Monitoring networks in a common pool resource dilemma:
experimental evidence on extraction, punishment and beliefs
Ganga Shreedhar1, Alessandro Tavoni2, Carmen Marchiori3
Abstract
Experimental evidence suggests the careful design of monitoring institutions is critical to mitigate a
tragedy of the commons. However most of this evidence is drawn from the implicit assumption of
perfect monitoring i.e. everyone can observe and punish everyone else. This experimental study
investigates how alternative monitoring institutions, modelled through networks, influences
extraction, beliefs, punishment and efficiency in a common pool extraction dilemma. We focus on
differences between the complete network, undirected circle, directed circle and line networks. Our
results show that the structure and properties of monitoring network significantly affects extractions
from the common pool resource, beliefs about other’s expected extractions, punishment and
efficiency. We find that complete networks, are the least efficient, with higher extraction, beliefs
over other’s expected extraction and punishment. Lastly, we show that higher beliefs over others
expected extractions are associated with higher extraction from the common pool resource.
JEL Codes: Q57, D83, D62, D70, C91, C92
Keywords: Common pool resource, Monitoring, Networks, Punishment, Beliefs, Experiment
1
PhD candidate in Environmental Economics, Department of Geography and Environment, LSE
Assistant Professorial Research Fellow, Grantham Research Institute on Climate Change and the Environment
3
Visiting Fellow, Grantham Research Institute on Climate Change and the Environment and Lecturer in
Environmental Economics, LSE
2
1
1. Introduction
Monitoring institutions are a critical means to mitigate a ‘tragedy of the commons’ of shared
ecological resources such as fishing grounds, forests and water basins (Hardin 1968). This is
supported by abundant evidence that extractors monitor and punish high extraction even at a cost
to themselves (Ostrom 1990, Poteete, Janssen, and Ostrom 2010, Dietz, Ostrom, and Stern 2003).
However lab experimental evidence highlights that costly peer-punishment has only a modest and
lagged effect on limiting extraction in non-linear common pool resource (CPR) dilemmas (Ostrom,
Gardner, and Walker 1994, Casari and Plott 2003, Cason and Gangadharan 2015, Ostrom, Walker,
and Gardner 1992).4 These experiments implicitly model complete monitoring i.e. all individuals
within an experimental group can monitor and punish each other. But this is only one extreme case
of several possible monitoring institutions that actually exist.
In reality, extractors are embedded within complex socio-economic and geographical networks,
which determine local monitoring roles, information and punishment opportunity. These underlying
networks can either constrain or enhance cooperation, especially in contexts without strong formal
institutions (Scholz and Wang 2006, Currarini, Marchiori, and Tavoni 2015, Breza 2015). There is
mixed evidence from qualitative case-studies in the natural resource governance literature on how
local network structures can influence cooperation. On the one hand, denser or closely knit
networks can enhance collective action (Sandström and Carlsson 2008), but the homogenization of
information and norms can also lead to over-extraction (Janssen et al. 2006, Bodin and Prell 2011,
Bodin and Crona 2009). Evidence from economic experiments on prisoner dilemma and public goods
games, indicates that the monitoring network structure influences cooperation and punishment
(Choi, Gallo, and Kariv 2015, Carpenter, Kariv, and Schotter 2012, Leibbrandt et al. 2015, Fatas,
Meléndez-Jiménez, and Solaz 2010).
However, evidence on whether and how the structure of different monitoring networks influences
behaviour and outcomes in a CPR extraction dilemma is missing. Perfect information about other’s
extractions and punishment opportunity (as in the complete monitoring network) may enhance
cooperation because subjects can easily identify and sanction free-riding. On the other hand, there
may be a coordination failure and a second order monitoring dilemma, with an increase in the
number of potential punishers in a given network as punishment is costly. In this case, focused
monitoring opportunities provided by imperfect monitoring networks may result in a higher
likelihood that free-riders receive punishment, which may also be more severe.
In addition, there is growing evidence that beliefs over other’s expected extraction explains
conditional cooperation in public goods games (Gächter and Renner 2010, Fischbacher and Gächter
2010, Smith 2012, Croson 2000) and conformist preferences in CPR dilemmas (Velez, Stranlund, and
Murphy 2009). Beliefs about other’s expected extraction depend on information extractors receive
about other’s behaviour. As the monitoring network allows extractors to observe the actions of only
4
We use the term CPR extraction dilemma to refer to the ‘appropriation problem’ outlined in Ostrom et al.
(1994). It is assumed that the production relationship between the returns from the CPR and inputs (e.g.
effort) is fixed. The core of the problem is that the non-excludability of potential beneficiaries, results in the
excessive appropriation of subtractable resource units. The ‘appropriation externality’ is that one user’s
increased appropriation reduces the average return available to other appropriators. For the remainder of the
paper we will refer to the appropriation of these resource units as extraction. This is distinct from ‘provision
problems’ which are better captured by the public goods games with voluntary contribution.
2
those to whom they are connected, the information feedback on other’s extractions is network
dependent. Evidence from psychology and sociology indicates that subjects conform to the
behaviour of other’s in the group when they receive feedback of other’s actions (Schroeder et al.
1983, Shafir and Tversky 1992, Asch 1951, Henrich and Boyd 2001). In a CPR dilemma without
monitoring, Apesteguia (2006) finds that information on other’s extractions does not change
extraction signifcantly, however Becchetti, Conzo, and Degli Antoni (2015) finds that the public
disclosure of other’s actions decreases cooperation. Related theoretical investigations from social
learning on networks predicts that beliefs updating and learning stops more quickly in the complete
network. There is moreover a quicker convergence towards ’wrong herd behaviours’ (for instance
through imitating the most frequently observed action) because the entire past history of actions is
common knowledge in constrast to incomplete networks (Gale and Kariv 2003).5 It remains unclear,
how beliefs over others expected extraction vary with monitoring networks in a CPR dilemma, and
how that affects extraction decisions.
The novelty of our paper is to provide new experimental evidence from the lab on how different
monitoring networks influence behaviour, beliefs and outcomes in a non-linear CPR extraction
dilemma. We use a workhorse model of a CPR appropriation dilemma first used in Ostrom, Walker,
and Gardner (1992), Ostrom, Gardner, and Walker (1994). The choice of this model is supported by
the need to better understand behaviour in non-linear environment which better approximate
ecological dynamics and ambiguities faced by extractors in field (Ostrom 2006, Janssen et al. 2010,
van Soest, Stoop, and Vyrastekova 2016, Cardenas 2000). We use three incomplete and fixed
monitoring networks namely the undirected circle network, directed circle network and directed line
network, and the complete network is the baseline. The choice of these imperfect monitoring
networks capture how local factors such as where geographical (physical boundaries, space) or social
(status) distance can structure monitoring networks on the ground. They also allow for comparability
with existing literature. In stage one, extractors decide how much to extract from the CPR. Earnings
are determined by a non-linear production function associated with the CPR and the subject’s share
of the total extraction. We also elicit incentivised beliefs on the expected extraction of other
members in the group. In stage two, subjects can choose to punish only those to whom they can
observe in the monitoring network. We follow the experimental design used in Carpenter et al
(2012) in which subjects are randomly re-matched to a new group, keeping their role on in
monitoring network and the network itself fixed. We find that the structure of the network
significantly influences extraction, punishment, beliefs and punishment. Interestingly, the complete
network the least efficient, with higher extraction, beliefs over others expected extraction and
punishment. Lastly, we show that higher beliefs over other’s extractions are associated with greater
extraction from the common pool resource.
Lab experiments are particularly well suited to tackle these questions. In naturally occurring
monitoring networks, individuals may sort into monitoring roles based on their preferences and
information. Directly comparing behaviour and outcomes of different monitoring networks thus
presents an endogeneity problem (Jackson 2014, Choi, Gallo, and Kariv 2015). Additionally multiple
5
These studies examine a pure information externality (i.e. payoffs do not depend on other agents actions)
that occurs when the proportion of agents choosing a particular action is large enough. The public information
in favor of this action outweighs the private information of an agent and she ’follows the herd’ (Gale and Kariv
2003), Banerjee (1992), (Smith and Sørensen 2000).
3
relationships between extractors exist simultaneously, which will confound causal impacts of
particular network structure on behaviour and outcomes (Bodin and Crona 2009). Lab experiments
are thus an important first step to isolate the behavioural implications of structural properties of the
monitoring network and explore how individuals use network information. This is a key step towards
designing solutions to promote cooperation, and therefore an important complement to field
studies.
This study contributes to the literature on the role of behavioural factors and institutional design in
the overharvesting of shared common pool and public goods resources. Some important aspects
covered in these studies includes social preferences such as conditional cooperation and reciprocity,
social norms, conformity, reputation and the importance of institutional design such as endogenous
institutions, leadership, ostracism and communication and verbal sanctioning (Jager et al. 2000,
Anderies et al. 2011, Cardenas, Janssen, and Bousquet 2013, Cardenas 2011, Tavoni, Schlüter, and
Levin 2012, Fehr and Fischbacher 2002, Fischbacher, Gächter, and Fehr 2001, Sethi and Somanathan
1996, Hackett, Schlager, and Walker 1994, Balliet 2010, Levy et al. 2011, Masclet et al. 2003). We
also contribute to the literature on the role of social networks in natural resource governance
outlined above such as Bodin and Prell (2011), Janssen et al. (2006) and Bodin and Crona (2009), and
the literature on network perspectives in environmental and natural resource economics (Currarini,
Marchiori, and Tavoni 2015).
