Games and Economic Behavior 77 (2013) 271–283
Contents lists available at SciVerse ScienceDirect
Games and Economic Behavior
www.elsevier.com/locate/geb
Legitimate punishment, feedback, and the enforcement of cooperation
Marco Faillo a , Daniela Grieco b , Luca Zarri b,∗
a
b
Department of Economics, University of Trento, Via Inama 5, 38122 Trento, Italy
Department of Economics, University of Verona, Via dell’ Artigliere 19, 37129 Verona, Italy
a r t i c l e
i n f o
Article history:
Received 6 December 2011
Available online 1 November 2012
JEL classification:
C73
C91
D02
D63
Keywords:
Public goods games
Cooperation
Legitimate punishment
Feedback
Behavioral mechanism design
a b s t r a c t
In dealing with peer punishment as a cooperation enforcement device, laboratory studies
have typically concentrated on discretionary sanctioning, allowing players to castigate each
other arbitrarily. By contrast, in real life punishments are often meted out only insofar
as punishers are entitled to punish and punishees deserve to be punished. We provide
an experimental test for this ‘legitimate punishment’ institution and show that it yields
substantial benefits to cooperation and efficiency gains, compared to a classic, ‘vigilante
justice’ institution. We also focus on the role of feedback and we interestingly find
that removing the information over high contributors’ choices is sufficient to generate
a dramatic decline in cooperation rates and earnings. This interaction result implies that
providing feedback over virtuous behavior in the group is necessary to make a legitimate
punishment scheme effective.
© 2012 Elsevier Inc. All rights reserved.
1. Introduction
In naturally occurring environments, punishment is a widespread phenomenon. The ubiquity of sanctioning is due to
a significant degree to its importance for the proper functioning of society at large as well as the efficiency of small-scale
organizations and communities. Since Fehr and Gächter’s (2000) seminal paper, experimental economists have typically
concentrated on a cooperation enforcement device such as discretionary peer-to-peer sanctioning, where players are free to
castigate each other arbitrarily. By contrast, since in many environments meting out punishments implies inflicting (sometimes extremely severe) costs on the punishees, a defining feature of real-life sanctioning mechanisms is that their usage is
far from being unrestricted. In modern societies, punishment is usually viewed as socially and ethically acceptable only insofar as it is ‘legitimate’. Legitimate punishment means that specific requirements have to be met for a person or an institution
to be viewed as a potential punisher as well as a potential punishee.1
Everyday life abounds in situations where sanctioning systems have to be legitimate in order to be implemented. In the
case of centralized punishment, only some institutions (for instance, police and courts) are entitled to impose sanctions
on wrongdoers. Trade unions and employers’ associations usually set up arbitration boards entitled to monitor and enforce
the compliance of their members. However, it is important to note that legitimate punishment often takes the form of
*
Corresponding author.
E-mail addresses: [email protected] (M. Faillo), [email protected] (D. Grieco), [email protected] (L. Zarri).
1
In the Western world, centuries of normative argument in applied ethics, philosophy of law and political philosophy (with classical contributions from
prominent thinkers such as John Stuart Mill and, more recently, John Rawls, Jurgen Habermas and Ronald Dworkin, among many others) have convincingly
made clear that in a liberal democracy punishment needs to be legitimate, in order to be theoretically justified. In his influential classical paper on crime
and punishment, also Becker (1968) takes for granted that punishment must be legitimate in order to be permitted.
0899-8256/$ – see front matter © 2012 Elsevier Inc. All rights reserved.
http://dx.doi.org/10.1016/j.geb.2012.10.011
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M. Faillo et al. / Games and Economic Behavior 77 (2013) 271–283
decentralized, peer-to-peer sanctioning. In some situations, legitimate peer punishment characterizes the functioning of formal institutions, as it is the case with the well-known peer review system prevailing in the academic community at large.
In other cases, legitimate peer punishment operates informally, as there are domains where this principle holds though it
lacks formalization. In many parts of the world it is often the case that serious difficulties in establishing a central authority
arise due to lack or weakness of the rule of law. Under these circumstances, social norms typically act as substitutes of
formal institutions and decentralized legitimate punishment seems to be a better norm enforcement device than arbitrary
sanctioning.2 In the case of Turkana, a large-scale, politically uncentralized, egalitarian, nomadic pastoral community engaged in warfare in East Africa (Mathew and Boyd, 2011), antisocial behaviors like cowardice and desertions are severely
punished by community-imposed sanctions.3 At a lower scale, in small groups where problems due to principal–agent relationships frequently arise, self-monitoring via a fair rule appears to be a promising route to informally solve the free rider
problem in the absence of monitoring opportunities on the part of the principal (Mas and Moretti, 2009).
What these otherwise distant situations where peer punishment is at work have in common is an underlying principle
of legitimacy: only some people or institutions, thanks to their virtuous behavior within a given context, are entitled to
sanction and only those who misbehave deserve to be sanctioned. We investigate this legitimacy–punishment nexus experimentally within a finitely repeated public goods game framework. We aim at comparing the performance, in terms of
both cooperation and efficiency, of two decentralized sanctioning mechanisms such as a classic arbitrary punishment institution and a legitimate punishment one. While under arbitrary sanctioning everyone can punish everyone else in the group,
so that cooperators and free riders alike could be sanctioned, the institution studied in this paper prescribes that people can
punish only those who contribute to the public good less than they do. Our data provide clear evidence that legitimacy yields
substantial benefits to both cooperation and welfare. We also focus on the role of information and find that restrictions
on the punishment activity are effective only when feedback over how the most virtuous individuals do actually behave
(in terms of contribution choices) is provided. On the whole, then, our results interestingly suggest that it is the interaction
between the legitimate nature of the sanctioning system at work and feedback over peers’ behavior that plays a critical role
in determining final contributions and earnings levels.
