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ORIGINAL ARTICLE
Cooperation through collective punishment
and participation
Dominik Duell1, Friederike Mengel2, Erik Mohlin3,4 and Simon Weidenholzer2
1
Department of Political Science, University of Innsbruck, Innsbruck, Austria,
2
Department of Economics, University of
Essex, Colchester, UK,
3
Department of Economics, Lund University, Lund, Sweden and
4
The Institute for Futures Studies,
Holländargatan 13, 111 36 Stockholm, Sweden
Corresponding author: Dominik Duell; Email: dominik.duell@uibk.ac.at
(Received 6 January 2023; revised 26 May 2023; accepted 11 July 2023)
Abstract
We experimentally explore the role of institutions imposing collective sanctions in sustaining cooperation.
In our experiment, players only observe noisy signals about individual contributions in finitely repeated
public goods game with imperfect monitoring, while total output is perfectly observed as it is often the
case in collective action problems in society. We consider sanctioning mechanism that allows agents to
commit to collective punishment in case the level of cooperation among members of society falls short
of a target. We find that cooperation is higher with collective punishment compared to both no punish-
ment or punishment targeting individuals. Importantly, our results indicate that it is the combination of
making a commitment to be punished and the collective nature of punishment which induces cooper-
ation. Our findings show that punishing a group collectively for misbehavior of some of its members
induces cooperation when individuals participate in setting up the sanctioning institution. The study con-
tributes to the literature on institutional legitimacy and how to ensure good government performance
when dealing with collective action problems, and, by considering commitment, improves enforcement
methods criticized for their detrimental effects on some societal groups.
Keywords: collective action; collective sanctions; imperfect; participation; public goods game
1. Introduction
Sanctioning a group for the misconduct of some of its members is a common feature of how societies
are governed. Particularly in situations where individual cooperation cannot be easily detected, col-
lective punishment is an often employed enforcement regime. Historical examples include explicit
punishment in military and educational institutions, such as the ancient Roman practice of decima-
tionwhereoneintensoldiersofamilitaryunitwasrandomlychosentobeexecuted.Morecontem-
poraneously, fencing off a park, restricting access to a private road, or imposing curfews during a
pandemic as response to a small number of trespassers are frequently encountered policies. While
the ability to sanction has been shown to increase cooperation among members of many types of
groups (Ostrom et al.,1992), collective sanctioning is deemed less effective because it is usually
seen as unfair and crowds-out intrinsic motivation to comply. Collective punishment is particularly
contested and often even said to be counterproductive when carried out as racial profiling in policing
(Gelman et al.,2007), indiscriminate retaliation for terror attacks (Bueno de Mesquita and Dickson,
2007), or economic sanctions imposed on rogue regimes that hurt the civilian population (Gordon,
1999; Allen and Lektzian, 2013). We know, however, that the origins and kind of authority to carry
out punishment matters greatly (Dickson et al.,2015,2009), that sanctioning institutions established
© The Author(s), 2023. Published by Cambridge University Press on behalf of EPS Academic Ltd. This is an Open Access article, distributed
under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted
re-use, distribution and reproduction, provided the original article is properly cited.
Political Science Research and Methods (2023), page 1 of 27
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by a community through elections is seen as effective in inducing high levels of cooperation (Miguel
and Gugerty, 2005; Grossman and Baldassarri, 2012), in particular when democratically chosen
authorities stand repeated elections (Castillo and Hamman, 2021). And, we know that individual
actors are very willing to cooperate when the sanctioning institution is committed to credibly
carry out enforcement—especially in the long-run—as stipulated by its rules (Baldwin, 2013,
2019), or when such institution arose endogenously (Kosfeld et al.,2009; Markussen et al.,2014).
This leads us to ask, particularly in situation where individual behavior is hard to observe,
whether collective sanctioning can be effective in inducing successful collective action when it
is paired with commitment to be punished as a group as well as with individuals’participation
in the decision to establish such sanctioning institutions. Commitment to be punished constitutes
self-selection of individuals into a group or institution that is governed by a sanctioning regime.
Such institutions frequently exist: citizens in democratic regimes are subject to collective sanctions
(e.g., restrictions to consuming certain goods as response to misbehavior of a few) but would have
the option to exit (Warren, 2011) from this institutionalized pool punishment institution (Hilbe
et al.,2014), where individualized punishment is often explicitly forbidden (Balafoutas and
Nikiforakis, 2012). Other examples of organizations featuring self-selection into collective sanc-
tioning mechanism include labor unions engaged in collective bargaining where all of the union
can be held liable for the breach of industrial action regulations by some of its members (Bruun
and Johansson, 2014), credit unions where a few defaulting on their loans increases fees for all
members (Wheelock and Wilson, 2013), or condominium associations, which force their mem-
bers to build a fund for repairing damages incurred through the negligence of some (Van Der
Merwe, 2015). Importantly, the threat to carry out the collective sanction is credibly ensured
in any of these institutions, at least in developed societies, through legal provisions and contracts.
To answer whether collective sanctioning with commitment benefits collective action, we
study finitely repeated public goods games in a laboratory experiment where individual actors
receive noisy signals on the contributions of others but the sum of contributions is observed with-
out noise. Our treatments then vary the punishment technology individual actors have at their
disposal. We compare individuals’contribution and groups’welfare under the possibility for
the individual actors to commit to an ex-ante known regime of collective punishment of the
whole group to: simple collective punishment by a randomly chosen authority from among
the group; peer-to-peer punishment committed to by each individual actor and targeting the
individual for their behavior; non-committed peer-to-peer punishment; or, no punishment
altogether. The laboratory allows to make all individual action, including non-cooperation,
observable to the researcher—a situation that rarely occurs in the real world.
Imagine any group that aims to cooperate for achieving successful collective action, be it a
democratic society, a labor union, a credit union, condominium association, or any group of indi-
viduals with a common objective; further, consider a situation where information about the con-
tribution of each individual to the common objective is not perfect. The sanctioning technologies
we instantiate in the laboratory, then, mimics incentives that exist in interactions in all such
groups in the real world. What are these technologies and incentives? Individuals may punish
their peers on their own accord. Such peer-to-peer punishment could be based in law (e.g., as
a result of a civil court decision) or simply public shaming for not working toward the collective
goal. A game-theoretic analysis will tell us that, in equilibrium, no punishment should ever be
carried out and no contributions to the public goods should be made. At the point of decision
whether to contribute to the group goal, group members simply cannot credibly commit to pun-
ishing a perpetrator ex-post. Empirically, we often observe such individual punishment, often
even in excess and of those who actually contributed, leading to detrimental outcomes for the
welfare of the group. Avoiding the empirically observed excessive punishment but also the the-
oretically suggested commitment problem, a solution for this might be if we ask individuals to
commit to acting against their peers for not putting sufficient amount of effort into reaching
common goals. Committing to such punishment, in equilibrium, leads only to increased
2 Dominik Duell et al.
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compliance if the signals about who is free-riding or in violation of what is being expected is pre-
cise. In many cases, as argued, our information about who is not cooperating is not precise.
Which co-worker steals from the fridge in the common room, which neighbor is dumping
trash beyond what is taken away by public services, or which resident is trespassing in a natural
preserve is often not observed, only the consequences of those actions are. Once we lack infor-
mation, peer-to-peer punishment, even if individuals committed to it ex-ante, will often fail to
be carried out because we may not be able to identify the individual perpetrator. In these situa-
tions, if sanctions ought to be applied, punishing everyone is left as the only feasible option. The
fridge in the common room is taken away, public services increase fees for the whole building,
and the natural preserve is fenced off. Will such collective punishment increase cooperation?
The theoretical expectation would be no, since contributions are predicted to stay at zero and
no punishment is carried out. Again, empirically, we observe punishment of all, with similarly
bad consequences for the welfare of the group as with peer-to-peer punishment but additionally
putting a burden on the group and the institutions governing it because many contributors may
be sanctioned as well. Collective committed punishment solves, once more, the commitment
problem but will only avoid the problematic sanctioning of contributors if it induces high enough
levels of contributions leading to no punishment.
Indeed, we find empirically that both contribution rates and welfare are higher in the presence
of the possibility to commit to collective punishment than under either the absence of the pos-
sibility to punish or non-committed peer-to-peer punishment. Further, while welfare levels are
constant in the presence of the possibility to commit to collective punishment, they are steadily
decreasing in the other two cases. This points toward positive long-run welfare effects of being
able to commit to collective punishment. The combination of the participation in the decision-
making whether punishment occurs and social commitment to the punishment outperforms any
other form of sanctioning or the absence of punishment altogether in sustaining cooperation.
While contribution and payoff levels are in line with the no-punishment benchmark when no
punishment is committed, they are significantly higher when punishment is committed.
Our study speaks to a broad set of questions: which institutions are seen as more legitimate,
which institutions enable good government performance, and which institutions reduce inequal-
ities in policy outcomes? The ability to participate in the decision-making process of institutions
that govern individual lives increases system support (Finkel, 1987; Bowler and Donovan, 2002).
