) (2.059)
EN_LBL 10.071*** 9.884*** 8.183***
(1.392) (1.345) (2.139)
Period*LBL 0.228
(0.255)
Period*EN_LBL 0.367
(0.383)
Constant 10.229*** 12.427*** 14.168*** 4.162*** 6.515*** 7.080***
(0.762) (1.240) (1.287) (0.938) (1.222) (1.447)
R2 overall 0.09 0.15 0.18 0.24 0.30 0.31
N 461 449 449 427 410 410
26 TableA3 in the appendix uses regressions to compare the ratio of follower’s contribution to leader’s
contribution between self-selected and imposed leadership, respectively for each type of follower. The
results indicate that followers, in particular followers whose benefit type is different from the leader,
exploit self-selected leaders more strongly. Note that pure self-selection effects do not seem to explain
why followers exploit self-selected leaders more strongly, since we obtain similar results after controlling
for followers’ social preferences.
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we do not observe a significant difference in followers’ contributions between self-
selected and imposed leadership (p = 0.85 for HBL vs. EN_HBL; p = 0.33 for LBL
vs. EN_LBL),27 even though self-selected low-benefit leaders contribute signifi-
cantly more than imposed low-benefit leaders. The asymmetry in the group appears
to provide an excuse that leads to a reduction of a potentially positive leadership
effect for both exogenous and endogenous leadership, with an even more pro-
nounced reduction for endogenous leadership.28
Result 6: Relative to their same-type counterparts in treatment BASE, we find
marginally significantly higher contributions only of low-benefit followers in
Table 5 Followers’ contributions across treatments and states
The reference category is high-benefit members in BASE in Models (1) and (2) and low-benefit mem-
bers in BASE in Models (3) and (4). “HF”/“LF” represents high- and low-benefit followers respectively.
The variables “HBL”, “LBL” “EN_HBL”, “EN_LBL” are dummy variables indicating followers in those
treatments/states. “SVO” is the angle of the vector elicited in the social value orientation task: the larger
this value is, the more pro-social the subject. Clustered robust standard errors in parentheses (clustered
on group level). *p < 0.1, **p < 0.05, ***p < 0.01
Dependent variables: followers’
contributions
(1) HF (2) HF (3) LF (4) LF
HBL 1.303 1.442 1.824 2.124
(1.798) (1.744) (1.721) (1.597)
LBL 0.025 0.359 1.201 1.968
(1.568) (1.687) (1.409) (1.437)
EN_HBL 1.472 1.556 1.037 1.484
(1.328) (1.381) (1.200) (1.096)
EN_LBL 0.940 0.354 3.150** 3.266**
(1.106) (1.199) (1.600) (1.626)
Period −0.522*** −0.472***
(0.108) (0.072)
SVO 3.517** 2.751**
(1.401) (1.169)
Constant 10.229*** 12.187*** 4.162*** 5.642***
(0.760) (1.186) (0.936) (1.039)
R2 overall 0.01 0.07 0.03 0.12
N 835 801 869 850
27 Wald tests for Table5 show that this result holds for either type of follower, even when the time trend
and SVO are controlled for (p > 0.45).
28 As shown in TableA4 in the appendix, in the baseline treatment, there is considerable heterogeneity
across groups with regard to the contribution ratios between high- and low-benefit members. When look-
ing at the contribution ratios between leaders and low-benefit followers under high-benefit leadership,
however, we observe fewer cases in which the contribution ratio is around one, and more cases in which
the contribution ratio is proportional to benefits. Conversely, under low-benefit leadership, in particular
when leaders are self-selected, we observe similar contributions between high-benefit followers and lead-
ers in a large majority of groups.
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Leading byexample inapublic goods experiment withbenefit…
EN_LBL. Followers exploit leaders more strongly when leaders are volunteers than
when leadership is imposed.
This finding raises the question of how followers exactly respond to leaders’
examples. Table6 reports the results of a random effects regression on how fol-
lowers respond to their leaders’ contributions. Except for leader’s contribution, we
include the time trend, the follower type, the interaction term between leader’s con-
tribution and the follower type, and individual social preferences as independent
variables. Table6 indicates that, with high-benefit leaders, it is mainly the high-ben-
efit followers that reciprocate positively, irrespective of whether the leader has been
randomly assigned or volunteered. For every additional token the high-benefit leader
contributes in a given period, a low-benefit follower contributes, on average, about
0.15 tokens. The level of reciprocity of high-benefit followers is significantly higher,
with an average of about 0.6 tokens in HBL and 0.55 tokens in EN_HBL. Hence,
high-benefit leaders’ examples mainly have an impact on the same-type followers.