The study is also related to the theoretical literature on monitoring and community networks on
public goods games such as (Wolitzky 2012, Acemoglu and Wolitzky 2015, Nava and Piccione 2014,
Takahashi 2010). Wolitzky (2012) for instance suggests that grim trigger strategies can sustain
cooperation in in better connected monitoring networks (which specify information feedback and
punishment) in a public goods game. Other related theoretical literature examines the effect of
geographical, social and economic networks in public goods provision (Bramoulle and Kranton 2007)
and common pool extraction (Ilkilic 2011, Noailly, Withagen, and Van den Bergh 2007). There is a
conspicuous lack of experimental evidence on the effect of incomplete monitoring networks in a CPR
extraction dilemma in contrast to the rise of network experiments in prisoner dilemma and linear
public goods (PG) contribution games (Carpenter 2007, Carpenter, Kariv, and Schotter 2012,
O'Gorman, Henrich, and Van Vugt 2009, Leibbrandt et al. 2014, Choi, Gallo, and Kariv 2015, van
Leeuwen et al. 2015, Rosenkranz and Weitzel 2012, Boosey and Isaac 2014, Kosfeld 2004). The set of
experiments most relevant to the current study, manipulates monitoring networks in repeated
public goods game with a voluntary contribution mechanism (VCM). There is an emerging consensus
that connected networks can elicit at least as much contribution as complete networks (Carpenter,
Kariv, and Schotter 2012, Boosey and Isaac 2014). However it is unclear whether they are the most
efficient after punishment (O'Gorman, Henrich, and Van Vugt 2009, Leibbrandt et al. 2015).
Carpenter, Kariv, and Schotter (2012) is the closest to ours and examines how the graph theoretic
properties of the network influence contributions and punishment through eight different networks.
While the evidence is mixed across networks, they find cooperation is higher in connected and
complete networks against disconnected networks. They also find that directed networks elicit more
punishment and asymmetric monitoring roles elicit more punishment. They find both complete and
connected networks, which are also can more efficient than (some) disconnected networks, such as
the line networks. Leibbrandt et al. (2015) vary punishment networks and capacity through
complete, pairwise and untouchable networks. They find that the greater punishment results in
more contributions, but high cooperation is sustained only in complete and untouchable networks.
4
Unlike these studies, we model a CPR extraction dilemma, characterised by subtractability of
resource units and non-linearity in the strategy space. It has been pointed out that greater ambiguity
and complexity in the non-linear games and higher gains from defection can explain the weaker
effect of punishment and lower cooperation, relative to the standard public goods VCM game
(Cason and Gangadharan 2015, Sturm and Weimann 2006).6 There is therefore good reason to
suspect findings from the existing literature, may not hold in the current game. Moreover none of
these experiments model beliefs in conjunction with monitoring networks, which may be an
important factor in this non-linear setting.
We begin our analysis by outlining and motivating the choice for the different network treatments
and graph properties to be tested, followed by a description of the strategic game in section 2.
Section 3 outlines the experimental design and section 4 summarises the main results from our
experiment on extraction, beliefs, punishment and efficiency. We discuss our results in relation to
existing literature and conclude in section 6.
2. Monitoring networks in a common pool resource dilemma
The monitoring network determines which who subjects are connected to, which in turn determines
the information feedback that they receive on other’s extractions, and who they can punish i.e.
punishment opportunity. Figure 1.1-1.4 illustrates four network treatments and their network
properties. Assuming that the hypothetical CPR is a fishing ground, each four member group of
extractors constitutes a monitoring network and is represented as a graph with four nodes each
representing one extractor given by 𝑖 = 𝐴, 𝐵, 𝐶, 𝐷. Using the notation of Carpenter, Kariv, and
Schotter (2012), a bidirectional link between any two nodes implies they receive information
feedback (i.e. can observe each other’s extractions) in stage one and can punish each other in stage
two if they choose to. 𝑁𝑖 represents the monitoring neighbourhood of each node 𝑖, which lists the
extractors that 𝑖 monitors (where 𝑖 ≠ 𝑗). If the link is unidirectional or directed, only the extractor to
whom the link is pointed towards is monitored and not vice-versa. Thus, if a link runs from 𝑖 to 𝑗,
then 𝑖 can monitor 𝑗 (𝑗 ∈ 𝑁𝑖 ), but 𝑗 cannot monitor 𝑖 (𝑖 ∈ 𝑁𝑗 ). Importantly, all extractors within a
particular monitoring network have non-excludable access to the same CPR. This captures the nonexcludability characteristic of the CPR appropriation dilemma.
The complete monitoring network illustrated in Figure 1.1 represents a scenario where extraction is
completely transparent i.e. all extractors can observe and punish each other. As noted previously,
this is the monitoring institution implicitly analysed in previous CPR experiments (Cason and
Gangadharan 2015, Ostrom, Walker, and Gardner 1992), and serves as the baseline. Figure 1.2 is an
undirected circle network that represents an incomplete monitoring network, where extractors can
only observe and punish their immediate neighbour (A monitors only C and B), and not those
situated at some geographical distance from them (D) although they extract from the same fishing
ground. The only difference between the undirected circle and complete network is that the former
is incomplete. Figure 1.3 and 1.4 is a directed circle and directed line network respectively and
represents decentralised community monitoring institutions. In the directed circle, elected local
officials (A) can hire and monitor guards (B) to patrol sections of the fishing ground, who can
immediately apprehend extractors (C and D) if they are caught violating fishing restrictions. If an
official is caught violating agreed rules she can be punished through an open meeting of the whole
6
This is also reflective of ambiguity in ecological thresholds
5
community. If she cannot be monitored because of her status position, the directed circle becomes
the directed line network as extractors cannot punish or observe the official. The only difference
between the undirected circle and directed circle is the latter is a directed network. The only
difference between the directed circle and line networks are the latter is disconnected.
Figure 1: Network treatment groups and properties
[1.1] Complete
Network
(Baseline)
[1.3] Directed
Circle Network
Complete
Connected
Undirected
Incomplete
Connected
Directed
[1.2] Undirected
Circle Network
[1.4] Line Network
Incomplete
Connected
Undirected
Incomplete
Disconnected
Directed
Completeness, directedness and connectedness are global network properties, and allow us to
isolate how aggregate structural characteristics influences group and individual behaviour (Jackson,
Rogers, and Zenou 2015). Comparing behaviours, beliefs and outcomes across these four stylised
monitoring networks will allow us to explore how the structure and properties of the monitoring
network matters in a CPR extraction dilemma. Understanding the impact of each network property
can be especially important in institutional design to increase cooperation. The definitions of these
network properties are briefly summarised below;
1. Completeness [Network 0]: each pair of nodes is connected by a link and represents perfect
monitoring i.e. everyone can observe everyone’s extractions from stage one and can chose
to punish any other subject in stage two. Networks [1-3] are incomplete.
2. Directedness [Networks 2-3]: if the link between pair of nodes is not bidirectional (i.e. it does
not point in both directions), the network is a directed network; otherwise it is undirected
[Networks 0-1]. Directedness
3. Connectedness [Networks 0-2]: if every pair of nodes 𝑖 and 𝑗 is connected by a path, it is
connected; otherwise it is disconnected [Network 3]. A ‘path’ represents a one type of
connection between two nodes in a graph. It is a sequence of nodes wherein each node in
the graph may be used at most one time.
6
To model the CPR extraction dilemma itself, we follow the baseline experiment first used in Ostrom,
Walker, and Gardner (1992), Ostrom, Gardner, and Walker (1994). This strategic game is modelled
after the bio-economic fisheries problem (Gordon 1954), where a group of extractors decide
simultaneously how much effort to put into extraction or into a private activity that returns a fixed
rate of return. The return to extraction from the CPR depends on the extraction of all others in the
network, as access to the CPR is non-excludable. Thus in stage one, 𝑛 extractors have an fixed
endowment, 𝑒. Each extractor 𝑖 (𝑖 = 𝐴, 𝐵, 𝐶, 𝐷), simultaneously decides to allocate some portion of
her endowment (can be thought of as effort) to a common account (𝑥𝑖 in the CPR, where 0≤ 𝑥𝑖 ≤ 𝑒)
or a private account (an outside option, can be thought of agricultural wage labour). The private
account yields a constant marginal return, 𝑤 (can be thought of agricultural wage). The return to the
extractor from the CPR is proportional to the amount allocated to the common account by her, the
total allocation made by all extractors within the network and the CPR production function
represented as 𝐹(𝑋). If the total allocation to the common account is = ∑ 𝑥𝑖 , the return to 𝑖 is given
𝑥
by the 𝑖⁄𝑋 share of 𝐹(𝑋).