An observation that has been experimentally tested with respect to what sanctioning institutions
are seen as legitimate and which are successful in ensuring cooperation (Dickson et al.,2009,
2015; Grossman and Baldassarri, 2012). We track whether individuals’repeated willingness to
vote for setting-up collective sanctions, a measure of support of the punishment regime, sustains
high levels of cooperation, providing a controlled test of the link between levels of system support
and regime characteristics such as collectiveness and participation. A large literature sees partici-
pation as driver of particularly effective government (Fung and Wright, 2001; Agrawal, 2005) but
concerns are raised whether involvement of too many stakeholders creates bad policy outcomes
due to, for example, being elite dominated (Mansuri and Rao, 2004) or facing a trade-off between
equity and efficiency (Hong and Cho, 2018). The institutions we create in the laboratory vary
whether individuals are involved in setting them up, directly testing whether it is the participation
in the decision how one is governed, i.e., is collective sanctioning implemented, and holding equal
power over choosing the institution, that determines the quality of outcomes. We also provide
new avenues, by considering commitment, to improve those methods of enforcing a policy
that are criticized for their detrimental effect on some societal groups and are demonstrated to
be welfare inefficient in general, such as any kind of profiling or zero-tolerance policies (for a
review see Soss and Weaver, 2017). We deliver empirical evidence how commitment to collective
sanctions sets incentives to monitor and control wrongdoers within one’s group of peers as
debated in international law in particular, as the questions of how to punish groups committing
mass atrocities (Drumbl, 2004), and legal studies in general as the question whether delegation of
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deterring wrongdoing to the group creates better outcomes because it gives agency (Levinson,
2003).
We also add to the experimental literature in political economy, economics, and other behav-
ioral science disciplines that examines factors that may lead to the emergence of high effort equi-
libria in coordination games that model collective action problems (Brandts and Cooper, 2006;
Weber, 2006; Feri et al.,2010; Henrich et al.,2010; Riedl et al.,2015). We demonstrate that col-
lective punishment transforms the underlying public good game into a coordination game. We
contribute to this literature by showing that high effort equilibria may also be reached when
the coordination game is induced by the choice of players, rather than being exogenously given.
1.1 Cooperation under sanctioning with imperfect information
Ensuring compliance or cooperation through sanctioning is generally seen as effective. It is well-
documented in an experimental context that the ability to punish allows societies to move toward
socially optimal levels of compliance and contributions (see, e.g., Ostrom et al.,1992; Fehr and
Gächter, 2000,2002; Gintis et al.,2005). Even a randomly assigned individual singled out to pun-
ish defectors is able to increase contribution and welfare levels (Boyd and Richerson, 1992;
O’Gorman et al.,2009). Despite costly punishment being at odds with selfish preferences, a con-
siderable fraction of individuals is willing to sacrifice own payoffs to punish non-cooperators, a
pattern of behavior also observed in many populations around the world (Henrich et al.,2010).
A key prerequisite for punishment to be effective is the ability to identify non-contributors. If
it is not clear who the free-riders are, it becomes impossible to accurately target them. Perhaps
even worse, from time to time it will be the case that some contributors are falsely identified as non-
contributors and therefore punished. Indeed, a decline in contributions and welfare under imperfect
monitoring is well documented in the experimental literature (see e.g., Bornstein and Weisel, 2010;
Grechenig et al.,2010; Ambrus and Greiner, 2012). Such imperfect monitoring, more generally, is
one of the main reasons why voters are not able to induce behavior among elected officials that ben-
efits society (Powell and Powell Jr, 2000; Tavits, 2007) or for governments, as central authority, to
make citizens to comply with the law or to contribute to public goods easily even under the threat
of sanctioning. A government’s authority to sanction is eroded, in the eyes of citizens, and the incen-
tive for non-compliance rises when imperfect monitoring leads to increased punishment of coop-
erators (Dickson et al.,2009). Even when the punishment comes from one’s peers, sanctioning
cooperators for their pro-social behavior demoralizes and renders punishment as a tool to induce
cooperation useless (Herrmann et al.,2008). Considerations along these lines already two centuries
ago might have lead Blackstone (1966) to assert that “the law holds that it is better that ten guilty
persons escape than that one innocent suffers.”
1.2 Cooperation under a centralized authority or with collective punishment
In contexts where the state is empowered to sanction, such centralized authority is often said to
be effective. Such effectiveness arises, for example, through the legitimacy of the central authority
to carry out punishment (Baldassarri and Grossman, 2011) or by way of domestic backlash for
the regime leader sanctioned by an international authority (McGillivray and Smith, 2000,2006).
Centralizing the sanctioning authority in governmental institutions, however, is often outdone by
decentralized punishment exactly because misattribution is less frequent in the latter. Punishing
effectively relies on the legitimacy of the sanctioning institution (Dickson et al.,2009; Eckel et al.,
2010) undermined by punishing cooperators and not punishing culprits. Decentralization allows
for locally informed punishment avoiding that the bluntness of tools available to a central author-
ity is too clumsy (Ostrom, 1999). The positive effect of when punishment takes place at the local
level even extends back to the centralized authority when it is legitimized internally, for example,
through elections or appointment by the monitored communities (Miguel and Gugerty, 2005;
Grossman and Baldassarri, 2012).
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Independent of whether sanctioning is done by a centralized or decentralized authority, the
target of punishment, the individual actor alone or the whole group, matters as well.
Peer-to-peer punishment is effective but mostly only if done in small groups (Sigmund, 2007;
Taylor, 1982) and it needs the expectation of future interactions for sanctioning to be a threat,
an expectation that is mute in many large-scale societal interactions (Boyd et al.,2010). Legal
studies see collective punishment as a solution to this problem, and deem such sanctioning
tools as justified as well as effective in ensuring compliance and cooperation (Levinson, 2003).
Collective incentives are also an important part of salary schemes in the form of team incentives
(Ledford et al.,1995). There is also some empirical evidence that receiving a bonus lower than an
expected amount decreases individuals’satisfaction (Ockenfels et al.,2014) and that collective
punishment is experienced as unfair (Chapkovski, 2021). Additionally, group outcomes, which
are typically observed in a much less noisy way, anchor sanctions with collective punishment
making the problem of misattribution more severe (Holmström, 1982). Despite these drawbacks,
collective punishment may still play an important role by potentially enhancing welfare levels that
is the overall benefits to all members of society from the plus in cooperation induced by
sanctioning.
1.3 Collective punishment with commitment
Accepting for now that collective punishment potentially overcomes some of the shortcomings of
punishment targeting the individual, even if it generates a different set of problems, which form
of sanctioning then could ensure that collective punishment is seen as legitimate and therefore
effective in triggering cooperation? From above, we take that the process by which an authority
obtains the right to punish is important (Dickson et al.,2009; Grossman and Baldassarri, 2012)
as well as how this monitoring institution benefits from cooperation of others; individuals tend to
show an indirect free-rider aversion, where they want to give less if the monitoring institution
makes money contingently on the cooperation of others (Alventosa et al.,2021).
Participation in the decision-making process whether, whom, and how to sanction has also
been shown to improve cooperation, sometimes by helping the enforcement of the punishment
decision as in Dickson et al. (2009), by sustaining compliance (Cox et al.,2010), or by ensuring
the survival of the sanctioning institution itself (Falleti and Riofrancos, 2018). Still, mixed evi-
dence exists whether voting on the sanctioning authority could be an example of such beneficial
participation. DeCaro et al. (2015) find that the ability to vote on rules improves cooperation but
only if enforcement of compliance is certain, Chang et al. (2018) add that enforcement through
an elected authority is often undermined by, for example, political inequality across individual
actors, and Heap et al. (2020) find that including individuals in collective decisions through giv-
ing “voice”increases cooperation more than through participation in form of a vote. Baldwin
(2013,2019) even show that local decision-makers with centralized authority to punish, i.e.,
chiefs, are better suited to ensure compliance and cooperation than officials elected to represen-
tative legislatures. Specifically, Baldwin argues that the long-time horizon of the chiefs tenure in
ruling a community encourages cooperation. This argument seems to find empirical support in
many developing society concerned with public goods provision (Baldwin and Raffler, 2019).
Note, the suggested mechanism by which compliance or cooperation is ensured is not reliant
on the form of punishment, collective or individualized, but that the commitment to carry out
enforcement is ensured.
1
In general, individual actors are more likely to comply with authority when they are more cer-
tain that others are also likely to do so (Scholz et al.,1995; Scholz and Lubell, 1998), whether that
1
Previous literature from the laboratory documents that also under perfect monitoring the welfare calculations depend
crucially on the time horizon. Since in the short run punishment imposes a cost on individuals, societies might initially
be faring worse than in the absence of the opportunity to punish, as observed by Dreber et al. (2008). However, in the
long run the frequency of punishment decreases and social welfare with punishment may be higher (Gächter et al.,2008).
