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We have followed the suggested templates
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Added in S3 appendix
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All data necessary for replication has been updated under the Figshare repository
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N=256) that includes all questions used in our linear regressions. We did not include
the full survey because we did not use all questions in the analysis, and some questions
reveal delicate information about e.g. being victims of displacement or violence by
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affiliation stating “current affiliation:….” as necessary).
All affiliations listed are current.
6. We noted in your submission details that a portion of your manuscript may have
been presented or published elsewhere. [We are also submitting another manuscript
based on the same data entitled “Uncertainty can help protect the local commons in
the face of climate change” also available as a preprint at https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3468677. ] Please clarify whether this [conference proceeding or publication] was peer-reviewed
and formally published. If this work was previously peer-reviewed and published, in
the cover letter please provide the reason that this work does not constitute dual
publication and should be included in the current manuscript.
The manuscript “Uncertainty can help protect the local commons in the face of climate
change” is part of Caroline Schill’s PhD thesis defended at Stockholm University in
2016. The manuscript, from its initial draft, has benefited from the feedback from
her PhD review committee, and was presented at the 6th World Congress of Environmental
and Resource Economists in Gothenburg in 2018, and the International Conference for
the Study of the Commons in Peru in 2019.
While relying on the same experiments, both papers differ in terms of the subset of
data and methods (statistical analyses) used, level of analysis, metrics used, and
scope of the conclusions. The paper led by Schill deals with how groups exploited
shared resources in situations where climate change can introduce tipping points.
It is a group level analysis, thus it focuses on overall sustained stock sizes as
well as whether or not groups risk crossing the threshold as main variables of interests.
Moreover, it uses inequality in catch rates (Gini coefficient) as a proxy for group
cooperation. Schill’s paper has the advantage that group behaviour is independent
among groups, lending itself for a different statistical approach (logit regressions
with group level statistics). The disadvantage is that we cannot include individual
level statistics such as the survey data, or individual risk and ambiguity preferences
that we use on our PlosONE contribution.
Our paper submitted to PlosONE complements this group-level analysis used in the other
manuscript by using individual-level information from post-experimental surveys, and
risk / ambiguity elicitation tasks to better understand individual human behaviour
in our experimental setting. Due to our main interest in the effects of thresholds
on cooperation, we developed and introduced here a sophisticated metric of cooperation
(different from Schill’s paper), which allowed us to disentangle cooperation from
coordination effects at the individual level. For example, the PlosONE paper enables
the distinction between cooperators and defectors that is fundamental in the cooperation
literature, but inaccessible to the group level analysis. The PlosONE paper also develops
a different methodological contribution to deal with dependencies in time, groups
and individuals (3 potential sources of bias) on dynamic games. The manuscript led
by Schill has not been peer-reviewed and published yet. We are currently in the process
of getting it ready for re-submission. We will inform you if this status changes in
the course of the revision process for this paper.
## Detailed response to reviewers:
### Reviewer 1:
The authors present and discuss empirical results of an experiment with fisherman
in Columbia, conducted to study individuals’ decision in a common-pool resource dilemma.
Particularly, the authors design treatments to better understand how cooperation depends
on shocks in the resource growth, thresholds that determine that resource growth,
uncertainty and risk. The authors show that, in all the conditions tested, fisherman
cooperate more after the resource growth regime shifts. Notwithstanding, the risk
condition is the one presenting a higher increase in cooperation. The authors conclude
that uncertain thresholds increase the level of cooperation.
This work has several positive aspects: 1) first of all, it is noteworthy that the
common-pool resource game is actually played by individuals that deal with such dilemmas
in their daily lives; this makes, in my opinion, the collected data extremely valuable.
2) second, it is also remarkable that the experiments were conducted with “non-weird”
subjects. 3) last but not least, the results are interesting in that they point out
that uncertain thresholds increase cooperation. The analysis performed appears to
be sound and the results are, as far as I know, original.
Despite several worthy features, I also found some unclear points in the manuscript:
1) to start with, the authors use a very specific growth structure, characterized
by (not one, but) four thresholds defining different fish stock growth rates. What
was the reason behind such specific thresholds and growth rates?