The last two columns of Table6 show that low-benefit leaders have a signifi-
cant influence on low-benefit followers. For every additional token the low-benefit
leader contributes in a given period, low-benefit followers contribute 0.28 tokens
in LBL and 0.35 tokens in EN_LBL. The interaction term is positive in LBL but
not significant, implying that reciprocity from high-benefit followers is not signifi-
cantly stronger than the one from low-benefit followers when they face a low-ben-
efit leader.29 It seems that, for followers that are of a different type as the leader,
reciprocity towards the leader is based on a self-serving perception of contribution
norms: with high-benefit leaders, low-benefit followers tend to balance their pay-
off with high-benefit members, and thus reciprocate on a much lower level; with
low-benefit leaders, high-benefit followers try to balance the reciprocation level in
contributions with low-benefit members.30 We shall argue that imperfect conditional
cooperation by followers, combined with the self-serving perception of contribution
norms, is one important reason for the ineffectiveness of leadership in the presence
of benefit heterogeneity.
Result 7: Low-benefit followers reciprocate less strongly than high-benefit fol-
lowers under high-benefit leadership. The two types of followers reciprocate at a
similar rate under low-benefit leadership. The followership pattern is in line with a
self-serving perception of contribution norms.
Apparently, followers’ reciprocity is not sufficient to make setting good examples
the payoff-maximizing strategy for low-benefit leaders. On average, their costs of
29 The marginal responsiveness of followers is weaker under self-selected leadership, irrespective of the
leader type, however, none of the differences is significant (Chow-test, p > 0.25).
30 Leaders can influence followers’ contributions in two ways: one is through the direct reciproca-
tion, and the other is through followers’ beliefs about other followers’ cooperativeness. TableA5 in the
appendix augments Table6 with another independent variable: follower’s belief. Tables A6 and A7 in
the appendix further explore how follower’s beliefs towards other followers’ cooperativeness are influ-
enced by leaders’ contributions. Abstracting from potential endogeneity that we cannot fully control for,
the results indicate that leaders influence their different-type followers mainly through the indirect belief
effect. More specifically, for followers that are of a different type than the leader, their contributions are
mainly shaped by their belief about the cooperativeness of their same-type member. This belief is signifi-
cantly affected by the leader’s contribution, but the magnitude of the coefficient is rather small.
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contributing are higher than their benefits from increased contributions by follow-
ers. In addition, the more low-benefit leaders contribute, the more their earning falls
short of those of followers. In other words, setting good examples, on average, does
not pay for low-benefit leaders, but instead increases their earnings disadvantage
within the group. This is consistent with our finding that imposed low-benefit lead-
ers decrease their contributions very quickly and self-selection for leadership does
not pay off for low-benefit members.
For high-benefit leaders, their examples only have little influence on low-benefit
followers. However, since they obtain a comparatively large benefit from the pub-
lic good, their costs of contributing are, on average, lower than their benefits from
the increased contributions by followers, i.e. setting a good example is, on average,
profitable for them. This is consistent with our finding that average contributions of
imposed high-benefit leaders remain stable over time, and high-benefit members are
on average better off when they self-select for leadership than when nobody volun-
teers in the group.31
4 Conclusion
In collective action problems outside the experimental laboratory, group members
are likely to gain different benefits from the provision of a public good. This paper
examined the effect of leading by example on cooperation when individuals have
different benefits from the group account by using a linear public goods experiment.
We find that the effect of leading by example is limited in promoting cooperation.
Average contributions do not differ significantly between situations with and without
either type of randomly selected leadership, though we do observe a significantly
slower declining trend in contributions with (imposed) leadership. In line with pre-
vious research, we see significantly higher contributions with self-selected leaders
than without. Contributions with self-selected leaders, in particular self-selected
low-benefit leaders, are also significantly higher than those in our baseline treat-
ment with simultaneous contributions. However, we do not observe a high enough
willingness to lead for high-benefit members, and the motivation for low-benefit
members to self-select into leadership is decreasing quickly over time. This trend,
combined with the fact that contributions are low in case nobody in the group volun-
teers to become the leader, leads to contributions that are only marginally higher, on
31 This, however, does not mean that high-benefit members always have the motivation to set good
examples. In fact, contributions of both imposed and self-selected high-benefit leaders are strongly
affected by their beliefs on the cooperativeness of their high-benefit follower (p < 0.0001, with leaders’
beliefs towards the cooperativeness of others, leader’s SVO and the time trend as independent variables;
random effects regression, clustered for matching groups). Leaders that are more pessimistic about their
same-type fellow’s cooperativeness tend to contribute less. In the regression, the coefficient of “leader’s
SVO” is also significant and positive for imposed leaders (p = 0.01), indicating that for a given belief, the
less pro-social the imposed leader, the less she contributes. The results hold even when we control for
lagged contributions of other members and is thus consistent with Gächter etal. (2012), who find that
both leaders’ beliefs and cooperation preferences matter for contributions.