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joint compliance is ensured by a central authority committed to enforcing any rules or individual
actors committing themselves to be sanctioned before they even make their choice of whether to
cooperate. Authorities and individual members of society often rely on pre-committed sanctions
to save on decision costs (Sunstein and Ullmann-Margalit, 1999) but also for peer-to-peer pun-
ishment specifically, commitment devices are helping the effects of sanctioning. Ostrom et al.
(1992) and Balliet (2010) find peer-to-peer punishment most effective when people were able
to communicate beforehand indicating that a collective norm was established ex-ante. To a simi-
lar effect, when a norm of compliance is perceived as popular or when conformity is enforced,
compliance increases (Centola et al.,2005; Willer et al.,2009). Individuals are willing to sustain
mutual cooperation conditionally on the expectations that others will cooperate as well
(Yamagishi, 1986; Hayashi et al.,1999).
With commitment, individual members of society are now reassured that punishment will be
carried out for sure and that they all hold the same standard. At least two consequences emerge
from this collectiveness: First, it ensures that the second-order free-riding problem, by which ego-
ists let others shoulder the punishment costs, does not arise (Oliver, 1980; Heckathorn, 1989).
Second, as we argue here, when committed punishment is chosen as sanctioning device, the deci-
sion individuals face is driven by collective incentives which transform the underlying collective
action problem, such as a public goods game, into a coordination game. This means that a game
with one equilibrium, nobody contributes, turns into a game with multiple equilibria with one
where everybody contributes. Such equilibrium provides a focal point which allows participants
to coordinate on high contribution in the induced game.
2
In this coordination game, selfish individuals might prefer to contribute if this avoids collect-
ive punishment being imposed. Otherwise, they prefer to not contribute to the public good.
Provided that collective punishment is conditioned on high joint contribution levels qua commit-
ment, the resulting coordination game features, among other equilibria, an equilibrium where
everybody contributes and an equilibrium where nobody contributes. Commitment to collective
punishment opens the opportunity for a configuration where everyone contributes, solving the
underlying collective action problem. Collective incentive schemes alone involve a commitment
problem: once a team has produced a surplus, they have no incentive to destroy it or give it away
(Holmström, 1982). Thus, in the absence of commitment, the efficacy of collective sanctions
hinges on the presence of individuals who are willing to sacrifice own payoffs for punishment.
However, if members of a group can commit in advance to a mechanism that punishes everyone
in case contributions are below a target, then they can effectively decide in advance whether col-
lective action should take place under incentives that turn it into a public goods game or a coord-
ination game.
In this paper, we test which characteristic of the sanctioning regime ensures cooperation in
collective action problems. Following the discussion above, we argue that
the combination of collective punishment and commitment sustains highest levels of cooperation
(Hypothesis).
3
To test our hypothesis, we model a central authority in the laboratory by selecting a subject at
random to determine punishment, in line with the literature (see e.g., Dickson et al.,2009,2015)
and juxtapose such authority with decentralized sanctioning represented by peer-to-peer punish-
ment or no punishment at all. We then allow for collective punishment either by the central
authority or through peers committing to sanctioning when the joint level of cooperation does
not surpass a given threshold. In this way, we arrive at a 2 × 2 experimental design, with an
2
If collective punishment is conditioned on not reaching the full contribution level of the public good, then the resulting
coordination game is strategically similar to a minimum effort coordination game (Van Huyck et al.,1990). For a discussion
of experimental studies of coordination games, see Camerer (2003), chapter 7.
3
The experiment was not pre-registered. All treatments conducted within the research agenda are presented in the main
text or the online appendix and no observations are omitted.
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additional no punishment baseline treatment condition, varying the target of punishment, indi-
viduals or groups, and the existence of commitment to sanction.
2. Public good games with punishment and imperfect monitoring
Questions of cooperation in collective action problems and pro-social behavior are frequently
modeled as public goods game when investigating behavior of politicians or voters more specif-
ically or any members of society in general (see e.g., Ostrom et al.,1992; Baldassarri and
Grossman, 2011; Hamman et al.,2011; Butler and Kousser, 2015). We consider an n-player pub-
lic goods game where each player holds an endowment of eunits. Each agent ican either con-
tribute her entire endowment to the public good or not contribute at all, g
i
∈{0, e}.
4
We denote
the sum of contributions in a group by G=n
i=1gi. Each agent iobserves a noisy signal s
ij
∈
{0, e}=Son the true contribution level g
j
of each other agent j≠i.
5
This signal reveals the
true contribution level with a signal accuracy of Pr (sij =g|gj=g)[(0.5, 1]. By contrast, the
overall level of contributions Gis observed perfectly. We consider the case of a linear return func-
tion which implies that the payoff of iis given by
uPG
i(gi,g−i)=
a
G+(e−gi), (1)
where α, with 1
n,
a
,1, captures the marginal per capita return from contributing to the public
good. If players’utility functions are given by uPG
ithen in the only Nash equilibrium of this game
no player contributes, yielding payoffs of eto everybody.
6
On the other hand, welfare maximiza-
tion dictates contribution levels of efor all participants, resulting in payoffs of αne.
Testing our hypothesis means demonstrating which punishment regimes lead participants to
contribute to the public good and potentially achieve high levels of welfare. To this end, we dis-
cuss and analyze several such punishment regimes added to a public goods game. Some of these
punishment regimes retain the nature of the public goods game with the equilibrium prediction
of no contribution, while some might, depending on the participants’choices, instantiate a coord-
ination game with a no contribution and, among others, a high contribution equilibrium. In this
section, we focus on the predictions of the rational choice benchmark for each of these schemes.
This is done to give the reader a clear sense of the incentives participants face in the different
regimes we consider. Empirically, though, as laid out above, we frequently observe non-zero levels
of contributions in public goods games even when the equilibrium prediction calls for no con-
tribution, making a comparison of behavior across punishment regimes a empirically meaningful
endeavor. Throughout, we illustrate how deviations from this benchmark may lead to different
behavioral predictions and link it to other research which has established further explanations
for the choices observed in the discussion.
2.1 Collective punishment
Our primary focus is on collective punishment, i.e., forms of punishment where all members of a
group are subject to punishment.
7
Whenever a group is collectively punished, Ppoints are sub-
tracted from all members. In addition and in line with the literature, punishment is costly and its
costs are given by βPfor some
b
[R, where typically β< 1. We assume that all members of a
4
Binary contributions allow for a fairly straightforward and for participants comprehensible implementation of imperfect
monitoring (Ambrus and Greiner, 2012).
5
The level of noise was chosen to ensure that there is no symmetric cooperate equilibria in the individual-punishment case.
6
Naturally, if players have conditionally cooperative preferences and are sufficiently motivated by negative reciprocity and
the game is played more than once then cooperation may constitute an equilibrium, at least in early periods.
7
Alternatively, one can think of punishment mechanisms where subsets of agents are randomly singled out for punish-
ment. Provided the expected punishment is the same the analysis does not change for risk neutral decision makers.
However, risk aversion may well amplify the effect of punishing randomly selected agents.
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group share the cost of punishment equally, so that in case of collective punishment each group
members’payoff is lowered by P(1 + β). Due to their supposedly different properties, in particular
with respect to whether individuals see them as legitimate, we focus on two different scenarios,
depending on whether the decision to collectively punish is taken before or after the public goods
game has been played. This corresponds to whether there is a possibility to commit to collective
punishment.
2.1.1 Collective punishment without commitment
Suppose the decision whether to collectively punish is taken after the public goods game has been
played. One agent is drawn at random and decides whether to punish the group.
8
We denote the
chosen agent by jand let pC
j[{0, 1} denote her punishment choice. This gives rise to the follow-
ing payoff function
uC
i(gi,g−i)=
a
G+(e−gi)−pC
jP(1 +
b
).
As the punishment decision is taken after the contribution stage, player jwill decide not to punish
and thus in the only sub-game perfect equilibrium no player will contribute.
If players are motivated by negative reciprocity (i.e., players are not entirely selfish) or if the
players or the players perceive the interaction to be indefinitely repeated rather than finite (i.e.,
players do not have a correct understanding of the game) then there may exist equilibria with
full cooperation.
9
2.1.2 Collective punishment with commitment
In this scenario, there is an institution that allows players to commit to collective punishment
before the public goods game. When participants have committed to collective punishment, pun-
ishment is automatic and contingent on the overall contributions to the public good. More pre-
cisely, everybody will be punished in case the sum of contributions falls short of an exogenously
set target level
G. Otherwise, there is no punishment. This is formalized by the indicator function
1[G,
G]. As above, one randomly selected agent may decide whether collective punishment is
implemented.
10
We denote her choice by pC−Comm
j[{0, 1}. This gives rise to the following payoff
function
uC−Comm
i(gi,g−i)=
a
G+(e−gi)−pC−Comm
j1[G,
G]P(1 +
b
).
We restrict attention to the case where
G=ne, so that a group is punished if one or more mem-
bers did not contribute.