𝑥𝑖
⁄𝑋 is referred to as proportional quota rule which gives that the extractor’s payoff
from the common production function depends on both her own contribution and on the
contribution of all other extractors in her group (Beckenkamp 2006). This captures the
subtractability characteristic of the CPR extraction dilemma, as group payoffs are rival. This strategic
game allows us to capture field settings where it is initially more profitable to allocate some portion
of the endowment to the common account, but allocating all the endowment in the CPR is
counterproductive (F ′ (0) > 𝑤 and F ′ (ne) < 0). We use a concave and quadratic production
function where 𝐹(𝑋) = 𝑎𝑋 − 𝑏𝑋 2 . Assuming subjects have standard self-interested preferences,
the payoff from stage one is;
This fraction
𝑥
𝜋𝑖1 = 𝑤(𝑒 − 𝑥𝑖 ) + ( 𝑖⁄𝑋)(𝑎𝑋 − 𝑏𝑋 2 ) if 0 < 𝑥𝑖 ≤ 𝑒
𝜋𝑖1 = we if 𝑥𝑖 = 0
In the second stage, extractors can choose to punish others after observing their extractions at some
cost. Each 𝑖 can punish 𝑗 (𝑗 ∈ 𝑁𝑖 ) to reduce 𝑗’s payoff 𝜋𝑗1 from the first stage by 𝑝𝑗𝑖 at a unit cost 𝑐1 ,
with 0 < 𝑐1 ≤ 1. Each token received reduces the other’s earnings by some factor 𝑐2 (0 ≤ 𝑐2 ). The
payoffs from stage two are the maximum between 0 and the net payoff from stage one (after
punishment received and given);
𝑗
𝜋𝑖2 = max {0, 𝜋𝑖1 − 𝑐1 ∑ 𝑝𝑖 − 𝑐2 ∑ 𝑝𝑗𝑖 }
𝑗 𝜖 𝑁𝑖
𝑗 𝜖 𝑁𝑗
If extractors are self-interested and maximise expected payoffs, then the predicted Nash equilibrium
extraction in stage two would be to not punish those within the network as punishing is costly. This
𝑗
gives 𝑝𝑖 = 0 for all 𝑖 who can monitor𝑗 ∈ 𝑁𝑖 . By backwards induction, punishment cannot
discourage free-riding in stage one. In Stage one, the predicted group Nash equilibrium extraction is
𝑛 𝑎−𝑤
(𝑛+1) 𝑏
versus the corresponding group’s socially optimal or Pareto optimal equilibrium extraction
7
of
𝑎−𝑤
.
2𝑏
Therefore the predicted sub-game perfect equilibrium from this game is to give no
punishments in stage two, and to choose the Nash equilibrium extraction in stage one, irrespective
of the opportunities to punish given by each network. As expressed in Ostrom (2006) this strategic
game approximates some of the complexities and non-linearity in the field by using the classic
textbook example of a non-linear common-pool resource dilemma (pg. 152) (Ostrom, Walker, and
Gardner 1992, van Soest, Stoop, and Vyrastekova 2016). In addition, this set-up reflects the essence
of actual decisions taken by extractors in a field setting (Cardenas 2000), as it represents situations
where the socially optimal choice is not to allocate one’s entire endowment to the common good as
both the selfish and socially optimal strategies are in the interior of the strategy set. Finally, as noted
by Cason and Gangadharan (2015), the share-based returns to the common pool creates higher
gains from defecting from cooperation in this setting, (relative to the standard VCM public goods
game). This makes cooperation more challenging and can reduce the effectiveness of punishment
(Ibid.). The four stylised monitoring institutions outlined above capture local network aspects of CPR
dilemmas, where punishment is not possible without feedback on extractions. Importantly, they
allow us to test how these different network properties affect behaviour, beliefs and outcomes.
3. Experimental design
The experiment took place in 10 sessions during November-December 2015, at the LSE Behavioural
Research Lab using z-Tree (Fischbacher 2007). Subjects were restricted to students and recruited
through ORSEE software (Greiner 2004). Table 1 presents the experimental design, and shows that a
total of 192 students participated in the experiment, with the highest number of subjects in the
complete (baseline) treatment. The network treatment and node position (i.e. A, B, C, D) is fixed
throughout each session. The two stage game was played for fifteen rounds. In each round, subjects
were randomly re-allocated into a new network (or group) of four with a subject of each type to
mitigate reputation effects. This follows the experimental design used in Carpenter et al. (2012) to
allow for comparability. In total we have 720 group-level observations and 2880 individual-level
observations. Annex table A1 presents subject attributes by treatment group and indicates that
subjects in all treatment groups are roughly comparable across sex, education level, discipline and
previous experience in experiments.7
7
There are a majority of females in all treatments (on average 59% of the subjects were female), enrolled in a
Master’s (49%) or Undergraduate degree (47.4%). On average 50.5% of the students has previously
participated in less than 5 experiments. In the complete network there was a slightly lower share of subjects
with no previous experience in any lab experiment (15% versus an average of 31% in the other treatment
groups) and in the undirected circle network has subjects with slightly lower share of subjects with experience
in more than 5 experiments (11% versus an average of 31% in the other treatment groups).
8
Table 1: Experimental design
Network
Complete
Complete [0]
Yes
Circle [1]
No
Directed Circle [2]
No
Directed Line [3]
No
Connected
Yes
Yes
No
No
Directed
No
No
Yes
Yes
N
60
36
40
56
Groups
225
135
150
210
Obs
900
540
600
840
Total
192
720
2880
Note: N= number of subjects, Groups= number of group-level observations, Obs= number of individual-level observations
Table 2: Features of the experimental game
Features
OGW 1994
Endowment
25
a
23
b
0.25
w
5
Group size (n)
8
Fee-to-Fine Ratio
0.25 to 0.50
𝑥𝑛 -tokens
8
𝑥𝑛 -payoff
70
𝑥𝑝 -tokens
4.5
𝑥𝑝 -payoff
83
Nash (N)/Pareto (P) tokens
1.8
N%P payoff
84
AMR 2006*
100
6
0.0125
1
4
80
180
50
225
1.6
80
CG 2015
12
18
0.4
2
4
0.33
8
37.6
5
52
1.6
72
KL 2014*
50
6
0.25
1
4
40
112.5
25
90
1.6
80
Experiment
25
25
0.25
5
4
0.33
16
189
10
225
1.6
84
OGW 1994: (Ostrom, Gardner, and Walker 1994); CG2015: (Cason and Gangadharan 2014); AMR2006: (Apesteguia and
Maier-Rigaud 2006); KL 2014: (Kingsley and Liu 2014); Experiment refers to our study. * no monitoring.
The non-linear CPR experimental environment is standard, where subjects have to allocate tokens to
either or both a common and a private account in stage one. As explained in the previous section,
the allocation of an additional token to the common account creates a negative externality for all
members in the group. We refer to higher allocation to the common account as higher ‘extractions’
to capture this negative externality. The game parameters, predicted Nash equilibrium and Pareto
optimal extraction are presented in table 2 in relation to comparable CPR experiments. Parameters
were chosen to ensure whole integers for the equilibrium extractions and comparability with
existing literature (endowment = 25 tokens, a=25, b= 0.025, w=5, n=4). An important feature of the
CPR dilemma is that the Nash and Pareto equilibrium extractions (𝑥 𝑛 and 𝑥𝑝 ) are relatively close to
each other in the interior choice space at 16 and 10 tokens allocated to the common account
respectively. The ratio of the Nash to Pareto equilibrium extraction (N/P) ranges from 1.8 to 1.6 in
the literature. This ratio is determined by the number of subjects in the network (the 𝑛 extractors),
which in turn determines the size of the externality caused by greater extraction from the commons
account. As we keep the network size fixed at 4 members, the ratio of the Nash equilibrium
extraction and Pareto extraction is fixed at 1.6.
The framing of instructions is also standard in the literature (e.g. punishment points are referred to
as ‘deduction points’, subjects can choose to ‘place’ tokens in the common or private account etc.).
Instructions and an earnings table were provided, and the former was read aloud during the start of
the experiment. All subjects had to complete five test questions, which were checked and corrected
before the start of the experiment, to ensure common knowledge of rules of the game. After the last
round, a questionnaire explored the motivation behind decisions taken. This serves as a second
9
check to ensure internal validity and is also used to motivate our results. The conversion rate was 25
tokens equal GBP 0.50. Each session lasted for around 70 minutes and the average earnings of the
participants were around GBP 11.5.8
Subjects can calculate their expected payoffs using their guesses of the other subject’s tokens before
inputting their final decisions in stage one. This allows us to record beliefs about the expected
extraction other group members in each period, and also serves as a third check to ensure internal
validity.9 We incentivise guesses so subjects can earn 25 tokens for each correct guess, with total
potential earnings reaching GBP 1.5. As the guess is incentivised, it promotes truth telling by subjects
(Schotter and Trevino 2014, Schlag, Tremewan, and Weele 2014). One possible concern is that
participants could behave strategically by hedging their guesses to maximise earnings from both the
CPR appropriation dilemma and the guess game. However we believe this may not be a serious
concern as hedging options are not very clear and expected payoffs from hedging are low in relation
to the payoff from the CPR game which is already cognitively demanding (Schotter and Trevino
2014). We additionally randomise actual payment from the guessing game by selecting a single
round for payment, which may incentivise subjects to reveal truthful beliefs to maximise probability
of getting payment in every round (Schlag, Tremewan, and Weele 2014). We refer to average beliefs
over other members extractions as ‘beliefs’ for the remainder of the analysis.
In the second stage, subjects can assign or receive deduction points depending on their network
position as explained in the previous section. The cost of assigning deduction points is one token
(𝑐1 = 1) and the cost of receiving a deduction point is three tokens (𝑐2 = 3). This corresponds to a
fee-to-fine ratio of 0.33, in line with the literature. The maximum deduction points a subject can
assign is bound by her earnings in the first stage. Negative earnings are possible, but this was very
uncommon (it occurred in only 7 out of 2880 observations), and were given a value of zero for
payment purposes. Subjects only know the total punishment received in the second stage and the
network structure which specifies which type of subject can punish them (i.e. A, B, C, D) but cannot
identify the subject punishing them.