We should point out that our game builds on a dynamic common-pool resource game originally
designed for the lab (i.e. with students as participants) by Lindahl et al. (2016),
and further developed by Schill et al. (2015). The point of reference for the underlying
growth function of that design is a logistic growth function with a sigmoid term (in
particular a “Holling-type” III predation term to capture resource dynamics with a
threshold. Such a non-concave growth function has been shown to approximate the dynamics
of ecosystems with the potential for regime shifts, such as forests or coral reefs.
Like Lindahl and Schill et al. we use for our study also a discrete version of this
growth function in order to reduce complexity of experiment instructions.
According to our definition of thresholds, our study has only one threshold. Below
a stock size of 28 fish, the fish resource recovery rate drops from 10 to 1 fish.
Here the use of “threshold” is understood as a critical point below which the dynamics
of the system change to a qualitatively different behaviour (a bifurcation or critical
transition). The other discrete steps in the recovery rate correspond to natural dynamics
of ecological populations, including fish. Low recovery rate at higher densities ensures
that the population has a carrying capacity, that is, it cannot grow to infinity.
It reflects the situation when too many fish are already in the system and available
resources become scarce for them. Low recovery rate at lower densities reflects depensation,
or the fact that it is difficult for individuals to find partners for mating, and
crowding benefits such as schooling in fishes are lost when the population has low
numbers. As a result, fishes spend more time hiding or avoiding predators than feeding
and reproducing, known in the literature as the Allee effect (Allee 1932). These two
assumptions are necessary to keep the realism of our experiment: the population does
not grow to infinity, and at lower densities it is harder to reproduce. These two
assumptions are also necessary conditions to recreate the maximum sustainable yield
in our experimental design, that is, an intermediate population size at which the
recovery rate is maximised (in our case from 20-28 stock size).
In our experimental design the possibility of a threshold is induced and framed as
a climate event in three out of 4 treatments. Crossing the threshold however is a
response to fishing effort by the group of players, not to the climate event alone.
We explained the threshold and the different growth rates to our fisher participants
through the game instructions. We further checked that fishers were familiar with
regime shifts like dynamics (bifurcations) in the survey when asking whether they
have experienced abrupt collapses in their resources. Most of them confirmed experience
of regime shift dynamics. The theory of critical transitions requires that multiple
equilibria can co-exist under similar conditions (parameters). These equilibria in
our game are the high and low reproduction rates, and the similar conditions are the
climate event.
Allee WC, Bowen E (1932). "Studies in animal aggregations: mass protection against
colloidal silver among goldfishes". Journal of Experimental Zoology. 61 (2): 185–207.
doi:10.1002/jez.1400610202.
2) related with the previous point: what are the general characteristics of the interaction
that results from such thresholds, growth rates and number of players per group? (e.g.,
what would be a pareto optimal set of strategies? or fair? or Nash equilibria?). The
authors provide metrics of cooperation and coordination to characterize their results,
but would be relevant to, beforehand, state what is the expected/efficient behaviour
of individuals in this interaction
The Pareto optima in our game are all sets of decisions that maintain the stock size
at 28 (just before crossing the threshold) for treatments, and at 20 in the baseline.
Given that players can only extract a discrete number of resources, the strategy often
evolves towards a rotation scheme where the 10 fish reproduced per round are splitted
equally among the 4 players over the long term. The Pareto optima then assumes a fair
distribution of resources, an assumption that permeates to our metrics of cooperation.
The Nash equilibria, on the other hand, depends on a number of assumptions that are
violated in our experimental design. A Nash equilibrium exists in non-cooperative
games when people cannot form coalitions. Our game allows communication and coalition
forming. The dynamic feature of our game (that current decisions can affect the pay-off
table of future decisions) make our game very sensitive to the last round effect.
That is, an optimal (Nash) strategy is to collapse the resource if one believes the
game is about to end. But since the end of the game is unknown to players, the Nash
equilibria become taking all the fish stock on the first round to avoid others doing
it before yourself. We intentionally designed the game to avoid the last round effect.
We have discussed the relevance of these equilibria in previous theoretical work that
introduces our game design. For the intuition underlying these expectations please
consult Lindahl et al. (2016) and Schill et al. (2015) on which the design of our
game is built. We have not included analytical clarifications on these equilibria
because 1) they are described elsewhere, and 2) they do not clarify the key findings
of our paper.