11
Note that if player jdecides not to introduce committed collective punishment, pC−Comm
j=0,
the game reverts to the initial public goods game where all players choose g
i
= 0 in equilibrium. If
committed collective punishment is introduced, pC−Comm
j=1, and provided punishment and its
associated cost exceed the net benefit of not contributing, (1 + β)P≥(1 −α)e, a group members
best response is to keep her contributions in line with the group member with the lowest contri-
bution level. Thus, the profile where everybody contributes and the profile where nobody
8
Results generalize to other collective decision-making mechanisms (i.e., majority vote).
9
As we show in online appendix A.2, the conditions for cooperation are nevertheless more favorable under collective pun-
ishment with commitment than under collective punishment without commitment.
10
Such procedure models sincere voting, avoiding the influence of strategic considerations often present in vote choice, and
implies that individuals are more likely to be pivotal than in large-scale elections but still not influential in all decisions (for
the use of this procedure, see Morton and Ou, 2015,2019).
11
More lenient punishment institutions may feature lower target levels,
G,ne. Such institutions may however only par-
tially overcome the free rider problem as a subset of ⌊
G/e⌋−nagents prefers not to contribute.
8 Dominik Duell et al.
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contributes are both Nash equilibria. The payoffs in these states are given by αne and e−p(1 + β),
respectively. The socially optimal payoff is thus achieved in one of this sub-game’s equilibria.
Given the equilibria in the sub-games, there are two sub-game perfect equilibria in the induced
extensive form game: one where player jdecides against the institution and nobody contributes in
the public goods game arm (and nobody contributes in the hypothetical coordination game arm)
and one where the institution is formed and everybody contributes in the coordination game arm
(and nobody contributes in the hypothetical public goods game arm). There does not exist a
sub-game perfect equilibrium where collective punishment is implemented and players do not
contribute in the implied coordination game. Thus, the presence of a collective punishment insti-
tution may act as a focal point that provides a rationale for the payoff dominant equilibrium of
the coordination game.
2.2 Peer-to-peer punishment
We benchmark our collective punishment regime against the standard peer-to-peer punishment
regimes (Ostrom et al.,1992; Fehr and Gächter, 2000,2002; Gächter et al.,2008) in addition to a
condition without punishment. In noisy environments, these peer-to-peer punishment regimes
have a number of downsides, most notably that they are very prone to both type I and type II
errors, i.e., punishing contributors or not punishing non-contributors. It is for this reason that
collective punishment mechanisms seem particularly appealing in such high-noise environments.
2.2.1 Peer-to-peer punishment without commitment
Under this sanctioning regime, after the public good each player ican decide whether to punish
each player j,pS
ij [{0, 1}. In case of punishment, Ppoints will be subtracted from the punished,
resulting in a cost of βPto the punisher. Under peer-to-peer punishment, the payoff function is
given by,
uS
i(gi,g−i)=
a
G+(e−gi)−P
n
j=i
pS
ji −
b
P
n
j=i
pS
ij.
Since punishment is costly, no rational and selfish player will engage in it. This observation holds
regardless of whether information about contributions is noisy. Thus, in the only sub-game per-
fect equilibrium of this game, no player will be punished and no player will contribute. Of course,
empirically, we have seen that people do sometimes punish and that punishment can be effective
in sustaining contributions in environments without noise or in low-noise environments (Fehr
and Gächter, 2002). In environments characterized by high-noise levels, this punishment regime
has been much less effective empirically, as shown in, e.g., Ambrus and Greiner (2012).
As noted in the above in the context of collective punishment without commitment, if players
are motivated by negative reciprocity or if the players or the players perceive the interaction to be
indefinitely repeated rather than finite then there may exist equilibria with full cooperation.
12
2.2.2 Peer-to-peer punishment with commitment
With this punishment technology, before the public goods game, each player iannounces a con-
tingent plan under which circumstances each other player is punished. When choosing their con-
tribution levels in the public goods game, agents know the punishment plan of all agents. Once
signals on contribution levels have been received, punishment is automatic. We use
pS−Comm
ij [{0, 1} to denote whether player ihas committed to punish player j. Punishment is
contingent on the noisy signal received by player ion j’s contributions, s
ij
. When icommits to
12
Still, even under these alternative assumptions, the conditions for cooperation are still more favorable under collective
punishment with commitment than under peer-to-peer punishment without commitment (see online appendix A.2 ).
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punish j, the indicator function 1[sij ,e] captures that jis punished whenever ireceives the sig-
nal that jdid not contribute. The payoff function in the case of peer-to-peer punishment under
commitment is, thus, given by
uS−Comm
i(gi,g−i)=
a
G+(e−gi)−P
n
j=i
pS−Comm
ji 1[sji ,e]−
b
P
n
j=i
pS−Comm
ij 1[sij ,e].
For high signal accuracy, there exist sub-game perfect Nash equilibria where (at least some)
agents commit to punish and all agents contribute in the public good game. Note that for positive
noise levels, these equilibria will involve punishment of contributors. Conversely, for low signal
accuracy, there do not exit sub-game perfect equilibria where agents commit to punish or con-
tribute in the public good game. The reason behind this is that even for a high committed
level of punishment, the payoff from not contributing exceeds the payoff from contributing as
contributors and non-contributors are almost observationally equivalent.
13
3. Experimental design
Our experiment featured five main treatments. Our baseline treatment (N) studies imperfect
monitoring without the possibility to punish others. The four different punishment mechanisms
described in the previous section correspond to a 2 × 2 factorial design. One dimension is defined
by whether there is peer-to-peer punishment or collective punishment. The other dimension is
defined by whether participants can commit to punishments.
14
Our main treatments are summarized in Table 1. In all treatments, participants interacted in a
50-period repeated public good game. The reason to choose such a long horizon is to allow for
learning and hence to allow us to observe mature decisions of participants once they have become
familiar with the environment they make decisions in.
Subjects were randomly matched in groups of four which remained constant for the entire
duration of the experiment. In this way, we obtain as many independent observations as there
are groups in the experiment. In each period of the public goods game, each participant received
an endowment of 20 tokens and could decide to either contribute all of her endowments to a
group account or not contribute at all. In order to mitigate the effects of possibly excessive pun-
ishment, and to make sure that participants did not leave the experiment with negative earnings,
in each period each agent additionally received a payment of 10 tokens which could not be con-
tributed. In addition, the minimum payoff per round was set at zero.
15
While endowments that
were kept by agents only benefited themselves, endowments that were contributed to the group
account benefited each agent by 10 tokens. Thus, the payoff function in the public good game was
given by (1) with α= 0.5 and e= 20.
All of our treatments featured imperfect monitoring of actions. After the public good stage,
each player ireceived a noisy signal s
ij
on the true contribution level of player j. Signals were inde-
pendently distributed across players, implying that two players may receive different signals on
the behavior of a third player. With probability 0.6, the signal reflected the true behavior of a par-
ticipant.
16
With the remaining probability 0.4, a contributor was labeled as a non-contributor and
13
See online appendix A.1 for a formal proof of this statement. It remains true even if players are motivated by negative
reciprocity or misperceive the game as indefinitely repeated, as discussed in online appendix A.2.
14
In addition, we implemented a treatment with a strong punishment technology, see Ambrus and Greiner (2012), which
we discuss in Section E.1 in the online appendix. In addition to the treatments featured here, we ran treatments with lower
noise rates and slightly different information structures. See online appendix E.
15
This limited liability constraint was not reached a single time in our experiment.
16
For high signal accuracy/low-noise environments, we found that peer-to-peer punishment was successful in solving the
free-rider problem. As we are interested in situations where peer-to-peer punishment fails to do so, we focus on low signal
accuracy/high-noise levels. See Appendix E.
10 Dominik Duell et al.
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a non-contributor was labeled as a contributor. Hence, signals are informative but there is a sub-
stantial chance both that a contributor appears to be a non-contributor and vice versa. Note, for a
signal precision of 0.6, there does not exist a symmetric sub-game perfect equilibrium in which
everyone contributes.
In addition, in all treatments, participants were correctly informed about the sum of contribu-
tions to the group account, G. Subjects were made aware of this information structure in the
instructions and on the feedback screens. Our choice of imperfect monitoring of contributions
but perfect monitoring of the sum of contribution levels is motivated by the observation that
individual efforts are often observed in a more noisy way than the results of a collaborative effort.
While the information participants receive is identical in all treatments, and therefore none of the
technologies can be accused of being more likely to present false positives when it comes to iden-
tifying non-contributors than another, treatments exclusively differ in the punishment technol-
ogy available to participants.
In the no punishment treatment, Nparticipants simply played the contribution game without
a punishment stage. In the punishment treatments without commitment, participants could
decide on punishing other participants after the contribution stage where they received a noisy
signal of individual choices but were perfectly informed about total contributions. In the standard
peer-to-peer punishment treatment S, each participant iwas asked whether she wanted to sub-
tract p= 15 punishment points from each other participant jor not. Punishment costs are set at
b
=1
3, implying that punishing another player costs 5 tokens. After the punishment stage, the
punishment points received and the cost for punishment of others were subtracted from the earn-
ings in the contribution stage. Afterwards, the final payoffs for a round were presented to
participants.