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Leading byexample inapublic goods experiment withbenefit…
average, in the endogenous treatment than in the baseline treatment with simultane-
ous contributions.
Via exploring followers’ reciprocity towards leaders, we notice the usual pattern
of imperfect conditional cooperation by followers. In addition, we find that followers
who are of a different type than the leader appear to condition the level of reciproc-
ity on their preferred contribution norm. Specifically, while low-benefit followers
reciprocate to the high-benefit leader at a particularly low rate, high-benefit follow-
ers reciprocate to low-benefit leaders to a similar extent as low-benefit followers.
Followers’ insufficient reciprocity not only impairs the effectiveness of leaders’ role
models, but also demotivates (potential) leaders when it comes to volunteering for
leadership. In fact, even if it actually pays off for leaders to provide a good example,
on average, pessimistic beliefs about followers’ reciprocity also seem to deter some
high-benefit leaders to self-select into leadership.
With respect to the comparison of imposed and self-selected leadership, we
find that self-selected leaders—in particular low-benefit leaders—tend to set bet-
ter examples than imposed leaders. However, followers, in particular those that
are of a different type than the leader, do not increase contributions enough. Our
results remain qualitatively unchanged when controlling for subjects’ social prefer-
ences, which makes it unlikely that pure self-selection effects into leadership drive
our main results. Moreover, in contrast to some existing evidence that assigning the
advantageous type to leadership results in higher contribution levels, our findings do
not support the conclusion that high-benefit leadership is more effective than low-
benefit leadership.
Table 6 Followers’ responses to leader’s example
“High-benefit follower” is a dummy variable which is 1 if the follower is of the high-benefit type.
“SVO” is the angle of the vector elicited in the social value orientation task: the larger this value is, the
more pro-social the subject. Clustered robust standard errors in parentheses (clustered on group level).
*p < 0.1, **p < 0.05, ***p < 0.01
Dependent variables: follow-
ers’ contributions
(1) HBL (2) EN_HBL (3) LBL (4) EN_LBL
High-benefit follower –0.106 1.146 2.994 3.691*
(1.186) (1.621) (2.409) (2.074)
Leader’s contribution 0.156*** 0.143*** 0.282*** 0.352***
(0.059) (0.042) (0.106) (0.103)
High-benefit follower 0.452*** 0.391*** 0.219 –0.015
*Leader’s contribution (0.105) (0.117) (0.159) (0.149)
Period –0.422*** –0.461*** –0.138 –0.393*
(0.122) (0.077) (0.108) (0.230)
SVO 5.299*** 2.685*3.600** 4.629***
(1.857) (1.631) (1.679) (1.621)
Constant 4.681*** 4.736*** 3.694*** 3.440**
(1.078) (0.837) (0.987) (1.493)
R2 overall 0.42 0.37 0.26 0.27
N 330 325 337 199
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Overall, our findings are in line with the suggestion that, when there is benefit
heterogeneity in a group, the conflict between different equity and contribution
norms is difficult to overcome, even with a mechanism—leading by example—
that has often been proven as useful in homogenous populations. They also pose
some questions for future research: How can groups with heterogeneity overcome
the coordination problem regarding different contribution norms, when there is a
leader? Perhaps, in such a situation the leader needs more than just the good exam-
ple. For instance, it would be interesting to study situations with benefit heterogene-
ity in which leaders have additional coercive power such as a punishment option or
ostracism power. An alternative would be introducing a communication option for
leaders in order to alleviate the coordination problem. Another promising route of
research in view of our results is appropriate selection mechanisms for leaders. It
seems that type and nature of leaders matter when it comes to the effectiveness of
leadership. Relevant characteristics could be considered in appointment or selection
(voting) procedures. It should also be noted that in our setting, there are two high-
benefit and two low-benefit group members. Since high-benefit leaders influence
high-benefit followers more strongly, the effectiveness of high-benefit leadership
might depend on the distribution of the two benefit types within the group. Future
research could look at groups that consist of three high-benefit members and one
low-benefit member and vice versa.
Supplementary Information The online version contains supplementary material available at https:// doi.
org/ 10. 1007/ s00355- 023- 01459-1.
Funding Open access funding provided by University of Vienna.
Data availability The datasets generated during and/or analysed during the current study are available
from the corresponding author on request.
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License,
which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as
you give appropriate credit to the original author(s) and the source, provide a link to the Creative Com-
mons licence, and indicate if changes were made. The images or other third party material in this article
are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the
material. If material is not included in the article’s Creative Commons licence and your intended use is
not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission
directly from the copyright holder. To view a copy of this licence, visit http:// creat iveco mmons. org/ licen
ses/ by/4. 0/.
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