The remainder of the paper is structured as follows. Section 2 reviews the related literature. Section 3 illustrates the
experimental design. Section 4 reports our main results and Section 5 concludes the paper.
2. Background
In a laboratory public goods game or voluntary contribution mechanism (VCM), there is a group of subjects who, as the
game starts, receive an individual monetary endowment, from which they may contribute any amount to a public good that
returns a payoff to each of them. The structure of monetary payoffs in the VCM makes it a classical ‘social dilemma’, as each
agent has a dominant strategy to free ride, while at the social optimum each individual contributes his entire endowment.
Therefore, the straightforward prediction based on the material self-interest hypothesis (and common knowledge of it) is
that everyone should free ride, both in the one-shot and in the finitely repeated version of the game. By contrast, in the
latter setting, initial cooperation turns out to be relatively high and, as time unfolds, the well-known ‘decay’ pattern typically
occurs (Ledyard, 1995). In the last decades, an increasing number of VCM experiments have been investigating the role that
institutions can play in the enforcement of cooperation. In particular, decentralized sanctioning systems are among the
most widely studied in the experimental literature (Ostrom et al., 1992). In their pathbreaking studies, Fehr and Gächter
(2000, 2002) demonstrate that while in non-punishment treatments cooperation rates indeed tend to fall over time, decay
does not occur insofar as players are allowed to incur a cost to decrease others’ monetary payoffs. This is due to the fact
that many participants are willing to engage in individual punishment of inappropriate behavior (despite the net monetary
costs associated with its usage) both with anonymous random matching and with fixed groups playing a finite number of
times. However, recent work convincingly indicates that a long overlooked ‘dark side’ of arbitrary costly punishment needs
to be seriously taken into account.
First, this institution in many cases significantly undermines the scope for self-governance, as, since everyone is free
to punish everyone else, sanctioning may take the form of misdirected, ‘antisocial’ punishment – that is, low contributors
punishing high contributors. Available evidence reveals that antisocial punishment is quantitatively significant (Anderson
and Putterman, 2006) and substantially reduces contribution rates (Cinyabuguma et al., 2006), to the point that in some
subject pools cooperation in the presence of sanctioning can be even lower than in its absence (Gächter and Herrmann,
2011). The negative effect of antisocial punishment on contribution levels is larger as long as it is targeted at outgroup
members when competition between groups is created (Goette et al., 2012) and when it occurs within less industrialized
societies (Herrmann et al., 2008). Second, when multiple stages of punishment are allowed, so that immunity of sanctioners from reprisals is removed, counterpunishment and feuds are likely to be triggered, limiting, once again, successful
self-governance and leading, eventually, to a demise of cooperation (Denant-Boemont et al., 2007, Nikiforakis, 2008 and
2
In some environments, the locally prevailing social norms prescribe that not only cheaters but also non-punishers have to be sanctioned. See, on this,
Kandori’s (1992) classical paper.
3
Neighborhood crime watches and ‘naming and shaming’ practices provide further examples along these lines, though within socio-economic contexts
where social norms and formal institutions appear to be complements, rather than substitutes.
M. Faillo et al. / Games and Economic Behavior 77 (2013) 271–283
273
Nikiforakis and Engelmann, 2011). Since the opportunity to retaliate punishments exists in many real-life decentralized interactions (Nikiforakis, 2008), these negative results show that arbitrary sanctioning is not robust to realistic institutional
changes. Third, a further drawback is that insofar as punishment exclusively relies on deterrence, that is on extrinsic motives to cooperate, the risk is either not to elicit people’s intrinsic motivations to comply (if any) or even to crowd them out,
especially when incentives are weak (see Gneezy et al., 2011 and Bowles and Polania-Reyes, 2012). Fourth, it is important to
note that successfully dealing with the free rider problem is only one step towards the solution of the problem as a whole.
Recent papers document that, even in the presence of a single stage of sanctioning, the success of discretionary punishment
in enforcing cooperation comes at a substantial cost. Botelho et al. (2005) analyze Fehr and Gächter’s (2000, 2002) data and
find lower earnings when punishment is allowed than under no punishment (see also Bochet et al., 2006 and Cinyabuguma
et al., 2006, Herrmann et al., 2008 and Dreber et al., 2008 for similar results). This evidence shows that ‘vigilante justice’ is
a double-edged sword (Goette et al., 2012), as it raises cooperation levels but, unless we consider a significantly longer time
horizon (Gächter et al., 2008), leads to average earnings which are lower than in the absence of sanctioning options (see on
this also Denant-Boemont et al., 2007). This is a serious shortcoming of unrestricted punishment, as it risks to determine
welfare losses and, therefore, to turn into a wasteful activity for those societies or organizations that adopt it.
3. Experimental design
3.1. Procedures
A total of 168 subjects participated voluntarily in the experiment at the CEEL Lab of the University of Trento. A total
of 9 sessions were conducted, between December 2009 and November 2010. The experiment was programmed by using
the z-Tree platform (Fischbacher, 2007). Subjects were undergraduate students (64.3% from economics, 49.5% females, 80.3%
Italians). We employed a between subjects design: no individual participated in more than one session. In each session,
the participants were paid a 5 euros show up fee, plus their earnings from the experiment. The average payment per
participant was 15.70 euros (including the show-up fee) and the sessions averaged approximately 1 hour and 30 minutes.