4. Results
We present results from the group-level analysis to examine whether there are any differences in
extraction, beliefs, punishment and efficiency across monitoring networks. We use non-parametric
Wilcoxon-Mann-Whitney to complement the graphical analysis and check if these differences are
statistically significant across treatments. In addition, t-tests are also used to supplement the
analysis, with very similar results. They are thus presented in annex table A1, with the results of
Wilcoxon-Mann-Whitney tests. These results are further motivated by group-level Ordinary Least
Squares regressions (OLS, with time fixed effects) to econometrically estimate differences in
behaviour across monitoring networks relative to the baseline complete network.10 Individual-level
8
Supplementary materials in Annex 3 contains including instructions, test and motivational questions and
sample game interface.
9
Eliciting beliefs in experiments may have the effect of making subjects more selfish or ‘think like a game
theorist’ (Croson 2000), however Gächter and Renner (2010) find that it can make subjects more cooperative.
We cannot test whether subjects behave differently without belief elicitation, because our study objective was
to explore how beliefs vary by networks and whether they are related to extraction.
10
Tobit regressions show nearly identical results, so we only present the OLS results in the text.
10
random effects regressions are also used to dig deeper into the factors affecting behaviour,
outcomes and beliefs (with time fixed effects, and subject attribute controls).
4.1. Extraction
Figure 2 (a-c) plots the average extraction for all 15 rounds, entire period and by three sub-periods
(rounds 1-5, 6-10 and 11-15). The bar graphs are constructed with 95% confidence intervals (CI) and
the numbers on top of the bar-graphs are the average values. Average extraction pooled across
treatments starts near the Pareto equilibrium extraction at 11.4 tokens in round one and rises to
13.9 tokens on average or 55.7% of the endowment over rounds 1-5. In the complete network,
extraction in the first round is 11.8 tokens, and increases towards the Nash equilibrium extraction
(i.e. 16 tokens) at 14.5 tokens or 58% of the endowment. This is in line with comparable CPR
experiments which implicitly model the complete network i.e. 50% of endowment was allocated to
the common account in Cason and Gangadharan (2015), 60% in Kingsley and Liu (2014) or 66.9% in
Apesteguia and Maier-Rigaud (2006). A Wilcoxon sign-rank test rejects the null hypothesis that the
mean extraction equals the Pareto optimal equilibrium extraction of 10 tokens in both the first
round or the average of the first five rounds (|z| = 3.351 and Prob >|z| = 0.001 for all treatments).11
Extraction increases with time across all other networks and also approaches the Nash equilibrium
extraction. Average extraction for the last five periods is not significantly different from the Nash
equilibrium extraction in directed circle and line networks (the Wilcoxon-Mann-Whitney |z|= 0.710;
Prob >|z|= 0.478 and |z|= 1.599; Prob > |z|= 0.11 respectively). It is marginally lower and
significantly different from the Nash equilibrium extraction in the complete network (the WilcoxonMann-Whitney |z|= 1.773; Prob > |z|= 0.0762) and undirected circle (|z|= 2.153, Prob > |z|=
0.031).12 This echoes the consistent findings of increasing free-riding with time in both CPR and
public goods experiments.13
When we compare across networks, average extraction is significantly higher in the complete
network relative to the undirected circle and directed line (|z|=2.796; Prob > |z| = 0.005 and
|z|=1.825; Prob > |z| = 0.068 respectively), and is higher but not significant relative to directed
circle network (z=1.558; Prob > |z| = 0.119). Differences in average extraction are not statistically
significant across the undirected circle, directed circle and directed line networks. From table 3,
model 1, OLS regressions return negative coefficients on all network indicators when regressed
against group-level extraction of the complete network which is the omitted category. The
coefficients for the undirected circle, directed circle and directed line are significant at 1%, 10% and
5% respectively. This leaves us with the following result:
11
The Wilcoxon sign-rank tests the equality of matched pairs of observations under the null hypothesis that
the median of the differences is zero. No further assumptions are made about the distribution of the variable
of interest.
12
This is again comparable to existing literature- Cason and Gangadharan (2015) record the average allocation
to CPR was 6.97 tokens in last periods of play (rounds 6-10) against Nash equilibrium allocation of 8 tokens.
Similarly Apesteguia and Maier-Rigaud (2006) record allocation of 75.6 tokens to CPR against Nash equilibirum
allocation of 80 tokens in last 5 rounds of play (16-20).
13
For exhaustive reviews of lab and field experimental literature on common pool and socio-ecological
systems see Ostrom (2006), Anderies et al. (2011), Janssen et al. (2010), Cardenas (2000), Cardenas and
Carpenter (2008). Chaudhuri (2011) provides a recent review of the PG experimental literature, apart from
Ledyard (1995).
11
Result 1: Extraction starts above the Pareto optimal equilibrium extraction and increases with time in
all networks, and reaches the Nash equilibrium extraction in the directed circle and directed line
networks in the last five periods. Group-level average extraction is highest in the complete network.
Figure 2: Average extraction by network
(a) All rounds
(b) Entire period
12
(c) Sub-periods
Table 3: Group-level regressions
Model
Dependent variable
Independent variables
Undir circle
Dir circle
Dir line
(1)
X
(2)
X
(3)
B
(4)
Pun
(5)
PS
(6)
Earn
-0.861***
(0.279)
-0.568*
(0.293)
-0.562**
(0.278)
-0.793***
(0.286)
-0.471
(0.298)
-0.514*
(0.277)
0.0631
(0.0560)
11.23***
(0.747)
-1.071***
(0.185)
-1.538***
(0.196)
-0.758***
(0.223)
-4.923***
(1.386)
-9.085***
(1.306)
-8.638***
(1.282)
-0.171
(0.174)
-0.431**
(0.200)
-0.281
(0.180)
16.41***
(3.678)
16.90***
(3.663)
16.35***
(3.624)
10.78***
(0.338)
10.04***
(1.318)
1.101***
(0.198)
196.6***
(3.796)
Beliefs1
Constant
11.91***
(0.461)
Observations
720
720
720
720
720
720
R-squared
0.139
0.141
0.297
0.118
0.028
0.103
Time fixed effects
Yes
Yes
Yes
Yes
Yes
Yes
Robust standard errors in parentheses. *** p<0.01, ** p<0.05, * p<0.1. Complete network is the omitted category.
4.2. Beliefs
Figure 3 (a-c) plots beliefs over other’s expected extraction for all 15 rounds, entire period and by
three sub-periods. Beliefs pooled across treatments starts at 10.03 tokens in round one (10.4 tokens
in complete network), and averages to around 11.98 tokens over rounds 1-5 (12.4 tokens in
13
complete network).14 We cannot reject the null hypothesis that the average beliefs equal the Pareto
optimal equilibrium extraction of 10 tokens using Wilcoxon sign-rank tests for the first round in all
treatments. Beliefs increases with time across treatments, but are significantly lower than the Nash
equilibrium extraction of 16 tokens in all treatments. This suggests some ‘optimism’ in beliefs, as
subjects expect other group member’s to extract less than they do themselves. Such optimism has
been similarly recorded in common pool games (Velez et al. 2009) and public goods contribution
games (Gächter and Renner 2010, Croson 2000). However, optimism about other’s expected
extractions declines, as subjects update their beliefs.
When we compare the complete network to the undirected circle, the Wilcoxon-Mann-Whitney
|z|=4.752; Prob > |z| = 0.000. Similarly, when we compare the complete network to the directed
circle and directed line, the Wilcoxon-Mann-Whitney |z|=6.399; Prob > |z| = 0.000 and z=3.004;
Prob > |z| = 0.003 respectively. Beliefs are also significantly higher in the undirected circle relative to
the directed circle (z=1.866; Prob > |z| = 0.062) but not significantly different compared to the
directed line (Wilcoxon-Mann-Whitney |z|=1.294; Prob > |z| = 0.196). Beliefs over other’s
extraction are significantly lower in the directed circle relative to the directed line (Wilcoxon-MannWhitney |z|=-2.904; Prob > |z| = 0.004). Thus beliefs are highest in the complete network, followed
by the directed line, undirected circle and directed circle. This is supported by the econometric
results (table 3, model 6) which show negative coefficients on all network indicators (significant at
1%) when regressed against group-level beliefs of the complete network which is the omitted
category. This leaves us with the following result:
Result 2: Beliefs start at the Pareto optimal equilibrium extraction and increases with time in all
networks, although it doesn’t reach the Nash equilibrium extraction in any network. Beliefs are
highest in the complete network, followed by the directed line, undirected circle and directed circle.
14
There are 13 subjects who inputted low (e.g. only 1s) or no beliefs (zeros; this constitutes 6.8% of the total
number of subjects). Of these, 6 subjects were in the complete network treatment, 2 subjects in the
undirected and directed circle each and 3 subjects in the directed line network. We classify these subjects as
outliers under the condition that their average beliefs were equal to or less than 5 for more than 5 periods of
play. We may be concerned that the attrition from the beliefs game was non-random. 10% of the total
subjects dropped out of the guessing game by this criteria, compared to 5.6% of subjects in undirected circle,
5% of subjects in the directed circle and 5.4% of subjects in directed line. Annex table A3 shows the mean
beliefs, and share of observations for both observations with and without outlier beliefs. In the main body of
the text we present results only for beliefs of those subjects who are not classified as outliers. We conduct the
same analysis for all subjects (including those classified as outliers), and report the results (which are similar) in
the annex.