In the collective punishment treatment C, each participant was asked, again after receiving a
noisy signal on the contributions and being informed about total contributions, whether she
would like to subtract 15 points from everybody (including herself) at a cost of 5 to everybody.
17
Subjects were made aware that the decision of one of the players would be chosen at random for
implementation.
18
The fact that everybody had to bear the cost of punishment allows us to dir-
ectly compare collective to peer-to-peer punishment.
In the punishment treatments with commitment, participants could commit to punishing
other participants before the contribution stage. Subjects were informed about the punishment
decisions of others at the contribution stage and punishment was carried out automatically
given the information received from the contribution stage. In the peer-to-peer punishment
with commitment treatment S-Comm, each participant was asked whether they commit to
Table 1. Main treatments
No commitment Commitment
Peer-to-peer punishment S(2400,12,48) S-Comm (4600,23,92)
Collective punishment C(2600,13,52) C-Comm (4600,23,92)
No punishment N(1600,8,32)
Note: The table shows the main treatments. In brackets number of observations, number of 4-player groups, and number of players.
17
Thus, under collective punishment, 20 points are subtracted from everybody. We have chosen to represent this in terms
of a cost (5 points) and a punishment (15 points) to ensure comparability of the results to our other treatments and the
previous literature.
18
We have chosen this collective decision-making rule, as it (i) yields a higher number of observations of punishment deci-
sions than ex-ante chosen decision makers in each round, (ii) empowers all participants as compared to one constant decision
maker, (iii) avoids the tie splitting problem with four participants, and (iv) avoids certain indifference cases as compared to
majority vote.
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punish another participant if they receive the noisy signal that (i) the participant contributed or
(ii) did not contribute. Thus, each participant had to make six decisions at this stage.
In the collective punishment with commitment treatment C-Comm, participants were asked
whether they commit to punishing everybody (including themselves) in case somebody did not
contribute. Before the contribution stage, the choice of one participant was randomly implemen-
ted and everybody was made aware whether a collective punishment mechanism was in place.
19
Figure 1 below summaries the sequence of moves shared by all treatments and those steps that are
specific to only some or just one of the treatments.
Quantifying the effect of punishment, we compare the standard peer-to-peer punishment (S)
to the no punishment treatment (N). The effect of collective punishment as well as of the ability
to commit to punishment is then estimated by (1) comparing standard peer-to-peer punishment
(S) to collective punishment (C); and standard peer-to-peer punishment (S) to peer-to-peer pun-
ishment featuring the ability to commit to punishment (S-Comm) as well as to collective pun-
ishment with commitment (C-Comm). Measuring whether individuals choose to turn the
public goods game into a coordination game by committing to punishment, we further contrast
cooperation and payoffs when individual participants choose no commitment to when they do
(in treatment C-Comm). Finally, and most importantly, we identify the joint effect of commit-
ment and collective punishment by juxtaposing cooperation and payoffs across treatments S,
S-Comm, C, and C-Comm.
We report the estimated regression models throughout the results section. Since we do not
expect equilibrium predictions to matter until participants have had time to learn and adapt
their behavior, we run our analysis on the last 10 periods, in addition to on the full set of rounds,
as it is common practice in experimental tests of public goods or coordination games; we argue
that behavior in those last periods is most stable and we run hypothesis tests over treatment
effects on this subset of data. For assessing learning, we further compare the first half or
the second half of periods separately, show results for the last 10 rounds only, and show regres-
sion models including a linear time trend. We analyze the data using linear panel regression
Figure 1. Sequence of moves within one round of the public goods game by treatment.
19
Collective punishment only conditions on whether the sum of contributions is maximal and thus requires even less
information than is available here. Our formulation is just one possible form of collective punishment and one may think
of alternative forms that are more forgiving in the sense that only a fraction of individuals is required to contribute. Such
rules may however be subject to coordination problems as it is not clear who will free ride.
12 Dominik Duell et al.
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models which allow us to cluster standard errors at the group level and to account for
auto-correlation.
20
4. Results
4.1 Efficacy of collective punishment with commitment
In a first step, we assess the performance of collective punishment with commitment. We focus
on the collective punishment treatment with commitment as a benchmark for testing our
hypothesis. We first compare contribution and payoff rates under collective punishment with
commitment to the two natural benchmark scenarios of standard peer-to-peer punishment
(treatment S) and the case where the possibility of punishment is absent (treatment N). Those
are the benchmark cases most prominently studied in the literature and most frequently observed
in the field. In Section 4.3, we then include our other treatment variations in order to gauge the
relative importance of the effects of commitment and collectiveness.
Figure 2 plots contribution rates over time for the three treatments under consideration. While
cooperation levels appear to be fairly high and stable over time under collective punishment with
commitment, they are decreasing over time in the other two scenarios; more than halving over
the course of the experiment.
To compare the effects on cooperation/contribution, we run the following regression.
Ct
i=
a
+
b
1
d
S+
b
2
d
C−Comm +
e
t
i(2)
Here the dependent variable Ct
iis a dummy for whether player icontributes in period t, and the
independent variables δ
S
and δ
C−Comm
are dummy variables for treatments S and C-Comm,
respectively. The constant αcaptures the baseline effect in the case of no punishment.
Figure 2. Contribution rates in the cases of no punishment (“No”), standard peer-to-peer punishment (“Standard,”S), and
collective punishment with commitment (“Collective,”C-COMM).
20
Whenever we report a finding as significant, we either report the level of significance applied or the exact p-value. Giving
a fuller account of uncertainty in our results this way should enable readers to evaluate better the robustness of our results.
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Standard errors are clustered at the matching group level. Table 2 shows the results. The columns
differ according to how many periods are taken into account in the regression. Column (2) differs
from the other regressions in that it includes a linear time trend. Column (5) presents the results
for the last 10 periods upon which much of the analysis draws.
It turns out that collective punishment with commitment has a positive effect on cooperation,
relative to the baseline of no punishment, and this effect is significant at the 1 percent-level. In
contrast, peer-to-peer punishment leads to lower cooperation than the baseline of no punish-
ment, though this effect is not statistically significant. A test of whether the coefficients for S
and C-Comm are equal confirms that collective punishment with commitment yields higher
cooperation than peer-to-peer punishment. Column (2) in Table 2 shows that contributions
are decreasing over time in the no punishment scenario. Further post-regression tests reveal
that this is also the case under peer-to-peer punishment (β
3
+β
4
≈−0.06, p= 0.00) while the
time trend for collective punishment with commitment is not significantly different from zero
(β
3
+β
5
≈0.00, p= 0.70). Summarizing our findings so far we have:
Result 1: Contribution levels are higher under collective punishment with commitment com-
pared to the no punishment scenario or to peer-to-peer punishment. There is no difference
between the no punishment scenario and peer-to-peer punishment. While contribution levels
are stable under collective punishment with commitment, they are decreasing under peer-to-peer
punishment and in the no punishment scenario.
Collective punishment supports relatively high contribution levels over time. We now move on to
assess its relevance for overall welfare; taking into account the welfare loss incurred if punishments are
executed. The evolution of net profits over time for the different treatments is displayed in Figure 3.
Table 3 reports the results of the following regression
p
t
i=
a
+
b
1
d
S+
b
2
d
C−Comm +
e
t
i(3)
where π
i
are player i’s net profits at t, i.e., their earnings from the public good game net off any
costs incurred for punishment or being punished.
We find that collective punishment with commitment has a positive effect on payoffs relative
to the baseline of no punishment, this effect is significant at the 10 percent-level. Peer-to-peer
Table 2. OLS estimates of regression equation (2)
(1) (2) (3) (4) (5)
Variables All periods Time trend 1st Half 2nd Half Last 10 periods
S(β
1
)−0.095 −0.202** −0.154* −0.036 −0.053
(0.087) (0.084) (0.086) (0.094) (0.105)
C-Comm (β
2
) 0.107 −0.141* −0.023 0.238*** 0.279***
(0.064) (0.074) (0.068) (0.068) (0.077)
period (β
3
)−0.010***
(0.001)
period × S(β
4
) 0.004**
(0.001)
period × C-Comm (β
5
) 0.009***
(0.001)
Constant (α) 0.500*** 0.761*** 0.635*** 0.365*** 0.341***
(0.045) (0.060) (0.054) (0.041) (0.052)
p-value Test β
1
=β
2
0.025** 0.1074 0.009*** 0.003***
Observations 8600 8600 4300 4300 1720
R
2
0.031 0.056 0.016 0.068 0.098
Note: LPM estimates of cooperation regressed on treatment dummies (equation (2)). Robust standard errors clustered at the matching group
level are in parenthesis. ***p < 0.01, **p < 0.05, *p < 0.1.