At the beginning of each session, participants were welcomed and asked to draw lots, so that they were randomly assigned
to terminals. Once all of them were seated, the instructions4 were handed to them in written form before being read aloud
by the experimenter. The participants had to answer several control questions and we did not proceed with the actual
experiment until all participants had answered all questions correctly.
For each treatment, participants in each session were randomly assigned to groups of size N = 4, so that they did not
know the identities of the other members of their group. Like other experimental studies (see e.g. Cinyabuguma et al., 2006;
Denant-Boemont et al., 2007), we used a partner protocol that kept the composition of each group constant over rounds,
so that, at the end of each period, individuals remained in the same group. However, individuals’ labels were randomly
reassigned in each period. For example, the same player could be designated as player 45 in period t, as player 6 in
period t + 1, and as player 38 in period t + 2. Therefore, our partner protocol was also characterized by anonymity of the
components of the group and change of participants’ labels across rounds. The parametric structure of the experiment is
based on Fehr and Gächter (2000).
3.2. Treatments
In all treatments, participants played a finitely repeated public goods game with punishment options for T = 20 periods.
In every period, the experimental game consists of two decision stages: at stage 1 (contribution stage), players choose how
much to contribute to the public good and at stage 2 (punishment stage) they have access to punishment options. In each
treatment, participants were informed about these features of the game to be played. The following three treatments were
implemented: (1) a baseline, unrestricted punishment and full information (Baseline) treatment, (2) a restricted punishment
with full information (Full R.) treatment and (3) a restricted punishment with partial information (Partial R.) treatment.
There were 3 sessions (20 subjects in two sessions and 16 in the other) for the Baseline, 3 sessions (with 20 subjects in two
sessions and 16 in the other) for the Full R. and 3 sessions (with 20 subjects in two sessions and 16 in the other) for the
Partial R. Overall, the three treatments differ along two dimensions (see Table 1): nature of peer punishment (unrestricted vs.
restricted) and feedback about others’ contribution levels (full vs. partial) in the group.
3.2.1. Baseline
In the Baseline treatment, punishment is unrestricted and subjects are provided with full information, that is there is
feedback about all their group co-players’ individual contributions. This is a replication of the standard VCM with punishment and partner protocol (Fehr and Gächter, 2000), where everyone can freely punish everyone else in the group. In stage 1,
each participant receives a fixed amount e = 20 of tokens and has to decide whether she wants to invest or not an amount
g i e into a public project. Decisions are made simultaneously and with no information about peers’ choices. At the end
4
A translation of the instruction sheet is provided in the supplementary material. Original instructions were written in Italian. They are available upon
request from the authors.
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M. Faillo et al. / Games and Economic Behavior 77 (2013) 271–283
Table 1
Treatments.
Restrictions
Yes
No
Full
Full R.
(3 sessions;
14 groups;
56 subjects)
Baseline
(3 sessions;
14 groups;
56 subjects)
Partial
Partial R.
(3 sessions;
14 groups;
56 subjects)
Information
Table 2
Cost function.
Points
Costs
0
0
1
1
2
2
3
4
4
6
5
9
6
12
7
16
8
20
9
25
10
30
of stage 1, each participant is informed about her current earnings, which are calculated by the computer in the following
way:
πi = (20 − g i ) + 0.4
4
g j.
j =1
In stage 2 subjects are informed about the contribution by the other members of their group and can decide to assign
between 0 and 10 punishment points to any of them. Points assignment is costly and costs are charged according to
a convex cost function as in Fehr and Gächter (2000) (Table 2).
Each point that a subject receives reduces her earnings at stage 1 by 10%, with 100% as the maximum total reduction.
Punishment is anonymous: subjects do not know the identity of the peer who has punished them. Each participant’s net
earnings at the end of stage 2 are given by her earnings at the end of stage 1 minus the costs of assigned and received
punishment points and are calculated by the computer.
3.2.2. Legitimacy-based treatments
The other two treatments are characterized by the presence of legitimacy. Both in the Full R. and the Partial R. treatment, stage 1 is exactly the same as in the Baseline, but now at stage 2 some key restrictions are imposed over both who
is allowed to punish and whom punishers can punish5 : player i is entitled to sanction player j in stage 2 only if, at stage 1,
g i > g j . Therefore, only virtuous participants (i.e. relatively high contributors) earn the right to sanction and only free riders
(i.e. relatively low contributors) can be sanctioned. This implies that punishment has to be ‘prosocial’ and that antisocial
punishment is not permitted,6 so that high contributors are (partially) immune from punishment, as they cannot be sanctioned by players who contributed less or the same amount as them. While under legitimate centralized punishment it is
one’s belonging to the institution itself that entitles one to sanction others,7 under legitimate peer punishment it is one’s
behavior that entitles her to punish her peers. These assumptions are in line with what happens within several naturally
occurring environments like the ones recalled in the Introduction, where it is often the case that the social acceptance of
punishment is conditional on (i) the punisher being entitled to punish and (ii) the punishee being a wrongdoer and, therefore, deserving to be punished. When these two requirements are met, we say that punishment is legitimate (i.e. a principle
of legitimacy holds). Like in a standard, finitely repeated VCM with punishment options, insofar as all the subjects are supposed to be driven by material self-interest only and this information is common knowledge, the unique subgame perfect
equilibrium is for all agents to never punish and never contribute.