3) it is hard to grasp the meaning of several expressions used in the text, namely
“Uncertain thresholds” or “risk of thresholds”. The threshold seems to be defined
on the stock size, below which fish stock growth rate is reduced. Events can occur
and reduce fish stock growth rate below the threshold. It seems that there can be
risk and uncertainty on the future growth rate, but the threshold is always defined
at 28 or 20. How come the threshold is said to be uncertainty or risky?
The threshold is indeed the point at which the dynamics tips and if it exists (depending
on the treatment) it is always at the same stock size, known by participants. Below
a stock size of 28, the growth rate drops drastically (from 10 to 1 fish only). According
to our definition (see our answer above in 1), there is no threshold at a stock size
of 20.“Uncertainty” and “Risk” refers to the probability of a climate event occurring
which would induce a threshold in the resource dynamics. In other words, uncertainty
and risk of a threshold do not refer to where the threshold is located but whether
or not a threshold exists. In the risk treatment, the probability that the conditions
enabling the threshold (the arrival of a climate event) were 50-50 (p = 0.5), and
that probability was constant and known to all. In the uncertainty treatment, the
probability range is known (p = 0.1-0.9) but the exact p is unknown to all. In the
risk and uncertainty treatment, at any time after round 6, the players do not know
if the climate event has happened and, hence, whether the threshold is activated or
not — unless they cross it and realise that the recovery rate is not as high as it
used to be.That’s why we refer to “uncertain thresholds” or the “risk of thresholds”.
The third treatment was “Threshold” or when the threshold situation arrived for sure,
with p = 1.
We realised that some formulations in the text (e.g. where we explain our cooperation
index) could indeed let the reader assume that also baseline had a threshold (at stock
size 20). We corrected for this, see line 206
4) one key conclusion of the paper is that “Fishers do reduce fishing in presence
of thresholds”. But no scenario without thresholds was tested, as far as I understood.
With or without event, the fish reproduction rate is always defined by thresholds
defined on the stock size; lower growth rates when the stock approaches depletion
is a feature present in all control and treatment scenarios. How can then be argued
that “thresholds” increase cooperation? Compared with what?
We did test a scenario without a threshold. It is called baseline. Only the threshold,
risk and uncertainty treatments have thresholds below which the growth rate reduces
drastically. To highlight this clearly and early on in the paper, we revised the description
of the treatments in the “Fishing game” section accordingly. See line 100-107. It
is compared to the baseline treatment, where there is no threshold modifying the maximum
sustainable yield (MSY) area of the recovery rate. As clarified in the previous question,
the other levels in the recovery rate as function of stock size are simply the necessary
assumptions to make the game biologically realistic. In fisheries, the MSY is defined
as a concave continuous function between the recovery rate and the population size.
Here to reduce the level of details when explaining the game, we simplified the concave
function to a step function with 3 levels: 0 in the extremes, 5 in intermediate levels,
and 10 in the MSY area. The simplification was made to make the game easier to understand
and follow for the fishers.
5) seems rather strange that cooperation increases even in the baseline condition,
where the second-stage is exactly the same as the first one. Actually, from the first
to the second stage, the stock is replaced, which would imply that users are free
to extract more without consequences. Any hypothesis for cooperation increasing also
in the baseline condition?
Indeed, as time passes in the game, the stock size is reduced and even in the baseline
scenario, it is not optimal to bring the stock size below 20 fishes. So people adjust
their strategies to maintain the stock in the MYS area and thus maximise their own
utility. That is why we observe fishing reduction in the baseline treatment. That
is also why we used a difference-in-difference regression approach to detect treatment
effects. Given that there is a decline in fishing effort in the baseline treatment,
the real effect is whether the decline in the treatment is larger and significantly
different from one expects to occur in the baseline. That’s indeed what we found.
6) if all treatments have threshold, why is a specific one called “threshold”? It
seems that the distinctive feature of that treatment is for the event to occur deterministically.