14 Dominik Duell et al.
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punishment is associated with lower payoffs than the baseline of no punishment, although this
effect is not statistically significant across the last 10 periods. However, collective punishment
with commitment yields significantly higher profit than peer-to-peer punishment without com-
mitment, as revealed by the t-test of equality of coefficients β
1
and β
2
. The effect is substantial and
corresponds to an increase of 6.585 ECU, or roughly 20 percent. Studying time trends reveals that
profits in the no punishment case are decreasing over time. Additional post-regression tests con-
firm that there are no significant time trends in payoff rates under peer-to-peer punishment (β
3
+
Figure 3. Profits in the cases of no punishment (“No”), peer-to-peer punishment (“Standard”,S), and collective punish-
ment with commitment (“Collective”,C-COMM).
Table 3. OLS estimates of regression equation ((3)
(1) (2) (3) (4) (5)
Variables All periods Time trend 1st Half 2nd Half Last 10 periods
S(β
1
)−6.508*** −11.790*** −9.117*** −3.900* −3.354
(1.979) (2.352) (2.127) (2.099) (2.350)
C-Comm (β
2
)−1.209 −7.271*** −4.257** 1.839 3.231*
(1.567) (1.843) (1.650) (1.665) (1.856)
period (β
3
)−0.205***
(0.026)
period × S(β
4
) 0.207***
(0.057)
period × C-Comm (β
5
) 0.238***
(0.041)
Constant (α) 40*** 45.22*** 42.70*** 37.30*** 36.81***
(0.906) (1.200) (1.082) (0.828) (1.043)
p-value Test β
1
=β
2
0.0192** 0.0733* 0.0337** 0.0218** 0.0154**
Observations 8600 8600 4300 4300 1720
R
2
0.043 0.055 0.059 0.044 0.061
Note: OlS regression with profits regressed on treatment dummies (equation (3)). Robust standard errors clustered at the matching group
level are in parenthesis. ***p < 0.01, **p < 0.05, *p < 0.1.
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β
4
≈0.00, p= 0.97). While payoffs seem to be increasing under collective punishment, this effect
is not significant (β
3
+β
5
≈0.03, p= 0.31), i.e., we cannot reject β
3
+β
5
=0.
Result 2: Payoff levels under collective punishment with commitment are higher than in the no
punishment scenario and are higher than under peer-to-peer punishment. Payoff levels in the no
punishment case are not significantly higher than under peer-to-peer punishment. While payoff
levels are decreasing in the no punishment scenario, they are stable under collective punishment
with commitment and under peer-to-peer punishment without commitment.
Collective punishment restores relatively high levels of welfare in a noisy environment where
peer-to-peer punishment does not work as well as in the noiseless case. While positive payoff impli-
cations of collective punishment with commitment (as compared to the no-punishment case) start
to become evident only toward the end of the experiment, the pattern of time trends documented in
column (2) of Tables 2 and 3points toward long-term positive welfare effects. This interpretation is
reinforced by focusing on groups where collective punishment is committed.
4.2 Collective punishment as a coordination device
As previously noted, whenever collective punishment is committed participants face a coordin-
ation game with two Nash equilibria: in one nobody contributes and in the other everybody con-
tributes. By contrast, when no collective punishment is committed the resulting sub-game
corresponds to the original public goods game. By choosing whether to commit to implementing
collective punishment agents may decide whether to play the normal public goods game or a
coordination game. In the latter case, the resulting extensive form game has two sub-game perfect
Nash equilibria: in one collective punishment is implemented and everybody contributes whereas
in the other collective punishment is not implemented and nobody contributes (see Section 2).
There is no sub-game perfect equilibrium where collective punishment is implemented and the
no contribution equilibrium of the coordination game is played. The presence of collective pun-
ishment acts as a focal point in the implied coordination game.
In order to asses this prediction, in the C-Comm treatment, we now contrast contribution rates
in groups where collective punishment is committed to those where it is not committed. Figure 4
plots contribution rates in these two cases over the course of the experiment and includes the no
punishment (N) treatment as benchmark.
While behavior in groups in the collective punishment treatment where collective punishment
was not implemented closely resembles behavior in the no-punishment treatment, contributions
in groups with implemented collective punishment are significantly higher and increasing over
the course of the experiment, amounting to 94 percent in the last round.
21
Analysis of the effect of actually committed collective punishment on cooperation suffers from
endogeneity problems, as which groups choose to commit to collective punishment is not
exogenous. Typically, we would think of the groups who commit and those who do not as dif-
ferent, in the sense that they have a different distribution of types. We can address this selection
problem by exploiting the design feature that, while all group members make a choice on whether
they would like to implement collective punishment, only the decision of one randomly selected
group member is implemented (see Section 3). We can hence compare groups where the same
number of participants opt for collective punishment, but where the random (and exogenous)
selection procedure implemented a different decision circumventing issues of post-treatment bias.
21
This is in stark contrast to previous work on minimum effort games (see, e.g., Van Huyck et al.,1990) where participants
were unable to reach high effort equilibria. While one may argue that these experiments feature more complex games with
more than two strategies, there is evidence showing that even in simpler two-person 2 × 2-games coordination on high effort
equilibria is fairly demanding (see Battalio et al.,2001).
16 Dominik Duell et al.
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Table 4 (upper half) shows the results.
Horizontal comparisons illustrate the selection problem. Irrespective of whether collective
punishment is implemented or not, there is always more cooperation when more people voted
in favor of the institution. Indeed, the correlation between past individual contributions and vot-
ing for punishment is statistically significant (ρ= 0.1872***) and so is the correlation between
group past contributions and the share of group members voting for the punishment technology.
These correlations may reflect a number of things. There might be different types in society and
those who tend to vote for punishment institutions are also those who are more likely to contrib-
ute; or that the institution is successful in sustaining cooperation and people vote for these insti-
tutions, the institution successfully keeps contributions high and then people vote for them again.
Vertical comparisons illustrate the effect of the punishment institution being implemented.
Conditional on the number of people who voted in favor of the institution (1,2, or 3), whether
it is implemented is exogenous. The table shows that there is always more cooperation if the insti-
tution is implemented, though the difference is not statistically significant with one vote in favor
(t-test, p= 0.32). It is statistically significant for 2 votes ( p < 0.01) and 3 votes (p = 0.02).
Figure 4. Contributions with and without collective punishment committed.
Table 4. Contributions and profits when collective punishment is and is not committed
Votesinfavor 01234Average
Contribution rates
Coll. Pun. committed −0.55 0.76 0.92 0.98 0.81
Coll. Pun. not committed 0.33 0.44 0.43 0.56 −0.43
Profits
Coll. Pun. committed −33.8 35.1 44.4 48.1 40.5
Coll. Pun. not committed 36.6 37.8 34.6 40.6 −37.3
Observations 172 331 256 308 83
Note: The table shows average contribution rates (across all periods) depending on how many group members voted in favor of
implementing the collective punishment mechanism and whether or not it was actually implemented.
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Result 3: On average, contribution levels are significantly higher when collective punishment is
committed compared to the no punishment scenario and compared to the case where collective
punishment is not committed.
We now proceed to assess the implications of committed collective punishments for welfare.
Figure 5 plots the evolution of payoffs in the two subgroups and contrasts it to the no punishment
treatment. While profits of participants in groups where collective punishment is not implemen-
ted are statistically indistinguishable from profits made by participants in the no punishment
treatment, the profit of participants in groups with implemented collective punishment is clearly
higher in the later periods of the experiment. Further, payoffs are evidently increasing for parti-
cipants in groups where punishment is committed (β= 0.1635***) and are decreasing for the
other two reference groups (non-committed: β=−0.099***; N: β=−0.204***). Thus, while pay-
offs in groups with implemented collective punishment are initially lower than in the no punish-
ment case, this picture is reversed by the end of the experiment. This suggests that it takes time
for agents to learn to coordinate on the high contribution equilibrium when punishment is
introduced.
Table 4 (lower half) shows payoff comparisons when we condition on the number of group
members who voted in favor of establishing the institution. Interestingly, in relatively uncoopera-
tive groups where only one person voted in favor of the mechanism, payoffs are lower when the
mechanism is implemented (though not statistically different, p = 0.42). As the cooperation rate is
low in these groups, punishment is relatively often executed, which lowers payoffs. As expected
payoffs are higher when the institution is implemented both when two voters are in favor
(p = 0.06) and when three voters are in favor ( p = 0.12).
Result 4: On average, payoff levels are higher when collective punishment is committed com-
pared to the no punishment scenario and compared to the case where collective punishment
is not committed.
Figure 5. Profits with and without collective punishment committed
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4.3 The role of commitment and collectiveness
In order to assess the relative importance of commitment and collectiveness for cooperation and
profit, we now combine the data from treatments S, C, S-Comm, and C-Comm. To investigate the
effect on cooperation, we run the following regression
Ci=
a
+
b
1
d
Comm +
b
2
d
Coll +
b
3(
d
Comm ×
d
Coll)+
e
i(4)
Here δ
Comm
is a dummy indicating that the treatment was one with commitment (S-Comm or
C-Comm) and δ
Coll
is a dummy indicating that the treatment was one with collective punishment
(C or C-Comm).