The difference between the two treatments regards the feedback that subjects receive at the end of stage 1, in each
period: while in the Full R. subjects are informed about the whole contribution vector (like in the Baseline), in the Partial R.
subjects are informed only about the average contribution level and the specific contribution levels of their group co-players
who contributed strictly less than them. Therefore, in the latter treatment no specific information about more virtuous peers
5
It is important to make clear that we never used loaded terms such as ‘legitimacy’, ‘punishment’ and ‘free riding’ during the experiment.
Related papers where punishment is not unrestricted include Casari and Plott (2003), Casari and Luini (2009), Xiao and Kunreuther (2012) and Carpenter
et al. (2012). Some recent studies have concentrated on institutions which derive their legitimacy from a process of endogenous choice (Gürerk et al., 2006;
Ertan et al., 2009; Kosfeld et al., 2009; Sutter et al., 2010).
7
In turn, the possibility for a person to be hired by a legitimate centralized punishing institution often depends on one’s previous conduct. For example,
in many countries, you need to have a clear criminal record to apply for jobs such as police officer or judge, where you will need to punish violators
on a daily basis. For a recent theoretical and laboratory analysis of the ‘hired gun’ mechanism in a public goods game setting, see Andreoni and Gee
(forthcoming).
6
M. Faillo et al. / Games and Economic Behavior 77 (2013) 271–283
275
Fig. 1. Average contributions.
(if any) is provided to the players. The reason why we also studied this third treatment is that we conjectured that the
impact of legitimate punishment on cooperation could also depend on the amount of information about others’ behavior,
a variable which in the last years has been receiving growing attention among experimental economists within the rich
punishment literature,8 and which could have a significant influence on the perception of the legitimacy of the sanction.
4. Results
4.1. Contribution levels
Fig. 1 displays the time pattern of average contributions by period in the three treatments.
In neither treatment does average contribution decline over time. In particular, comparing the first five and the last five
periods in the Baseline and in the Partial R., we do not observe significant differences in average contributions (Wilcoxon
Rank-sum Test with group averages as independent observations: Baseline z = −0.46, p-value: 0.64; Partial R. z = 0.73,
p-value = 0.46), while in the Full R. contributions increase over time (the average contribution of the last five periods is
significantly higher than that of the first five periods; Wilcoxon Rank-sum Test: z = −2.09, p-value = 0.03).
Result 1. Punishment prevents the decline of cooperation over time in all the treatments.
Besides this well-known general positive effect of punishment, our data (Table 3) show that, given the same type of
restrictions over the punishment activity, subjects who are informed about the contributions of all the other members of
their group (Full R. treatment) contribute significantly more than subjects who are informed only about the average contribution of their group and on less virtuous peers’ contributions (Partial R. treatment) (Wilcoxon Rank-sum Test with group
averages as independent observations: z = 2.43; p-value: 0.014). At the same time, given the same level of information,
contributions in the Full R. are on average significantly higher than contributions in the Baseline (z = 2.61; p-value: 0.008).
The introduction of restrictions on the punishment activity has a positive effect on the level of contributions. Results 2
and 3 follow.
Result 2. The introduction of restrictions significantly increases the level of cooperation.
Result 2 indicates that legitimacy effectively raises cooperation, compared to unrestricted punishment.
It is worth noting that this finding is not an obvious one, as in previous public goods game experiments with punishment
options it was the case that exogenously introducing institutional changes turned out to backfire, leading to lower cooperation and less efficiency (see e.g. Fuster and Meier, 2010). In general, it is not possible to rule out that external interventions
8
See on this Carpenter (2007), Nikiforakis (2010), Fudenberg and Pathak (2010), Grechenig et al. (2010), Xiao and Houser (2011) and Ambrus and Greiner
(forthcoming).
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M. Faillo et al. / Games and Economic Behavior 77 (2013) 271–283
Table 3
Mean contributions.
Group
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Mean
Baseline
Partial R.
Full R.
13.76
(7.34)
18.40
(3.31)
4.94
(1.32)
11.30
(4.03)
12.85
(4.04)
4.58
(2.95)
6.46
(0.85)
2.18
(0.72)
4.39
(2.37)
1.64
(0.94)
2.84
(2.11)
15.13
(4.77)
7.05
(1.63)
11.11
(2.95)
16.06
(3.26)
4.05
(3.75)
3.43
(1.59)
5.44
(0.85)
1.74
(2.21)
9.59
(1.85)
19.20
(2.20)
3.70
(2.79)
14.50
(2.03)
3.10
(1.01)
15.06
(5.37)
9.53
(1.97)
8.63
(3.39)
3.89
(1.17)
18.69
(3.40)
10.76
(2.19)
16.90
(2.38)
0.81
(0.33)
18.34
(1.67)
17.70
(3.51)
5.69
(3.54)
18.91
(2.68)
16.85
(3.42)
18.95
(2.28)
13.73
(4.63)
14.38
(3.24)
13.56
(1.96)
18.09
(2.29)
8.42
8.33
14.53
Standard deviations in parentheses.
(including the introduction of sanctions themselves) end up undermining intrinsic motivations to engage in prosocial behaviors (see Bowles and Hwang, 2008 and Carpenter et al., 2009). In their survey on motivational crowding theory, Frey and
Jegen (2001) point out that, according to a psychological mechanism such as the ‘impaired self-esteem’ process, external
regulations may induce intrinsically motivated individuals to feel as if their intrinsic motivation to behave prosocially is not
acknowledged and, as a consequence of this, they may act less cooperatively. Therefore, in principle, in our setting it was not
possible to rule out ex ante that an institutional restriction exogenously prohibiting antisocial punishment could undermine
virtuous subjects’ intrinsic motivations to punish prosocially due to an impaired self-esteem process. However, our finding
does not offer support for this conjecture.