14
Figure 3: Average beliefs by network
(a) All rounds
(b) (b) Entire period
15
(c) Sub-periods
As noted previously, contributions in public goods games are positively associated with higher
beliefs over other’s extractions (Fischbacher and Gächter 2010) and it argued that this relationship
may be causal (Smith 2012). By including beliefs as a control variable in CPR extraction dilemma, we
control for the propensity of individuals to extract more if they believe others will also extract more.
Omitting beliefs from the model 1, table 3 may lead to biased coefficients on the network indicators,
due to omitted variable bias. Model 2 in table 3 includes beliefs, which shows a positive but
insignificant coefficient on beliefs. Thus individual-level regressions, will allow us to get a more
precise relationship between networks, extraction and beliefs as we can control for subject
attributes and lagged variables which are found to significantly affect behaviour in the experimental
literature (Leibbrandt et al. 2015). Table 4 presents the results on random effects regressions on
individual-level extractions by the network indicators (models 1-4).15 Model 1 shows the coefficients
on the three incomplete networks on the undirected circle network are negative, but significant at
5% only for the undirected circle network, when we control for subject attributes and time fixed
effects16. When we add lagged variables of extraction and punishment, the negative coefficients on
the indicators of the undirected circle and directed circle networks are both significant at 5%. Lagged
extraction is positively associated with extraction and this is significant at 1%. Lagged punishment
received and lagged extractions of other members have negative and small coefficients, which are
significant at 5% and 1% respectively.
15
In our model, random effects may be preferable to fixed effects because the treatment variable (network
indicators) is a factor variable (Wooldridge 2010). We attempt to control for any other omitted variables which
may bias extractions by using controls for subject attributes, as in the previous regressions. As the treatment is
randomly assigned, we are not concerned it is correlated with an omitted variable in the error term.
16
These are included in the annex table A3. The coefficient on sex is negative and significant in model 3,
suggesting females extract significantly less than males. Similarly we find that subjects studying political
science extract less than those in accounting and finance, and those enrolled in a PhD extract less than those in
a first year undergraduate course. Barring for subjects in political science and those enrolled in a PhD, the rest
of the observables are not significant in models 7 and 8 in the second stage Instrumental Variables Regression.
16
In model 3, the coefficients on beliefs and lagged beliefs are insignificant. We are concerned that
there endogeneity between extractions and beliefs due to simultaneity bias i.e. higher beliefs may
drive higher extraction but higher extraction may also lead to the formation of higher beliefs over
other’s extraction. This may bias the coefficient upwards; however we find that the coefficient on
beliefs is negative. However we are also concerned that there may be some measurement bias as we
use subject’s stated elicited beliefs. This would attenuate the coefficient on beliefs. We thus follow
Smith (2012) in using an instrumental variables (IV) approach by using the second and third period
lag of beliefs and the second lag of the average contribution of other’s in the group as instruments.
As in Smith (2012) we assume that these instruments have no direct effect on contributions, and
only have an indirect effect through beliefs (i.e. there is no correlation between instruments and
error term and there is a correlation between the instruments and the endogenous regressor i.e.
beliefs).17
This is supported with post-diagnostic tests whose results are reported in the annex with the firststage results. Model 4 in table 4 present results of the second stage IV regression. We find that the
coefficients on the network remain negative but insignificant for the undirected and directed circle
networks. The sign of the coefficient on beliefs however becomes positive and significant at 5%. This
suggests that a unit increase in beliefs is associated with higher extraction by 0.404 in models 4.
Post-diagnostic tests indicate that the exclusion restriction is just about satisfied for model 4 as the
first-stage F-statistic is 10.75. The Sargan-Hansen test of over-identifying restrictions18 that tests the
null hypothesis that the instruments are exogenous also cannot be rejected as the Sargan-Hansen
statistic (and Hansen-J statistic) is 2.126 and is insignificant. Thus model 4 seems to satisfy the
instrument relevance and exogeneity conditions. The coefficient on lagged extraction, punishment
received and other’s average extraction retain their previous signs and are all significant and either
1% or 5%. In summary, higher beliefs about other’s extraction has a positive and significant impact
on extraction. Extractions by subjects are further influenced by lagged extraction, punishment
received and extractions of others in their group. The first-stage results are reported in Annex table
A4.19
Result 3: Higher beliefs about other member’s extractions are positively associated with higher
extractions from the common pool resource.
17
Smith (2012) additionally uses subject dummies to control for unobserved heterogeneity that remain fixed
across time but is constant for each subject. For the reasons mentioned in footnote 11, we use random effects
rd
instrumental variables regression. We also omit the 3 lag of other’s average extraction as it does not explain
any of the variation in beliefs and is a weak instrument. When we include this F-stat in the first stage falls to
8.16 from 10.75 and 18.71 from 19.97 in models 5 and 6 respectively. As suggested by Stock and Watson
(2012), it is preferable to discard the weakest instrument, and use the most relevant ones, when the
endogenous regressor is over-identified.
18
The Sargan-Hansen test tests the joint null hypothesis is that the instruments are valid instruments, i.e.,
uncorrelated with the error term, and that the excluded instruments are correctly excluded from the
estimated equation.
19
When the model is replicated for all 192 subjects (including those with outlier beliefs), we find that the
coefficient on beliefs in the second stage is 0.294 and significant at 5%. The coefficient on the directed circle
network is -0.823 at significant at 5%. The first stage F-statistic is much higher at 19.97 for this model, with
insignificant Sargan-Hansen statistic (and Hansen-J statistic) of 2.392. Th results are presented in annex table
17
Table 4: Individual-level extraction
VARIABLES
Undir circle
Dir circle
Dir line
(1)
RE
(2)
RE^
(3)
RE
(4)
RE-IV
-1.162**
(0.592)
-0.938
(0.621)
-0.529
(0.682)
-0.820**
(0.345)
-0.685**
(0.346)
-0.510
(0.438)
0.440***
(0.0390)
-0.0201***
(0.00588)
-0.580
(0.374)
-0.660*
(0.370)
-0.0971
(0.411)
0.408***
(0.0368)
-0.0144**
(0.00565)
-0.424
(0.421)
-0.317
(0.452)
0.211
(0.460)
0.372***
(0.0437)
-0.0124**
(0.00633)
-0.0802**
(0.0349)
-0.231***
(0.0636)
0.404*
(0.221)
-0.129
(0.0986)
8.921***
(1.767)
1,992
166
Lagged extraction
Lagged punishment
Lagged
others
extraction
of
12.81***
(0.956)
10.42***
(0.805)
-0.0975***
(0.0359)
-0.0224
(0.0497)
0.0605
(0.0405)
10.65***
(0.957)
2,880
192
2,492
178
2,324
166
Beliefs
Lagged beliefs
Constant
Observations
Number of subjects
Controls for subject
attributes
Yes
Yes
Yes
Yes
Time fixed effects
Yes
Yes
Yes
Yes
Outlier beliefs
No
No
No
No
First-stage F statistic
10.75***
Sargan-Hansen statistic
2.927
Robust standard errors in parentheses. *** p<0.01, ** p<0.05, * p<0.1. Complete network is the omitted category. ^14
subjects assigned to role A in directed line excluded as they receive no punishment. ^^ Total of 26 subjects excluded (role A
in directed line and those with outlier beliefs).
From table 3, model 3 and the non-parametric tests, we see that monitoring networks directly
impact beliefs. This is corroborated by results from the individual-level random-effects models on
beliefs presented in table 5. They confirm that beliefs in the complete network are higher than in the
undirected and directed circle networks, and this difference is significant at 1%, when we consider
models 1, 2 and 3 (controlling for subject attributes and time fixed effects)20.
To control for learning from past beliefs and feedback from observing other’s extraction in the
group, we include lagged beliefs and lagged average extraction by others in the group in model 4.
This follows the belief formation model presented in Fischbacher and Gächter (2010). This model
suggests current period beliefs are based on past period beliefs (first and second period lag) and
other member’s average contribution. We find that both the coefficients on the undirected and
directed circle networks fall, but remain significant at 10% and 1% respectively. The coefficients on
lagged beliefs and lagged average extraction by others in the group are positive and significant at
1%. This suggests that beliefs are formed on the basis of lagged beliefs and the feedback of what
20
Across all models, subjects enrolled in humanities courses believe others extract less relative to accounting
and finance subjects and this is significant at 10-5%.
18
other’s extracted in the previous rounds in this common pool extraction dilemma. In our setting the
network determines the feedback of information and thus influences individual’s beliefs. As the
undirected and directed circle network have a statistically significant effect on beliefs, relative to the
complete network, this supports the observation that monitoring network affects extraction, not
just through punishment, but also information feedback and the formation of beliefs.
Result 4: Beliefs over other’s extraction are influenced by beliefs in the previous periods and the
observed average extraction of others in the network. Beliefs are significantly lower in the undirected
circle and directed circle networks, after controlling for lagged beliefs and average extraction of
other’s in the network.