We hope we could clarify well enough with our answers above that according to our
threshold definition a discrete step in the underlying growth function is a necessary
but not a sufficient condition for a threshold. As explained in our answer to comment
1) above, we use a discrete version of a logistic growth function with a sigmoid term
to simplify the explanation of the game. A threshold, as we understand it, would be
a discontinuous jump in a continuous function. That is, under certain parameter values
in the dynamics of the system, two or more regimes can co-exist. Once the system hits
that tipping point, the dynamics will jump from two (or more in certain cases) qualitative
modes of behaviour, or equilibria. In our design, that qualitative change (or bifurcation)
is reflected by changing the recovery rate from 10 to 1 below a stock size of 28.
While the critical point is deterministic, its occurrence is stochastic depending
on the treatment, because it can only be crossed if the climate event conditions are
activated. That activation depends on a lottery that was played in every round in
the second part of the game. We have added a figure with the recovery rates (as suggested
by reviewer 2) to clarify the differences in recovery rates between treatments.
Overall, I believe that this work can become a good contribution to PLOS ONE. In my
opinion, it should be revised to clarify, at least, the points mentioned above.
Minor details:
Line 80, page 2: Fishers facing thresholds tend to fish less -> compared with what?
Added text: “compared to the baseline”
Page 3, line 114: cooperation is maximized when C = 1 -> seems that efficiency is
maximized when C=1. As the authors mention, C<1 means cooperation as well.
Indeed, it is the most efficient cooperative outcome. However since we are describing
C (cooperation) in this sentence, we refer to 1 as being the maximum value possible
that C can get while still being cooperation. Values > 1 means less cooperation under
our formulation.
Fig. 1 caption: When the difference were -> was?
Change made to “was”
Fig. 1 caption: contorl
Corrected
Line 130, page 3: e regressed variables that summarizes -> summarize?
corrected
Line 180, page 5: Our findings supports -> support?
Corrected
Page 5: wihtout crossing
corrected
Fig. 3 caption: starndard
Corrected
SI: Page 1 line 26 -> sing up
Corrected
### Reviewer 2:
Review: Cooperation in the face of thresholds, risk, and uncertainty
This manuscript presents experimental evidence on the cooperative behaviours of individuals
when faced to the risk of environmental crisis. Its main contribution is to provide
insights on the behaviours of individuals used to manage resources, in contrast to
previous work mostly focusing on WEIRD societies.
On the positive side, the manuscript provides a valuable contribution because (i)
experimental evidence is always relevant (and this is particularly true in the field
of evolution of cooperation dominated by theoretical work), and (ii) because the results
of this study challenge previous conclusions mostly based on WEIRD societies. The
introduction and the discussion are well written and referenced. The goal of the manuscript
is well motivated. Previous work on the topic are cited and the authors do a good
work at contextualising their study, either to motivate the study as in the introduction,
or to connect their results in the discussion. The experimental design is solid. The
authors show an expertise in statistics and data analysis, even if the complexity
of the statistical analysis can sometimes limit the understanding of a reader.
The negative point is mainly the results section and the analysis (besides the statistical
analysis) presented. First, some choices in the experimental design and the analysis
lack justification (or alternatively, discussion of the consequences of these choices).
For instance, the index created to measure cooperation appears arbitrary (arbitrary
value in some cases, replenishment rate not taken in account, ...). The rationale
behind the effects of the climate event is not clear. Authors sometimes use median
and sometimes use the mean. Altogether, this can lead readers to doubt the robustness
of the conclusion of the study. Second, the results section strongly needs rewriting.
On the one hand, a large part of the results section is not result but the description
of the method. On the other hand, the space dedicated to the actual results and analysis
is limited with for instance, the main result on cooperation appears to be missing.
Moreover, the plots are too complex and often not clear. Ultimately, this results
in readers having to trust the conclusions and interpretations of the authors rather
than reaching the same conclusions than the authors throughout the analysis.
To conclude, I favour publication, but at the condition of rewriting the results section.
You can find below the detailed list of comments:
Title
Change the title to make it clear that the paper presents experimental evidence. For
instance, add “Experimental evidence on [...]” or “[...] in fishers communities from
Colombia”.
Title changed to: “Cooperation in the face of thresholds, risk, and uncertainty: experimental
evidence in fisher communities from Colombia.”
Introduction
Some details at the end of the introduction should be moved to the next section. Authors
should reconsider having a method section between introduction and results rather
than at the end.
Thanks for the suggestion. We have rewritten the manuscript with a methods section
after introduction and an extended results section.