Result 3. In the presence of restrictions, when partial information over other contributions is provided, a significant decrease in cooperation occurs.9
These results are supported by the regression analysis10 reported in Table 4, which takes into account the effect of a set
of control variables and sheds further light on the role of restrictions and information in shaping contribution levels.
4.2. Punishment behavior
As Result 2 shows, the introduction of restrictions in the aim of preventing the assignment of punishment points to
virtuous subjects results in higher contribution levels. In order to account for this evidence we shall give a closer look at
the punishment activity in the three treatments and assess the impact of antisocial punishment in the Baseline.
With regard to the distribution of punishment points, in all the treatments we observe the typical decreasing pattern,
which is faster in the Full R. (Fig. 2). The difference between the average quantity of points assigned in the three treatments
is not statistically significant (Table 5) (Wilcoxon Rank-sum Full R. vs. Partial R.: z = −1.19; p-value = 0.23; Wilcoxon Ranksum Full R. vs. Baseline: z = −0.87; p-value = 0.38).
9
The levels of contribution observed in the Partial R. and in the Baseline are not significantly different (Wilcoxon Rank-sum Test with: z = −0.046;
p-value: 0.96). Note however that a direct comparison between the Baseline and the Partial R. is not particularly useful, since Partial R. differs from the
Baseline both for the presence of restrictions and for the quantity of information provided to the subjects.
10
All the estimations have been carried out with STATA 11.
M. Faillo et al. / Games and Economic Behavior 77 (2013) 271–283
277
Table 4
Determinants of contribution levels.
Contribution
Random Effects Tobit
Partial R.
−8.11∗∗∗
(2.82)
−8.60∗∗∗
(3.17)
2.04
(7.32)
Baseline
Constant
Log-likelihood
Chi(2)
No. of obs.
−7685.39
25.72
3360
Random Effects Tobit (bootstrapped clustered standard errors
in parentheses).
The dependent variable takes values from 0 to 20. Baseline:
dummy variable taking value 1 if the treatment is the Baseline treatment; Partial R. dummy variable taking value 1 if the
treatment is the Partial R. treatment.
Controls: age, nationality, major, gender and number of experiments in which the subject has been involved in the past.
Estimation of a Tobit model with clustered standard errors and
pooled data gives similar results.
∗∗∗ Significant at 1%; ∗∗ significant at 5%; ∗ significant at 10%.
Fig. 2. Average quantity of punishment points given.
However, it is worth noting that in the Baseline a non-negligible percentage (about 20%) of punishment points are assigned to virtuous subjects. Table 6 reports the absolute quantities (column 2) and the percentage (column 3) of punishment
points assigned in the Baseline by a subject i to a subject j when the contribution of i is smaller than the contribution
of j. We define this type of behavior as “weak antisocial punishment”, as distinguished from “strong antisocial punishment”.
The latter is observed when i punishes another subject j whose contribution is greater than both the contribution of i and
the average contribution of the group (columns 4 and 5). In our sample 19.5% of the overall punishment activity (number of punishment points assigned in all periods) can be classified as weakly antisocial, while 12.2% is strongly antisocial.
On average 14.4% of group’s punishment points assigned is weakly antisocial and 9% is strongly antisocial.
The presence of a strong form of punishment of virtuous subjects (strong antisocial punishment) in the Baseline emerges
also in Fig. 3, which displays the relationship between the distance from the average contribution of the group and the
average quantity of points received. In the Baseline, in some cases strong positive deviations are still punished. This evidence
is supported by the results of the regression analysis reported in Table 7.
While in all the treatments the quantity of punishment points received decreases as the negative distance from the
average increases, the positive distance from the average has a significant effect on the quantity of points received only in
the two treatments with restrictions.
Result 4. When the punishment activity is unrestricted, a significant percentage of points are assigned also to subjects who contribute
more than the punisher (weakly antisocial punishment) and in some cases also to the most virtuous subjects (strongly antisocial
punishment).
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M. Faillo et al. / Games and Economic Behavior 77 (2013) 271–283
Table 5
Average number of punishment points given per period.
Group
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Mean
Baseline
Partial R.
Full R.
0.39
(0.59)
0.53
(1.04)
0.03
(0.08)
0.56
(0.53)
0.75
(0.89)
0.90
(1.05)
0.31
(0.62)
0.56
(0.45)
1.66
(1.10)
2.26
(0.81)
1.65
(1.04)
0.19
(0.25)
1.63
(0.77)
1.54
(0.37)
0.93
(1.05)
0.78
(0.52)
0.25
(0.43)
0.54
(0.53)
0.85
(0.82)
1.06
(1.33)
0.18
(0.46)
0.98
(1.06)
1.20
(0.85)
0.83
(0.49)
0.53
(0.51)
0.69
(0.63)
1.53
(0.78)
0.53
(0.47)
0.31
(0.83)
0.93
(0.78)
0.48
(0.57)
0.26
(0.27)
0.58
(0.73)
0.79
(2.10)
0.48
(1.29)
0.31
(0.76)
0.60
(0.67)
0.55
(0.93)
0.60
(0.39)
1.18
(0.75)
1.06
(0.77)
0.34
(0.36)
0.77
0.93
0.60
Standard deviations in parentheses.