Table 5: Beliefs
VARIABLES
Undir circle
Dir circle
Dir line
(1)
RE
(2)
RE
(3)
RE
(4)
RE
-1.083***
(0.412)
-1.485***
(0.390)
-0.743
(0.456)
-1.083***
(0.413)
-1.485***
(0.391)
-0.743
(0.457)
-1.193***
(0.423)
-1.642***
(0.389)
-0.755*
(0.452)
-0.365*
(0.219)
-0.550***
(0.187)
-0.247
(0.215)
0.362***
(0.0292)
0.105***
(0.0279)
0.111***
(0.0232)
Lagged beliefs
Lagged2 beliefs
Lagged3 beliefs
Lagged other’s
extraction
average
Constant
14.11***
(0.260)
10.77***
(0.438)
Observations
2,685
2,685
Number of subject
179
179
Controls
for
subject
attributes
No
No
Time fixed effects
No
Yes
rho
0.238
0.267
Robust standard errors in parentheses. *** p<0.01, ** p<0.05, * p<0.1
11.29***
(0.715)
0.266***
(0.0261)
2.760***
(0.664)
2,685
179
2,148
179
Yes
Yes
0.261
Yes
Yes
0
4.3. Punishment
Figure 4 (a-c) plots the average punishment received by monitoring network for all 15 periods, the
entire period and by three sub-periods. The bar graphs are constructed with 95% confidence
intervals and the numbers on top of the bar-graphs are the average values. Punishment is volatile
and irregular across all networks. This is similar to the erratic punishment behaviour recorded in
Cason and Gangadharan (2015) and Ostrom, Gardner, and Walker (1994). We also find that there is
no systematic decline in punishment between the first, second and last sub-periods. This is in line
with Cason and Gangadharan (2015) who also find the decline in punishment is not significant
between their two sub-periods of play.
19
We first compare the average punishment received pooled across all rounds between the complete
and undirected circle networks. Although the Wilcoxon-Mann-Whitney test statistic is not significant
(|z|= 0.252; Prob > |z| = 0.801), a t-test of means yields significant differences (|t|=2.961;
Pr(|T|>|t|)= 0.003). The complete network records significantly higher punishment received relative
to both the directed circle and line networks (Wilcoxon-Mann-Whitney |z|= 7.118; Pr(|T|>|t|)=
0.000 and Wilcoxon-Mann-Whitney |z|=6.790; Pr(|T|>|t|)=0.000 respectively). Punishment
received is therefore highest in the complete network relative to all other networks. This is
supported econometrically, where all network indicators show negative and significant coefficients
at 1%, when regressed against the punishment received of the baseline complete network (table 3,
model 4). The undirected circle records significantly higher punishment relative to the directed circle
and line networks as well (Wilcoxon-Mann-Whitney |z|= 7.596; Pr(|T|>|t|)= 0.000 and WilcoxonMann-Whitney |z|=7.019; Pr(|T|>|t|)=0.000 respectively). However average punishment received is
not significantly different between the directed circle and directed line networks (Wilcoxon-MannWhitney |z|=-1.162 and Pr(|T|>|t|)=0.245).
Given that a large literature has established that subjects do punish each other in the lab, it may not
be surprising that we see higher punishment received in complete networks where all subjects have
more opportunity to punish each other. We therefore also investigate the punishment ‘severity’ to
examine how intensely people punish each other in a network if given the opportunity. We define
punishment severity as the total number of punishment points received weighted by the number of
punishment opportunities. For instance, in the complete network each subject has three
opportunities to punish others in the group. Punishment severity is thus estimated by dividing the
group-level punishment received by twelve i.e. the number of punishment opportunities. Figure 3 (ac) plots the average punishment severity by monitoring network for all 15 rounds, the entire period
and by three sub-periods. It indicates that although punishment severity is not as starkly different
across networks as punishment received, punishment severity is still highest in the complete
network.
The Wilcoxon-Mann-Whitney tests indicate that punishment severity is significantly higher in the
complete network relative to all other networks. In model 5, table 3, we find a negative coefficient
on all network indicators, when regressed against punishment severity of the baseline complete
network. However, only the coefficient on the directed circle network is statistically significant at
5%. Punishment severity is higher and significantly so in the undirected circle relative to the directed
circle and line (Wilcoxon-Mann-Whitney |z|= 5.318; Pr(|T|>|t|)= 0.000 and Wilcoxon-MannWhitney |z|= 4.237; Pr(|T|>|t|)=0.000 respectively). The individual-level regressions confirm the
group-level results for both punishment received and punishment severity and are omitted from the
text for the sake of brevity.21
21
Individual-level RE model confirms that those subjects in complete networks receive highest punishment,
followed very closely by directed circle, directed line and directed circle. The results are stable with time fixed
effects, controls for subject attributes and lagged behaviour. Of the control variables, lagged extraction and
punishment received are significantly associated with punishment received at 10%. Punishment severity is not
statistically different between the undirected circle and complete network, is significantly lower in directed
line and directed circle. None of the controls are significant except for lagged extractions. Tables A5 report
these results.
20
Finally, it is also useful to observe how frequently subjects actually receive punishment if there is an
opportunity to punish. In total there are 2670 individual opportunities to receive punishment across
all monitoring networks, and positive punishment was received 32% of the time. Positive
punishment was received 45.55% of the time in the complete network (410 times), 43.70% of the
time in the undirected circles (236 times), 19.05% in the directed line (120 times) and 14.76% of the
time in the directed circle (85 times). Thus not only is the level of average punishment and severity
higher in the complete and undirected circle networks, so is the frequency of punishment. This
leaves us with the following result:
Result 5: Group-level punishment behaviour is erratic and volatile, and does not systematically
change with time in any monitoring network. Punishment received and severity is highest in the
complete network, followed by the undirected circle. Punishment frequency is highest in the complete
and undirected circle, directed line and undirected circle.
Figure 4: Average punishment received (95% CI):
(a) By rounds
(a) Entire period
21
(b) By sub-periods
Figure 5: Average punishment severity (95% CI):
(a) By rounds
(b) Entire period
22
(c) By sub-periods
Figure 6 highlights that subjects who deviate from the average extraction of the other’s in the group,
receive punishment irrespective of whether the extract more (positive deviation, higher than the
group norm or higher extractors i.e. HX) or less (negative deviation, lower than the group norm,
lower extractors i.e. LX) or exactly the amount of the group norm (0; the numbers above the bar are
the average punishment received values22). The first kind of punishment that targets high extractors
has been referred to as altruistic punishment, because subjects are punished for free-riding even at
a cost to the punisher. The second type of punishment, has been referred to as antisocial
punishment, as it penalises extraction below the average of the group (Herrmann, Thöni, and
Gächter 2008, Fehr and Gachter 2002). We observe both altruistic and antisocial punishment when
we model punishment received on positive and negative deviation from other member’s average
extraction. The regressors are interaction terms between the network indicator and absolute
positive and negative deviations from the average extraction of the other members of the group.
Following Fehr and Gachter (2000), positive deviations are constructed as the absolute difference
between the subjects extraction and the average extraction of the others in the group, and is zero
for all extractions equal to or below this group average. Negative deviations from the average of the
group of created analogously. Table 6 shows that the coefficient on other member’s average
extraction is positive and significant, indicating that higher extraction in the group is associated with
higher punishment. The coefficients on the interaction terms for positive deviation (higher
extraction) are positive across all treatments and are significant at 1% in the complete network,
undirected circle, 10% in the directed circle and 5% in the directed line. Coefficients of the negative
deviations from the average extraction are also positive and are significant at 1% for the undirected
circle, directed circle and directed line networks. Interestingly the complete network is the only
network where anti-social punishment is not statistically significant.
Result 6: We observe both anti-social and altruistic punishment across all networks, except the
complete network where we observe only altruistic punishment.
22
49.78% of the observations are HX, 47.94% are LX and 2.28% are SX and the shares are very similar across all
networks.
23
Figure 6: Average punishment received and deviation from other member’s extraction
Table 6: Punishment points received
VARIABLES
(1)
Complete X Positive deviation from other’s extraction
Undir Circle X Positive deviation from other’s extraction
Dir Circle X Positive deviation from other’s extraction
Dir Line X Positive deviation from other’s extraction
Complete X Negative deviation from other’s extraction
Undir Circle X Negative deviation from other’s extraction
Dir Circle X Negative deviation from other’s extraction
Dir Line X Negative deviation from other’s extraction
Average extraction of others
Constant
Controls for subject attributes
Observations
Number of subject
chi2 test for treatment differences
Robust standard errors in parentheses. *** p<0.01, ** p<0.05, * p<0.1
1.449***
(0.218)
1.676***
(0.402)
0.341*
(0.189)
0.217**
(0.0998)
0.199
(0.143)
0.357***
(0.125)
0.584***
(0.119)
0.473***
(0.121)
0.727***
(0.127)
-5.992**
(2.467)
Yes
2,670
178
100.39***
4.4. Efficiency
Figure 7 (a-c) plots the average earnings after punishment by monitoring network for all 15 rounds,
the entire period and by three sub-periods. The bar graphs are again constructed with 95%
confidence intervals and the numbers on top of the bar-graphs are the average values. Earnings
after punishment do not reach the Pareto equilibrium payoff of 225 tokens in any monitoring
24
network and declines after with time in all treatments. This is in line with higher extraction in the
later periods and erratic punishments. Average earnings after punishment pooled across all periods
are in fact significantly lower than the Nash equilibrium payoff of 189 tokens in the complete
network (|z| = 2.442; Prob > |z| = 0.015). Earnings after punishment are not significantly different
from the Nash equilibrium extraction in the undirected circle and circle networks (Wilcoxon-MannWhitney |z| = 1.050; Prob>|z|= 0.294 and |z| = 0.971; Prob > |z| = 0.3315 respectively). Earnings
after punishment are therefore lowest in the complete network relative to all other networks, and
this difference is significant at 1%. This is verified by the econometric analysis which reveals that all
the coefficients of the network indicators are negative and significant at 1% relative to the baseline
complete network which is omitted (table 3, model 6). However the earnings after punishment
across the three other treatments are not significantly different. This leaves us with the following
result:
Result 7: Earnings after punishment decrease with time across networks and are the lowest in the
complete network.