The authors might be interested by theoretical work by Francisco C. Santos on the
topic of cooperation with risk (for instance, https://www.pnas.org/content/pnas/108/26/10421.full.pdf) .
Thanks for the suggestion, we have added reference to the fascinating work of Santos
and Pacheco. Thanks for the lead, we were not aware of their theoretical model that
predicted some of our results in the public goods context, very relevant indeed!
Method
A figure that explains the replenishment rate would be helpful. For instance, the
figure could be a line representing the population size of the fish stock, divided
in sections for the different replenishment rate.
We have introduced the replenishment rate in text and a new Figure 1 as suggested
What are the effects of the diminishing returns? It could be argued that individuals
taking a lot of fishes are actually cooperating because they reduce the population
size down to the maximal productivity. If it does not matter e.g. it rarely happens,
add a sentence stating it.
That case is included in our measure of cooperation under the assumption of equal
sharing (because we divide by number of players in the group). So taking a lot of
fish at the beginning, as long as it is not by taking advantage of others and aggregated
extraction does not lead to crossing the threshold is considered cooperation. Cooperation
(C) will have a value of 1 or less.
The climate event (i) reduces replenishment rate of low population size and (ii) reduces
the interval of population size where the replenishment rate is optimal but does not
affect the replenishment rate of this interval. What is the rationale behind this
choice? For instance, why did not the authors consider that climate event simply reduces
replenishment rate for any population size? As far as I know, this differs from most
of theoretical work so how does this choice affects the results presented, and the
comparison with theoretical work?
The main purpose of our study was to test how individual resource users behave in
situations pervaded by thresholds when facing collective action dilemmas. In particular,
we were interested to what extent fishers reduce their fishing effort in order to
not contribute to cross the (potential) threshold. No matter whether the fishers face
the baseline (no threshold) or one of the treatment conditions (potential threshold),
it is best for the group to maintain stock sizes where the replenishment rate is the
highest. Changing the recovery rate for larger population sizes would have created
a confounding factor and reduced our ability to answer our research question. If we
introduce both, a threshold and a lower recovery rate for high population sizes, we
would have not been able to distinguish whether a change in response/behaviour was
because of the threshold in population size (x-axis) or the change in recovery rate
(y-axis).
The reviewer’s suggestion is excellent, and probably a good way forward to advance
our understanding of the role of recovery rates in fishing behaviour. In the scope
of our study, however, it would have created the necessity of including 3 treatments
(with and without change on the y axis), and increase our sample size; making the
test unfeasible with our limited budget.
An additional argument not to change homogeneously the climate effect to all population
sizes, is that the effect of climate change as reported in the literature is not homogeneous.
Changes in temperature affect species differently, and the effects can differ even
within the same species depending on their lifestage. While there is general agreement
that climate change and fishing pressure together have negative effects on marine
food webs (Kirby et al 2009), it is still an open question whether climate alone is
necessarily negative for food webs productivity (Buchholz 2019). For example, in Arctic
food webs some authors predict an increase of primary productivity under climate change
scenarios (Lewis 2020, Buchholz 2019), while others predict the opposite (Whitt et
al 2020). For tropical ecosystems it is likely to be negative, but the response on
the reproductive rate is species specific: some species will benefit from warming
conditions while others will see their niche reduced. That differential response is
what seems to happen in the sardine / anchovy shifts along the Peruvian and Californian
coasts, where the shift in species abundances is driven by climate (ENSO oscillations)
(Sugihara et al 2012).
Kirby, Richard R, Gregory Beaugrand, and John A Lindley. 2009. “Synergistic Effects
of Climate and Fishing in a Marine Ecosystem.” Ecosystems 12 (4). SPRINGER: 548–61.
doi:10.1007/s10021-009-9241-9.
Buchholz, Andrea Bryndum, Derek P Tittensor, Julia L Blanchard, William W L Cheung,
Marta Coll, Eric D Galbraith, Simon Jennings, Olivier Maury, and Heike K Lotze. 2019.
“Twenty‐First‐Century Climate Change Impacts on Marine Animal Biomass and Ecosystem
Structure Across Ocean Basins.” Global Change Biology 25 (2). John Wiley & Sons, Ltd
(10.1111): 459–72. doi:10.1111/gcb.14512.