Table 6
Antisocial punishment (A.P.) in the Baseline.
Group
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Total
Mean
(1)
Points given by i to j
29
42
2
45
59
72
25
45
133
181
132
15
130
123
1033
73.79
(2)
Weak A.P.
Contri < Contr j
5
0
0
12
10
29
0
2
5
48
18
0
66
7
202 (19.5%)
14.43
(3)
% Weak A.P.
17.2%
0.0%
0.0%
26.7%
16.9%
40.3%
0.0%
4.4%
3.8%
26.5%
13.6%
0.0%
50.8%
5.7%
14.71%
(4)
Strong A.P.
Contr j > Contri and
Contr j > AV_contr
5
0
0
8
3
16
0
1
3
36
7
0
41
6
126 (12.2%)
9.00
(5)
% Strong A.P.
17.2%
0.0%
0.0%
17.8%
5.1%
22.2%
0.0%
2.2%
2.3%
19.9%
5.3%
0.0%
31.5%
4.9%
9.17%
Result 4 is coherent with the higher level of contributions observed in the Full R., where both weakly antisocial and
strongly antisocial punishment are ruled out. Higher contributions in the Full R. also result in a higher level of efficiency
(Fig. 4). Taking group average earnings as independent observations, we observe that average earnings in the Full R. are
significantly higher than average earnings both in the Baseline (Wilcoxon Rank-sum Test: z = 2.52; p-value: 0.011) and in
the Partial R. (Wilcoxon Rank-sum Test: z = 2.89; p-value: 0.003).
Result 5. Average earnings are significantly higher when punishment is restricted and subjects have information on the contributions
of all the other members of their group.
M. Faillo et al. / Games and Economic Behavior 77 (2013) 271–283
279
Fig. 3. Average quantity of punishment points received as a function of the distance from the average of the group.
Table 7
Determinants of the quantity of punishment points received.
Received points at t
Baseline
Partial R.
Full R.
Positive distance from average
0.04
(0.10)
0.91∗∗∗
(0.13)
−0.60
(2.35)
−0.79∗∗∗
−0.98∗∗∗
(0.21)
0.60∗∗∗
(0.13)
−3.41∗∗
(1.81)
(0.23)
0.64∗∗∗
(0.10)
0.03
(1.68)
−1154.06
115.69
1120
−1128.12
96.28
1120
−874.43
90.42
1120
Absolute negative distance from average
Constant
Log-likelihood
Wald Chi(2)
No. of obs.
Random Effects Tobit (bootstrapped clustered standard errors in parentheses).
The dependent variable takes values from 0 to 30.
Positive distance from average is the difference between subject’s contribution and the average contribution of the
group; it takes value equal to zero when the subject contributes less than the average. Absolute negative distance
from average is the difference between average contribution of the group and subject’s contribution; it takes value
equal to zero when the subject contributes more than the average. Controls: age, nationality, major, gender and
number of experiments in which the subject has been involved in the past.
Estimation of a Tobit model with clustered standard errors and pooled data gives similar results.
∗∗∗ Significant at 1%; ∗∗ significant at 5%; ∗ significant at 10%.
Fig. 4. Average earnings (tokens).
4.3. Determinants of changes in individual contributions
A closer look at the data provides hints for why legitimate punishment effectively raises cooperation and welfare. As we
have shown in the previous subsections, the three treatments are significantly different in terms of contributions levels, but
not in terms of punishment points assigned. Hence, an analysis of the effects of punishment in altering contribution levels
280
M. Faillo et al. / Games and Economic Behavior 77 (2013) 271–283
Table 8
Determinants of the change in contribution levels.
Contribution at t – contribution at t − 1
Distance from average at t − 1
Points received at t − 1
Constant
Log-likelihood
Wald Chi(2)
No. of obs.
Below the average in t − 1
Not below the average in t − 1
Baseline
(1)
Partial R.
(2)
Full R.
(3)
Baseline
(4)
Partial R.
(5)
Full R.
(6)
−0.59∗∗∗
(0.10)
0.09
(0.09)
1.57
(2.15)
−0.49∗∗∗
(0.08)
0.50∗∗∗
(0.10)
−0.11
(3.17)
−0.78∗∗∗
(0.13)
0.60∗∗∗
(0.12)
−3.98
(2.27)
−0.78∗∗∗
(0.18)
−0.86∗∗
(0.33)
−1.38
(2.15)
−0.64∗∗∗
(0.12)
−0.02
(0.44)
3.13
(1.40)
−0.42∗∗
(0.17)
0.86∗∗
(0.37)
−0.56
(2.27)
−1165.19
43.92
468
−1194.05
92.33
456
−931.65
208.98
329
−1490.16
59.36
596
−1550.95
42.09
608
−1929.30
46.95
735
Random Effects Tobit (bootstrapped clustered standard errors in parentheses).
The dependent variable takes values from −20 to 20.
Distance from average at t − 1 is the difference between subject’s contribution at t − 1 and the average contribution of the group at t − 1.
Controls: age, nationality, major, gender and number of experiments in which the subject has been involved in the past.
Estimation of a Tobit model with clustered standard errors and pooled data gives similar results.
∗∗∗ Significant at 1%; ∗∗ significant at 5%; ∗ significant at 10%.
is in order. In particular, we test whether high contributors’ and low contributors’ reactions to sanctioning are different.11
Having observed that a non-negligible share of punishment activity in the treatment without restrictions can be classified
as antisocial, we shall investigate whether this punishment has also a perverse effect on the contribution level of the most
virtuous members of the group – i.e. whether it weakens their willingness to cooperate. In order to do this, we estimated
a Random Effects Tobit model for each treatment, distinguishing between subjects whose contribution is below the average
contribution of the group and subjects whose contribution is equal or greater than the average of the group.