Table 5 displays the results. As before, the columns differ according to how many periods are
taken into account in the regression, and again we focus on the results for the last 10 periods
(column (5)). In the baseline case (peer-to-peer punishment without commitment), the average
cooperation rate is around 28.7 percent in the last 10 periods. The commitment coefficient is sig-
nificant and positive, indicating that adding commitment to either peer-to-peer punishment (β
1
)
or to collective punishment (β
1
+β
3
) has a significant positive effect on the rate of cooperation,
increasing it to 49.7 percent in the case of peer-to-peer punishment and even 66.3 percent in the
case of collective punishment. By contrast, the collectiveness coefficient (β
2
), though positive, is
small and not significant, implying that without commitment, collective punishment does not
lead to higher contributions. The average cooperation rate in C is 29.7 percent. The sum of
the collective coefficient and the interaction term coefficient (β
2
+β
3
) shows higher contributions
for committed punishment when it is collective.
Result 5: The ability to commit to punishment increases contributions compared to peer-to-peer
punishment. While in the absence of commitment, collective punishment does not lead to higher
contributions, it leads to weakly higher contributions in the presence of commitment.
Table 5. OLS estimates of regression equation (4)
(1) (2) (3) (4) (5)
Variables All periods Time trend 1st Half 2nd Half Last 10 periods
commit (β
1
) 0.179** 0.106 0.138* 0.220** 0.210*
(0.085) (0.078) (0.078) (0.099) (0.110)
coll (β
2
) 0.0204 0.061 0.0307 0.0101 0.0106
(0.088) (0.080) (0.083) (0.101) (0.109)
coll×commit (β
3
) 0.0254 −0.120 −0.0374 0.0882 0.156
(0.116) (0.119) (0.111) (0.133) (0.146)
period −0.006***
(0.001)
period × commit 0.003
(0.002)
period × coll −0.002
0.002
period × comm × coll 0.006*
(0.003)
Constant (α) 0.405*** 0.559*** 0.481*** 0.328*** 0.287***
(0.075) (0.060) (0.067) (0.085) (0.090)
Observations 9800 9800 4900 4900 1960
p-value β
2
+β
3
0.5427 0.5084 0.9291 0.2592 0.0920*
p-value β
1
+β
3
0.0120** 0.8722 0.2073 0.0010*** 0.0004***
R
2
0.038 0.061 0.015 0.075 0.098
Note: LPM estimates of cooperation regressed on treatment dummies (equation (4)). Robust standard errors clustered at the matching group
level are in parenthesis. ***p < 0.01, **p < 0.05, *p < 0.1.
Political Science Research and Methods 19
https://doi.org/10.1017/psrm.2023.52 Published online by Cambridge University Press
One might wonder how successful the standard technology is depending on how many people
have committed to punishing how many others. To this end, we analyzed contribution rates in
treatment S-COMM separately for the cases where fewer than 4 individual punishments are com-
mitted in a group, where between 4 and 6 individual punishments are committed, 7–9 punish-
ments, or 10 or more punishments. (The maximum amount of individual punishments
committed is 4 × 3 = 12, the case where all group members decide to punish all others. This
case did not occur in the experiment, though.) The cooperation rate is 61 percent (52 percent
in the last 10 periods) if fewer than 4 punishments are committed. It is 56 percent (42 percent
in the last 10 periods) if between 4 and 6 punishments are committed. It is 52 percent if 7–9 pun-
ishments are committed, but there are only 23 observations for this case and none in the last 10
periods. There are no observations for the case of 10 or more committed individual punishments.
These cooperation rates are always lower than those under committed collective punishment.
This analysis shows that one of the reasons that standard punishment does not work as well
as collective punishment, even with commitment, is that under the standard technology indivi-
duals do not manage to coordinate on situations where a high level of punishment is overall com-
mitted. The more targeted punishments, by contrast, do not seem to raise contribution rates
sufficiently.
We now move on to discuss the relative importance of collectiveness and commitment on pay-
offs (net of punishments and punishment costs). To this end, we ran the following regression
p
i=
a
+
b
1
d
Comm +
b
2
d
Coll +
b
3(
d
Comm ×
d
Coll)+
e
i,(5)
the results of which are presented in Table 6. Neither the commitment coefficient nor the collec-
tiveness coefficient is now significant. However, both the sum of the commitment and interaction
coefficients and the sum of the collectiveness and interaction coefficients are significant. This
means that although neither commitment nor collectiveness is sufficient to increase payoffs,
they are effective when combined.
Result 6: Neither the ability to commit to punishment nor whether punishment is collective or
not have an effect on profits (taken on their own). The combination of collective and committed
punishment leads to higher payoffs than peer-to-peer punishment with commitment and higher
payoffs than collective punishment without commitment.
It is interesting to note that while the ability to commit to punishment has a positive effect on
contribution levels (as compared to peer-to-peer punishment), only the combination of collective
and commitment results in higher payoffs. The main reason for this is that peer-to-peer punish-
ment with commitment results in excessive welfare losses due to punishment, as all too often con-
tributors are incorrectly labeled as non-contributors and consequently punished. This can be
inferred from Figure 6 plotting the surplus loss due to punishment (allocated and received).
While participants lose approximately 5 points in the last rounds under peer-to-peer punishment
with commitment, the surplus loss is approximately half of that in the other treatments. An alter-
native way of analyzing the surplus loss associated with a punishment technology is to calculate
the ratio of net profits (after punishment) to the gross profits (before punishment), thus providing
a scaled efficiency measure for a punishment technology. The higher this profit ratio the less
wasteful the punishment. This fraction is 0.83 for peer-to-peer punishment (0.86 across the
last 10 periods) with commitment, 0.87 for peer-to-peer punishment (0.93, last 10 periods),
0.92 for collective punishment without commitment (0.93, last 10 periods), and 0.93 for collective
punishment with commitment (0.94, last 10 periods). A two-sided rank-sum test confirms sig-
nificant differences (at the 1 percent level) for all pairwise comparisons based on all periods,
except the one between the two collective treatments. For the last 10 periods, only the difference
between S-COMM and the remaining treatments is statistically significant. Collective punishment
20 Dominik Duell et al.
https://doi.org/10.1017/psrm.2023.52 Published online by Cambridge University Press
(with and without commitment) thus results in less surplus lost due to punishment. This shows
that the collective punishment technology is successful in that the threat of punishment contri-
bution is high without causing excessive surplus loss induced by punishment actually being car-
ried out.
Table 6. OLS estimates of regression equation (5)
(1) (2) (3) (4) (5)
Variables All periods Time trend 1st Half 2nd Half Last 10 periods
commit 0.746 −1.290 −0.358 1.850 1.646
(2.734) (3.396) (2.945) (2.933) (3.035)
coll 2.485 5.641** 3.694* 1.277 0.196
(1.987) (2.390) (2.131) (2.136) (2.359)
coll×commit 2.436 −0.613 1.465 3.406 6.159
(3.399) (4.25) (3.646) (3.635) (3.818)
period 0.002
(0.050)
period × commit 0.080
(0.083)
period × coll −0.124**
(0.061)
period × commit × coll 0.120
(0.101)
Constant 33.49*** 33.44*** 33.58*** 33.40*** 33.46***
(1.757) (2.020) (1.828) (1.926) (2.103)
Observations 9800 9800 4900 4900 1960
p-value coll+coll×commit 0.0806* 0.1594 0.0876* 0.1179 0.0395**
p-value comm+coll×commit 0.1216 0.4608 0.6090 0.0181** 0.0015***
R
2
0.028 0.037 0.027 0.040 0.073
Note: OLS regression with profits regressed on treatment dummies (equation (5)). Robust standard errors clustered at the matching group
level are in parenthesis. ***p < 0.01, **p < 0.05, *p < 0.1.
Figure 6. Surplus loss due to punishment.
Political Science Research and Methods 21
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5. Discussion and conclusion
We have demonstrated that collective sanctions may enable groups to achieve high contribution
and welfare levels in an environment where imperfect monitoring makes this inherently difficult.
Committed collective punishment induces a coordination game and at the same time provides a
rationale for playing the welfare maximizing equilibrium of this game. We find that a key pre-
requisite for the effectiveness of collective sanctions is the ability to commit to punishment before
the collaborative effort. We argue that it is precisely the combination of collectiveness of punish-
ment, influence on the decision to apply collective sanctions, and the insurance that sanctions
will be applied that ensures successful collective action, even over a longer period of time
where often the amount of free-riding rises.
In very general terms, we argue that a regime with the authority to punish only does so effect-
ively trying to ensure cooperation, when individuals voluntarily select to be governed by that
authority. Democracies, featuring the opportunity for (admittedly costly) exit, function better
in fulfilling its objectives, e.g., providing public goods, when they enjoy system support. Such sup-
port is higher when the institutions are trusted (Wagner et al.,2009), when they are responsive
(Kim 2009), or possess fair procedures (Magalhães, 2016). It also has been established that par-
ticipating in the decision-making process within these institutions, i.e., voting, increases system
support (Finkel, 1987; Bowler and Donovan, 2002). We randomly vary the opportunity to par-
ticipate in the decision how the institution will look like and establish that (1) individuals are
willing to submit themselves to such an institution over and over again, a measure of system sup-
port, even if it imposes collective sanctions, and (2) the existence of that choice improves group
cooperation particularly when collective sanctions are present.