Figure 7: Earnings after punishment (95% CI):
(a) By rounds
(b) Entire period
25
(c) By sub-periods
4.5. The effect of network properties
If the three global network properties of completeness, directedness and connectedness have no
effect on extraction and punishment behaviour, and beliefs, then there would be no difference in
group-level extraction and punishment across these networks with different properties. Specifically
we can formulate the following hypothesis to test the effect of both the local and global network
properties on behaviour, beliefs and outcomes;
If completeness does not influence behaviour (extraction and punishment), beliefs and outcomes
(total earnings after punishment), we should expect to see equal levels of extraction, punishment,
beliefs and earnings between complete and undirected circle networks, as the only difference
between them is the latter is incomplete. We can reject the null hypothesis that the property of
completeness does not affect behaviour, outcomes and beliefs, as the complete network records
statistically higher extraction, punishment received, earnings after punishment and beliefs. Thus
completeness is associated with higher extraction, punishment received, earnings after punishment
and beliefs. However, we cannot reject the null hypothesis with respect to punishment severity,
which is not statistically different between the complete and undirected circle network.
Similarly, if directedness does not influence behaviour, beliefs and outcomes we should expect to
see equal levels of extraction, punishment, beliefs and earnings between the undirected and
directed circle networks, as the only difference between them is the latter is directed. We can reject
the null hypothesis that directedness does not influence punishment received, punishment severity
and beliefs, as both punishment behaviour and beliefs are statistically higher in the undirected circle
compared to the directed circle. Thus directedness is associated with lower punishment, punishment
severity and beliefs. We cannot reject the null hypothesis that directedness does not influence
extraction and earnings after punishment.
If connectedness does not influence behaviour, beliefs and outcomes, we should expect to see equal
levels of extraction, punishment, beliefs and earnings between the directed circle and line networks,
as the only difference between them is the latter is disconnected. We can reject the null hypothesis
that connectedness does not influence beliefs, as beliefs over other’s extractions is significantly
26
lower in the directed circle network compared to the directed line network. Thus connectedness is
associated with lower beliefs over other’s extractions. We cannot reject the null hypothesis that
directedness does not influence extraction, punishment, punishment severity and earnings after
punishment. This leaves us with the following result regarding global graph theoretic properties:
Result 8: Completeness is associated with higher extraction, punishment and beliefs, and lower
efficiency. Directedness is associated with lower punishment and beliefs. Connectedness is associated
with higher beliefs.
5. Conclusion
This experimental study provides new empirical evidence on the impact of different monitoring
arrangements on extraction, punishment, beliefs and efficiency in a non-linear CPR extraction
dilemma. Most previous experimental evidence focuses on perfect monitoring and do not elicit
beliefs over other’s extractions. By examining the impact of different monitoring institutions that are
represent stylised monitoring institutions in the field, we provide a novel contribution to the
literature to help enhance the external validity of CPR lab experiments. Additionally we help tackle
the issue of internal validity by allowing subjects to explicitly note their beliefs in this complex and
non-linear decision space. We find that the monitoring network structure and properties
significantly influences extractions from the CPR, beliefs over other’s extractions, punishment
received, severity and frequency and finally social efficiency. However in all monitoring network
treatments, extraction behaviour starts near the Pareto optimal equilibrium extraction and moves
towards the Nash equilibrium extraction, as subject’s behaviour becomes increasingly selfish. We
find that the complete network, is the least efficient, as it elicits higher extractions and more
punishment which is also more severe and frequent. In addition, subjects hold higher beliefs over
other’s extractions in the complete network. We have demonstrated that this may have a causal
effect on extractions, as higher beliefs over other’s extractions are associated with higher extraction.
We have also shown that these differences can in part be explained due to the network properties
of completeness, directedness and connectedness.
From an institutional design perspective, this suggests that dense, transparent and complete
monitoring networks in non-linear CPR dilemma, maybe less desirable from a social efficiency
perspective, as subjects cannot coordinate at an efficient equilibrium and selfish behaviour is
reinforced. The findings are in accord with existing literature on peer punishment which highlight
that the long-run benefits of punishment maybe delayed or not realised in certain non-linear
environments (Cason and Gangadharan 2015, Gächter, Renner, and Sefton 2008). However our
findings must be interpreted with caution, given the limited external validity from the university
student subject pool and lab environment as per concerns expressed in Levitt and List (2007) and
Henrich, Heine, and Norenzayan (2010). We moreover only estimate the joint effect of both
information and punishment on behaviour. On the one hand, this represents monitoring
arrangements on the ground, where extractors can punish only those whose extractions they
observe. However it is possible that extraction maybe separately driven by information feedback,
which in turn may drive the conformist transmission of behaviour i.e. copying the most frequent
behaviour (Henrich and Boyd 2001). Carpenter (2004) for instance shows that free riding grows
faster when subjects have the information necessary to conform and if free-riding is frequent quite
early in the game. In this case, connected monitoring networks specifies the information necessary
27
to conform much more effectively that directed networks, and may subsequently elicit greater
defection. It is possible that this drives, extraction decisions in this experiment, as subjects in
connected networks, had more information necessary to conform. This is supported by related
literature on the emergence of over-harvesting norm and ecological collapse (Richter, van Soest, and
Grasman 2013, Tavoni, Schlüter, and Levin 2012), and environmental behaviours such as littering
(Dur and Vollaard 2015). It is also related to the literature that explores the dark side of social capital
(Satyanath et al. 2013, Sobel 2002). As a next step, it would be useful to disentangle these
information and sanctioning effects, within different monitoring networks. It is also interesting to
observe that subjects in all treatments had persistently optimistic beliefs over the expected
extraction of others, although they became less optimistic, as their beliefs were updated. This
echoes the finding that subjects fail to update bad news. For instance Oster, Shoulson, and Dorsey
(2013) show that at risk patients persistently underestimate the probability of the onset of
Huntington’s disease despite the availability of clinical information and worsening motor skills. We
also assume the monitoring institution is exogenously given, and communication between subjects
is not possible. Modifying these assumptions and pinning down the precise roles of beliefs,
conformity and social learning within different networks. Overall these results demonstrate that
there is a need to carefully consider the how to local environment impacts behaviour in CPR
extraction dilemmas. The effectiveness of different monitoring institutions varies significantly as
does the role of beliefs. Both these factors are critical but underexplored in the literature and
highlight the need for more research in this area.
28
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Data Annex
Table A 1: Summary statistics of subject characteristics
Treatment
Indicators
Sex
Female= 1
1st year=0
2nd year=1
3rd year=4
Masters=4
Education
Level
PhD=5
Accounts/Business=0
Economics=1
Political Science=2
Law=3
Humanities=4
Discipline
Other=5
exp=0
exp<5
No: of lab
experiments 5<exp<10
(experience) exp>10
Total number of subjects
Complete=0
%
N
55.0
33
13.3
8
11.7
7
16.7
10
55.0
33
3.3
2
20.0
12
15.0
9
11.7
7
18.3
11
8.3
5
26.7
16
15.0
9
51.7
31
18.3
11
15.0
9
60
Undir Circle=1
%
N
55.6
20
19.4
7
5.6
2
19.4
7
52.8
19
2.8
1
22.2
8
16.7
6
19.4
7
11.1
4
5.6
2
25.0
9
36.1
13
52.8
19
5.6
2
5.6
2
36
34
Dir Circle=2
%
N
67.5
27
35.0
14
20.0
8
10.0
4
32.5
13
2.5
1
27.5
11
17.5
7
15.0
6
2.5
1
7.5
3
30.0
12
32.5
13
42.5
17
15.0
6
10.0
4
40
Dir Line=3
%
N
60.7
34
12.5
7
21.4
12
8.9
5
51.8
29
5.4
3
32.1
18
16.1
9
5.4
3
7.1
4
10.7
6
28.6
16
26.8
15
53.6
30
10.7
6
8.9
5
56
Total
%
N
59.4
114
18.8
36
15.1
29
13.5
26
49.0
94
3.6
7
25.5
49
16.1
31
12.0
23
10.4
20
8.3
16
27.6
53
26.0
50
50.5
39
13.0
97
10.4
20
192
Table A 2: Group-level analysis: test of differences
Comparison
groups
Extraction
Punishment
received
Punishment
severity
Earnings after
punishment
Beliefs1
Mean(X1)
Mean(X2)
z
Pr>|z|
t
Pr(|T|>|t|)
NW01
15.370
14.509
2.796
0.005
2.836
0.005
NW02
15.370
14.802
1.558
0.119
1.826
0.069
NW03
15.370
14.808
1.825
0.068
1.927
0.055
NW12
14.509
14.802
-1.154
0.248
-0.859
0.391
NW13
14.509
14.808
-0.976
0.329
-0.905
0.366
NW23
14.802
14.808
0.147
0.883
-0.020
0.984
NW01
11.690
6.767
0.252
0.801
2.961
0.003
NW02
11.690
2.605
7.118
0.000
5.869
0.000
NW03
11.690
3.052
6.790
0.000
6.557
0.000
NW12
6.767
2.605
7.596
0.000
5.472
0.000
NW13
6.767
3.052
7.019
0.000
5.506
0.000
NW23
2.605
3.052
-1.162
0.245
-0.801
0.424
NW01
1.299
1.128
-1.683
0.092
0.879
0.380
NW02
1.299
0.868
4.304
0.000
2.096
0.037
NW03
1.299
1.017
3.342
0.001
1.551
0.122
NW12
6.767
2.605
5.318
0.000
5.472
0.000
NW13
6.767
3.052
4.237
0.000
5.506
0.000
NW23
0.868
1.017
-1.162
0.245
-0.801
0.424
NW01
172.360
188.768
-3.385
0.001
-3.899
0.000
NW02
172.360
189.257
-3.706
0.000
-4.147
0.000
NW03
172.360
188.709
-4.331
0.000
-4.382
0.000
NW12
188.768
189.257
-0.483
0.629
-0.146
0.884
NW13
188.768
188.709
-0.762
0.446
0.018
0.986
NW23
189.257
188.709
-0.232
0.816
0.165
0.869
NW01
14.121
13.051
4.752
0.000
4.483
0.000
NW02
14.121
12.584
6.399
0.000
6.493
0.000
NW03
14.121
13.363
3.004
0.003
3.040
0.003
NW12
13.051
12.584
1.866
0.062
1.935
0.054
NW13
13.051
13.363
-1.294
0.196
-1.115
0.266
NW23
12.584
13.363
-2.904
0.004
-2.831
0.005
NW01
13.249
12.685
2.545
0.011
2.184
0.030
NW02
13.249
12.261
3.755
0.000
3.779
0.000
NW03
13.249
12.946
1.052
0.293
1.109
0.268
NW12
12.685
12.261
1.329
0.184
1.707
0.089
NW13
12.685
12.946
-1.145
0.252
-0.886
0.376
0.018
-2.322
0.021
Beliefs2
NW23
12.261
12.946
-2.365
0- Complete, 1- undirected circle, 2- directed circle, 3- directed line
e.g. NW01- comparison between complete and undirected circle networks.