Table 8 also shows a regression to the mean in all the treatments observed also by Denant-Boemont et al. (2007): the
higher the distance from the average in the previous period, the higher is the absolute increase of the contribution level in
the current period.
Result 6. In all the treatments, regardless of the presence of restrictions, the increase in contribution levels is stronger the higher the
distance from the average in the previous period.
Result 7a. Punishment has a positive effect on low contributors’ willingness to cooperate only in the presence of restrictions (columns 2
and 3 of Table 8).
Result 7b. Punishment exerts a negative effect on high contributors’ willingness to cooperate in the Baseline treatment (column 4),
while it has a positive effect in the case of high contributors in the treatment with full information and restrictions (column 6).
Result 7a interestingly reveals that free riders who are punished in a given period increase their contribution in the
subsequent period only insofar as punishment is legitimate. This occurs both in the Full R. and in the Partial R. A possible
interpretation is that under this institution free riders feel bad for not adopting the situationally appropriate behavior (Ross
and Nisbett, 1991; see on this also Hopfensitz and Reuben, 2009) and positively react to what they perceive as a signal of
disapproval on the part of their virtuous peers. This would be in line with the ‘incentives-as-signals’ hypothesis suggested by
Bowles and Polania-Reyes (2012) as well as with Masclet et al. (2003), who analyze the effect of non-monetary sanctions and
find that free riders who receive more disapproval points significantly increase their contributions in the next period. As far
as high contributors are concerned, Result 7b indicates that under full information their reaction to received punishment
crucially depends on the nature of the sanctioning system at work: insofar as they perceive punishment as legitimate,
virtuous players (like free riders) are ready to enhance cooperation, whereas their willingness to contribute decreases under
a ‘vigilante justice’ institution where antisocial punishment is permitted.12
Finally, in the aim of exploring the role of feedback about others’ behavior in shaping contribution reactions to punishment, for each treatment we estimate a Random Effects Tobit model by considering only the subsample of subjects whose
contribution in the previous period was not the highest. We run two separate estimations, by distinguishing between subjects whose contribution level in the previous period is below the average of the group and subjects whose contribution
level in the previous period is above the average of the group (Table 9). In the case of subjects with contribution levels
11
The reason why we separately analyze low contributors’ and high contributors’ behavior is that we expect a legitimate punishment institution to
differentially impact them, compared to an unrestricted punishment scheme.
12
This is in line with Herrmann et al. (2008) and Ambrus and Greiner (forthcoming), showing that subjects who were ‘unfairly’ punished were less likely
to contribute in the next round. On the detrimental effects of unfair sanctions, see also Fehr and Rockenbach (2003).
M. Faillo et al. / Games and Economic Behavior 77 (2013) 271–283
281
Table 9
Impact of information about highest contributions in the group.
Contribution at t – contribution at t − 1
Distance from average at t − 1
Distance from the highest contribution at t − 1
Points received at t − 1
Constant
Log-likelihood
Wald Chi(2)
No. of obs.
Below the average in t − 1
Not below the average in t − 1
Baseline
(1)
Full R.
(2)
Baseline
(3)
Full R.
(4)
−0.83∗∗∗
(0.15)
−0.12∗∗
(0.06)
0.08
(0.10)
1.63
(3.33)
−0.66∗∗∗
(0.34)
0.08
(0.14)
0.59∗∗∗
(0.11)
−3.81
(2.46)
−0.52
(0.32)
−0.06
(0.13)
−0.51
(0.37)
5.64
(4.56)
−1.64∗∗∗
(0.64)
0.27∗∗∗
(0.08)
0.10
(0.61)
9.08
(4.77)
−1163.40
83.71
468
−931.33
176.09
329
−367.37
19.91
152
−306.42
45.37
127
Random Effects Tobit (bootstrapped clustered standard errors in parentheses).
The estimation is limited to the sub-sample of subjects whose contribution in the previous period was not the highest of the group. The dependent variable
takes values from −20 to 20.
Distance from average at t − 1 is the difference between subject’s contribution at t − 1 and the average contribution of the group at t − 1.
Distance from highest at t − 1 is the absolute difference between subject’s contribution at t − 1 and the highest contribution of the group at t − 1.
Controls: age, nationality, major, gender and number of experiments in which the subject has been involved in the past.
Estimation of a Tobit model with clustered standard errors and pooled data gives similar results.
∗∗∗ Significant at 1%; ∗∗ significant at 5%; ∗ significant at 10%.
below the average, information on the most virtuous peers per se does not affect the increase in contributions in the Full R.
(column 2 of Table 9), i.e. in the treatment where the vector of peers’ contribution is available, antisocial punishment is
ruled out and subjects have the possibility to use virtuous peers’ behavior as a reference point. The evidence on the Baseline is particularly interesting. In this case, for subjects who contribute below the average, the distance from the virtuous
subjects exerts a significant and negative effect on the change in contribution levels (column 1): the lower the subject’s contribution at t − 1 with respect to the highest contribution of her group at t − 1, the lower the increase in her contribution
moving from t − 1 to t. These subjects seem to strategically use the information on most virtuous peers to infer the extent
to which they can behave as free riders: the more altruistic their peers are, the more profitable the choice of behaving as
a free rider. In other words, in the Baseline, the information about the highest contributors is (opportunistically) interpreted
by the less virtuous subjects as the assurance that someone else is carrying the burden of the public good, so that there is
no need to do the same.