We further speak to the question which institutions enable the government to perform its
functions well. In particular, we contribute to characterizing those institutions fostering the pro-
vision of public goods and successful collective action. It is said that tackling the complexity of
modern societies, representative democracy with an attached ever-growing bureaucracy is
ill-equipped to solve the challenges of the day and participation in the process of governing at
lower levels—the neighborhood, the work place, the industry, etc.—is seen as providing better
outcomes (Fung and Wright, 2001). The World Bank, for example, has been pushing participa-
tory budgeting as standard for implementing its Billion-$ development programs world wide
(Goldfrank, 2012), an institution that seems particularly effective because it tends to stick around
(Touchton and Wampler, 2014). Participatory institutions yield better outcomes by creating
aware and involved citizens (Agrawal, 2005) but many examples are not benefiting all members
of the targeted group often being elite dominated (Mansuri and Rao, 2004), face a trade-off
between equity and efficiency (Hong and Cho, 2018), or lack any evidence of improving out-
comes at all (Mansuri and Rao, 2012). The institutions we create assign the ability to be involved
in creating it, directly testing whether it is the participation in the decision how one is governed,
i.e., is collective sanctioning implemented, and whether it is giving everyone the same power over
choosing the institution, which yields better government performance. Legal studies, a while ago,
have already discovered that “collective sanction incentivizes group members to monitor and
marginalize the conduct of conflict entrepreneurs (Drumbl, 2004, p.551).”What our theoretical
analysis shows, and the experimental evidence underscores, such incentives only arise when col-
lective action is paired with self-selecting into such regime to avoid a commitment problem.
When we differentiate between peer-to-peer punishment with commitment and collective
punishment with commitment, we find that a contract between all members of the group is
necessary and not just a contract to allow for high contributions; and, for groups where collective
punishment is committed, contributions are even increasing over time, pointing toward beneficial
long-term consequences of such institution. Our conclusion that participation of individuals in
the decision to apply collective sanctions is also generating high levels of contribution is partially
in contrast to findings by Baldwin (2013,2019) where members of society seem to appreciate the
22 Dominik Duell et al.
https://doi.org/10.1017/psrm.2023.52 Published online by Cambridge University Press
long-term horizon of non-elected enforcers more than their influence in picking those to carry
out sanctioning. However, our results are very much in line with the need for legitimate enforce-
ment that often arises from the way how enforcers are chosen (Dickson et al.,2015,2009)—where
such enforcers seem to be accepted even if the collective sanctioning of all for a rule violation of
just one individual seems dictatorial. Such seemingly harsh punishment of everyone is not
uncommon outside of the lab; sports fans have known the exclusion from games as punishment
for lighting fireworks or invading the pitch, an infringement mostly carried out only by a few. An
extension to our finding would also be to consider institutions where rewarding is collective, as
frequently observed in sports or at work (Heckathorn, 1988).
Clearly, the specific details of the sanctioning regime we implement determine what aspect of
the institution driving behavior we are able to identify; similarly, it sets boundaries on whether
and which motivations behind individual’s choices we are able to parse. Peer-to-peer punishment
and collective punishment, as implemented in the experiment, only differ in the target of
imposed sanctions while punishment mechanism with and without commitment differs not
only in whether participants bind themselves to punishment but also when they learn about
what that punishment would be (before or after they make their decision to contribute). In
other words, we cannot separate the effect of a binding decision and of information but consider
both to be crucial features of the commitment institution; separating both is left for future
research. Keeping the information structure constant across treatments allows us to cleanly iden-
tify the effect of the punishment institution on behavior. Variation in choices across groups, then,
gives an indication of what may drive the positive effects of committed collective sanctioning: (1)
the decision whether to commit to punishment empirically correlates with cooperation, presum-
ably because cooperatively minded people are more likely to build an institution in the first place.
(2) Observing how many others are willing to punish, as in the peer-to-peer sanctioning regime
with commitment where we find that pre-committed punishment of many or all of the other
group members is rare, suggests that individuals are not able to coordinate to widely applied pun-
ishment without an institution that commits them to doing so. This is interesting, given that the
commitment to imposing sanctions collectively means potentially punishing contributors, which
is usually seen as unfair and, in turn, should decrease the appeal of such an institution. It may be
that participating in the decision to set-up collective punishment, as a form of realized procedural
fairness, seems to be enough to make the threat of collective punishment acceptable; similarly,
setting up collective sanctions may be seen as a less involved decision than individuals targeting
each other and therefore preferred.
While our paper makes an important step toward understanding the efficacy and workings of
collective punishment, we believe there are several important dimensions which go beyond its
scope. Without the ability to commit to collective punishment participants may not hold consist-
ent or sufficiently strong expectations that the group will be punished in case of low total con-
tributions. One may consequently wonder whether collective punishment without
commitment could be effective if the fraction of those willing to engage in it is high enough,
so to create the expectation that it will follow under low total contributions. Experimentally,
this could be achieved, e.g., by manipulating its cost or by choosing a leader who is in charge
of collective punishment for a prolonged period of time.
In the present paper, the collective punishment decision is taken by members of the group.
This seems to be a realistic description of many political institutions or certain economic organ-
izational structures such as workers’cooperatives or self-managing work teams but is not an
accurate description of other organizations which feature a hierarchy between a principal and
a group of agents. Hence, it may be interesting to studying the interplay between a principal
in charge of collective sanctions and the internal and external dynamics of a group of agents
at the receiving end. It seems to be natural in such a setting that, while the principal holds the
power, individual agents have superior information about each others’conduct. Possible areas
Political Science Research and Methods 23
https://doi.org/10.1017/psrm.2023.52 Published online by Cambridge University Press
of interest include information sharing of agents with the principal and peer-to-peer punishment
and ostracism among agents.
22
Further, even without ensured collective sanctioning, allowing participants to opt into collect-
ive punishment, instead of exogenously enforcing it, may already help to maintain high and stable
contribution rates. Nalbantian and Schotter (1997) who study forcing contracts, which corres-
pond to exogenously imposed collective punishment, find contribution levels were decreasing
over time while we see an increase in our experiment giving individuals to choose to be sanc-
tioned collectively. Opting into punishment institutions provides players with means to signal
their willingness to punish, thus amplifying its deterrent effect. Kosfeld et al. (2009) and
Markussen et al. (2014) document an efficiency enhancing effects of institution choice, and
find that subjects prefer to form such institutions. Similarly, the literature on peer-to-peer pun-
ishment also finds that allowing people to choose increases cooperation rates (see, e.g., Sutter
et al.,2010, or Mellizo et al.,2017).
One may also wonder about situations where collective punishment and individual punish-
ment, either peer-to-peer or applied by a central authority, exist in parallel. Dickson (2007) ana-
lyzes in detail the interplay between an outside authority who can exert collective punishment
and a group of players who can additionally engage in peer-to-peer punishment. This work dif-
fers from the literature on standard peer-to-peer punishment in many aspects other than the
presence of collective punishment. In particular, private punishment by group members is
more expensive compared to most literature on standard punishment and the amount of max-
imally allowed punishment is fairly restrictive (well below the level required to impede free riding
with selfish preferences). Most importantly, a comparison of a setting with collective punishment
to one without collective punishment is missing which makes it impossible to assess the efficacy
of collective punishment in the Dickson (2007) setting.
Supplementary material. The supplementary material for this article can be found at https://doi.org/10.1017/psrm.2023.52.
To obtain replication material for this article, https://doi.org/10.7910/DVN/6ZGU1X.
Acknowledgements. We thank Eric Dickson as well as seminar audiences at the Universities of East Anglia, Fribourg,
Heidelberg, Linz, Lund, Siena, St. Andrews, and Venice for helpful comments and suggestions. We are indebted to Sara
Godoy for most valuable assistance in running the experiments as well as to Sandra Miltenyte and Axel Skantze for excellent
research assistance. Erik Mohlin is grateful to Handelsbankens forskningsstiftelser (grant #P2016-0079:1), the Swedish
Research Council (grant #2015–01751), the Oxford Economic Papers Fund, and the Knut and Alice Wallenberg
Foundation (Wallenberg Academy Fellowship 2016–0156) for their financial support. Weidenholzer acknowledges support
through a BA/Leverhulme Small Grant.
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Cite this article: Duell D, Mengel F, Mohlin E, Weidenholzer S (2023). Cooperation through collective punishment and par-
ticipation. Political Science Research and Methods 1–27. https://doi.org/10.1017/psrm.2023.52
Political Science Research and Methods 27
https://doi.org/10.1017/psrm.2023.52 Published online by Cambridge University Press