35
Table A 3: Average beliefs, with and without outliers by treatment
Beliefs>5
for
more than 5
periods
(Observations in
beliefs1)
Beliefs<=5
for
more than 5
periods
(Observations
included
in
Beliefs2)
Total
Complete
Undir circle
Dir circle
Dir line
Total
mean
14.1
13.0
12.6
13.4
13.4
sd
3.9
3.4
3.5
4.8
4.1
n
810
510
570
795
2685
Share
90.0
94.4
95.0
94.6
93.2
mean
5.5
6.8
5.3
5.5
5.7
sd
5.4
4.1
3.1
7.6
5.5
n
90
30
30
45
195
Share
10.0
5.6
5.0
5.4
6.8
mean
13.2
12.7
12.3
12.9
12.8
sd
4.8
3.8
3.8
5.3
4.6
n
900
540
600
840
2880
Share
100
100
100
100
100
36
Table A 4: Individual-level extraction
VARIABLES
Undir circle
Dir circle
Dir line
(1)
RE
(2)
RE
(3)
RE
(4)
RE^
(5)
RE
(6)
RE^
(7)
RE-IV
(8)
RE-IV^
-0.861
(0.599)
-0.568
(0.646)
-0.562
(0.702)
-0.861
(0.600)
-0.568
(0.647)
-0.562
(0.703)
-1.162**
(0.592)
-0.938
(0.621)
-0.529
(0.682)
-0.820**
(0.345)
-0.685**
(0.346)
-0.510
(0.438)
-0.580
(0.374)
-0.660*
(0.370)
-0.0971
(0.411)
-0.768**
(0.344)
-0.593*
(0.359)
-0.459
(0.426)
-0.424
(0.421)
-0.317
(0.452)
0.211
(0.460)
-0.823**
(0.383)
-0.550
(0.415)
-0.382
(0.448)
0.440***
(0.0390)
0.408***
(0.0368)
0.372***
(0.0437)
0.0201***
-0.0144**
0.432***
(0.0372)
0.0191**
*
0.398***
(0.0411)
0.0175**
*
(0.00588)
(0.00565)
Lagged
extraction
Lagged
punishment
Lagged
extraction
of others
-0.0802**
(0.0349)
Beliefs
Lagged
beliefs
Constant
15.37***
(0.401)
11.91***
(0.583)
12.81***
(0.956)
10.42***
(0.805)
(0.00569)
0.0124**
(0.00633
)
(0.00602)
0.0975***
(0.0359)
-0.0224
(0.0497)
-0.0808**
(0.0349)
0.00482
(0.0451)
0.231***
(0.0636)
0.404*
(0.221)
-0.180***
(0.0477)
0.294**
(0.136)
0.0605
(0.0405)
10.65***
(0.957)
0.0683*
(0.0363)
9.640***
(0.932)
-0.129
(0.0986)
8.921***
(1.767)
-0.0923
(0.0728)
9.118***
(1.352)
Observation
s
2,880
2,880
2,880
2,492
2,324
2,492
1,992
2,136
Number of
subjects
192
192
192
178
166
178
166
178
rho
0.337
0.351
0.332
0
0
0
0
0
Controls for
subject
attributes
No
No
Yes
Yes
Yes
Yes
Yes
Yes
Time fixed
effects
No
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Outlier
beliefs
No
No
No
No
No
Yes
No
Yes
First-stage F statistic
10.75*** 19.97***
Sargan-Hansen
statistic
2.927
2.126
Robust standard errors in parentheses. *** p<0.01, ** p<0.05, * p<0.1. Complete network is the omitted category.
^14 subjects assigned to role A in directed line excluded as they receive no punishment. ^^ 26 subjects assigned to role A in
directed line and those with outlier beliefs excluded.
37
Table A 5: First stage, IV regressions
(1 Stage)
(1 Stage)
VARIABLES
Model 7
Model 8
Beliefs Lag2
0.108***
0.161***
(0.0227)
(0.0220)
Beliefs Lag3
0.103***
0.161***
Others average extraction Lag2
(0.0206)
0.0252
(0.0199)
0.0100
(0.0226)
(0.0230)
nw1
-0.360*
-0.113
(0.210)
(0.213)
nw2
-0.596***
-0.209
nw3
(0.210)
-0.357*
(0.212)
-0.0527
(0.205)
(0.208)
Sex
-0.149
-0.248
(0.149)
(0.154)
Economics
-0.121
0.0950
Political Science
(0.231)
-0.176
(0.241)
-0.254
(0.274)
(0.271)
Law
0.00611
0.104
(0.258)
(0.265)
Humanities
-0.832***
-0.746**
Others
(0.308)
-0.471**
(0.306)
-0.352*
(0.196)
(0.200)
Undergrad2
Undergrad3
Master
PhD
-0.119
-0.149
(0.253)
(0.259)
-0.207
-0.134
(0.274)
-0.404**
(0.284)
-0.177
(0.197)
(0.201)
-0.202
-0.244
(0.444)
(0.442)
1-5
0.0118
-0.154
6-10
(0.172)
-0.255
(0.180)
-0.329
(0.230)
(0.238)
>10
0.189
-0.248
(0.283)
(0.287)
Lagged extraction
0.0234*
0.0275**
Lagged punishment
(0.0141)
-0.00337
(0.0139)
-0.00474
(0.00413)
(0.00411)
0.241***
0.233***
Lagged other's extraction
(0.0224)
(0.0229)
Lagged beliefs
0.339***
0.390***
Constant
(0.0226)
3.524***
(0.0215)
1.151
(0.744)
(0.724)
Observations
1,992
2,136
R-squared
0.318
0.446
No
Yes
Outlier beliefs
Standard errors in parentheses. *** p<0.01, ** p<0.05, * p<0.1
38
Table A 6: Beliefs
(1)
RE
(2)
RE
Undir circle
-1.083***
(0.412)
-0.564
(0.569)
Dir circle
-1.485***
(0.390)
-0.743
(0.456)
-0.988*
(0.560)
-0.302
(0.613)
VARIABLES
Dir line
(3)
RE
1.083***
(0.413)
1.485***
(0.391)
-0.743
(0.457)
(4)
RE
(5)
RE
(6)
RE
(7)
RE
(8)
RE
-0.564
(0.571)
-1.193***
(0.423)
-0.820
(0.592)
-0.111
(0.245)
-0.988*
(0.562)
-0.302
(0.614)
-1.642***
(0.389)
-0.755*
(0.452)
-1.167**
(0.553)
-0.276
(0.618)
-0.365*
(0.219)
0.550***
(0.187)
-0.247
(0.215)
0.362***
(0.0292)
0.105***
(0.0279)
0.111***
(0.0232)
-0.169
(0.220)
0.0892
(0.226)
0.405***
(0.0288)
0.152***
(0.0272)
0.159***
(0.0270)
0.258***
(0.0256)
0.822
(0.670)
Lagged beliefs
Lagged2 beliefs
Lagged3 beliefs
Lagged
other’s
average
extraction
Constant
14.11***
(0.260)
13.25***
(0.416)
10.77***
(0.438)
10.23***
(0.514)
Observations
2,685
2,880
2,685
2,880
Number
of
subject
179
192
179
192
Outlier beliefs
No
Yes
No
Yes
Controls
for
subject attributes
No
No
No
Yes
Time fixed effects
No
No
Yes
Yes
rho
0.238
0.376
0.267
0.402
Robust standard errors in parentheses. *** p<0.01, ** p<0.05, * p<0.1
39
11.29***
(0.715)
11.47***
(0.881)
0.266***
(0.0261)
2.760***
(0.664)
2,685
2,880
2,148
2,304
179
No
192
Yes
179
No
192
Yes
Yes
Yes
0.261
Yes
Yes
0.391
Yes
Yes
0
Yes
Yes
0