With regard to subjects who contribute above the average, in the Baseline the information about the highest level
of contribution in the group exerts neither a positive nor a negative significant effect on the increase in contributions
(column 3). In the Full R., the highest level of cooperation is taken as a reference point: the information about the highest
level of cooperation exerts a significant and positive effect on the increase in contributions (column 4).
Result 8. In the full information treatment with restrictions, subjects who contribute above the average of the group use the highest
contribution level in the group as a reference. In the full information treatment without restrictions, subjects who contribute below the
average of the group use the information on the most virtuous members strategically to infer the potential gain from free riding.
5. Conclusion
Legitimate peer punishment is a ubiquitous phenomenon within several real-life domains, from teamwork and scientific
research evaluation to neighborhood watch programmes and warfare communities. Yet, so far there was no clean evidence
concerning the effects of legitimacy-based sanctioning institutions and feedback on cooperation. Our work contributes to fill
this gap by means of a specially designed public goods game where antisocial punishment is prohibited.
We claim that our results yield relevant efficiency implications for the design of mechanisms intended to deter misconduct. By taking a behavioral mechanism design perspective, we wondered whether a legitimacy-based institution would
be conducive to significantly higher cooperation levels, compared to the classic VCM with unrestricted punishment options,
despite the lack of additional monetary incentives to cooperate and punish. Our results confirm that this is indeed the case,
as we provide evidence that legitimate sanctioning leads to substantial benefits to cooperation and higher welfare levels.
Thus, the effectiveness of using sanctioning mechanisms to encourage contributions to public goods appears to crucially
depend on the nature of the punishing institution at work: legitimate punishment turns out to combine the key advantages
of decentralized punishment (detecting wrongdoers is usually difficult because the relevant information on where and when
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M. Faillo et al. / Games and Economic Behavior 77 (2013) 271–283
wrongdoing occurs is hidden to central authorities13 ) with the key advantages of centralized punishment (which is usually
‘legitimate’ and, therefore, can easily rule out antisocial punishment).
Our findings suggest that (both virtuous and non-virtuous) individuals positively react to the presence of restrictions
allowing for legitimate punishment only. They complement results in a number of recent papers focusing on the ‘expressive
power’ of formal institutions, that is the positive signaling effects that some institutional arrangements can exert by relying
on subjects’ intrinsic motivations to act prosocially (see e.g. Galbiati and Vertova, 2008 and Cooter, 2000). In particular, our
data provide support for the view that also punishment institutions may have an expressive power, as they can influence
behavior not only by affecting material payoffs (as the classic optimal deterrence view maintains), but also by shaping
players’ perception of the environment in which they operate (Gneezy and Rustichini, 2000; Fehr and Rockenbach, 2003)
as well as by expressing cooperation norms (Masclet et al., 2003; Xiao, 2013).
We also show that the interaction between behavioral restrictions and feedback matters: exactly knowing what virtuous
peers are doing seems to be crucial for the success of a legitimacy-based institution. A plausible interpretation of this
finding is that people look to their peers for guidance, as the socially appropriate action to be taken within the game is
not obvious. This is in line with available empirical evidence on horizontal relationships in the workplace, indicating that if
a worker makes very little effort compared to her partner, she may induce resentment or face legitimate sanctions from her
(Mas and Moretti, 2009). Our result is also consistent with previous studies on the role of ‘leading by example’ in charitable
fundraising (Vesterlund, 2003) and social dilemma settings (Güth et al., 2007) as well as with a recent field experiment
documenting a positive impact of social information on the voluntary provision of public goods (Shang and Croson, 2009).
Finally, this paper leaves interesting avenues for further research, including the relative effectiveness of other legitimacybased enforcement devices (e.g. based on positive incentives to cooperate), the robustness of our major findings across
alternative designs as well as the performance of this mechanism across different cultural contexts. In this regard,
we speculatively argue that legitimate punishment institutions might turn out to be even more effective, compared to
vigilante justice, within developing societies, as recent research on cross-cultural differences (Herrmann et al., 2008;
Gächter and Herrmann, 2011) reveals that the level of antisocial punishment here is far higher than in industrialized countries.
Acknowledgments
We thank the associate editor and three anonymous referees whose comments helped us significantly improve the paper.
Our gratitude also goes to Manolo Ferrante, Laura Magazzini, Francesco Manaresi, Nikos Nikiforakis, Louis Putterman, Robert
Sugden, Chiara Tomasi, Giuseppe Vittucci and to the participants in the ESA conferences in Copenhagen and Luxembourg,
the 2010 IAREP/SABE Conference in Köln, the 2010 EALE Conference in Paris, the 2011 IMEBE Conference in Barcelona,
the 2011 Urrutia Elejalde Summer School in San Sebastian, the 2011 SIE Meeting in Rome, the workshops in Maastricht,
Siena and Southampton and the colleagues of the Departments of Economics of the Universities of Verona, Siena, Padova,
Florence, Trento and Cagliari for useful suggestions and comments. The usual caveats apply. We gratefully acknowledge the
Italian Ministry of Education, University and Research (2008 Prin project on “Social Capital, Corporate Social Responsibility
and Performance” – Padova unit) and the Departments of Economics of the Universities of Trento and Verona for financial
support.
Supplementary material
The online version of this article contains additional supplementary material.
Please visit http://dx.doi.org/10.1016/j.geb.2012.10.011.
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