Lewis, K M, G L van Dijken, and K R Arrigo. 2020. “Changes in Phytoplankton Concentration
Now Drive Increased Arctic Ocean Primary Production.” Science 369 (6500): 198–202.
doi:10.1126/science.aay8380.
Whitt, Daniel B, and Malte F Jansen. 2020. “Slower Nutrient Stream Suppresses Subarctic
Atlantic Ocean Biological Productivity in Global Warming.” Proceedings of the National
Academy of Sciences of the United States of America 117 (27): 15504–10. doi:10.1073/pnas.2000851117.
Lotze, Heike K, Derek P Tittensor, Andrea Bryndum-Buchholz, Tyler D Eddy, William
W L Cheung, Eric D Galbraith, Manuel Barange, et al. 2019. “Global Ensemble Projections
Reveal Trophic Amplification of Ocean Biomass Declines with Climate Change.” Proceedings
of the National Academy of Sciences of the United States of America 116 (26): 12907–12.
doi:10.1073/pnas.1900194116.
Sugihara, G, R May, H Ye, C h Hsieh, E Deyle, M Fogarty, and S Munch. 2012. “Detecting
Causality in Complex Ecosystems.” Science 338 (6106). American Association for the
Advancement of Science: 496–500. doi:10.1126/science.1227079.
Why does the fish stock is restored at turn 7? Did fishers know about this? Can it
affect the results?
At the beginning of the game, we informed all participants that the game lasts several
rounds and that it has two stages. We also told them that we will tell them when the
first stage finishes and explain then what will happen in the second stage. In other
words, they did not know beforehand that we would reset the stock size, i.e. results
were not affected. After 6 rounds, we informed the fishers that they are now going
to play the second stage of the game. Apart from the new information they received
depending on which treatment their group was randomly allocated to, they were all
told that we will reset the stock to 50 fish. The reason for restoring the stock is
twofold. On the one hand it allows to make within-group comparisons (i.e. compare
behaviour of the same individuals and groups before and after the treatments were
introduced). Additionally, due to the dynamic nature of our game individual groups
are likely to maintain different stock sizes over time and so we would have been faced
with introducing treatments while some groups maintain very high stock sizes, others
very low ones (e.g. below the not yet introduced thresholds). Hence, we could not
disentangle to what extent a change in behaviour would be due to the introduction
of a treatment or due to where exactly the group was at after 6 rounds.
L266 “There was no reproduction ...” -> Move this sentence up, where you explain the
different replenishment rates.
Sentence moved
L259: “The event was meant to reduce ...” -> “The event reduces ...”
Changed
L297: remove the “than expected” and “initially planned”.
deleted
Did the fishers know the details about the different replenishment rates?
The fishers had complete knowledge about the different replenishment rates as well
as every other aspect of the game design. See the instructions protocol in the SM.
We also did 2-3 practice rounds before the game to make sure they understood how the
replenishment rate worked.
L299: Add a reference for similar surveys in the literature to motivate the choice
of the
survey (if it exists).
It is very common to complement behavioural economic experiments with post-experimental
questionnaires or surveys see e.g. Anderies et al. 2011. The survey we used in this
project is partly based on and inspired by post-experimental surveys used by the author
team in previous studies. In particular: Maldonado and Moreno-Sanchez (2016) and Schill
et al. (2015). We added this motivation and references to the text in the survey section.
In revising the paper, we also realised that it would be more useful for the reader
to highlight in the survey section only the questions we actually use for this study
rather than providing a detailed overview of all the sections of our large survey.
We hope you agree with this revision.
References:
Anderies, J. M., M. A. Janssen, F. Bousquet, J.-C. Cardenas, D. Castillo, M.-C. Lopez,
R. Tobias, B. Vollan, and A. Wutich. 2011. The challenge of understanding decisions
in experimental studies of common pool resource governance. Ecological Economics 70(9):1571–1579.
Maldonado, J. H., and R. Del Pilar Moreno-Sanchez. 2016. Exacerbating the tragedy
of the commons: Private inefficient outcomes and peer effect in experimental games
with fishing communities. PLoS ONE 11(2):1–17.
Schill, C., T. Lindahl, and A.-S. Crépin. 2015. Collective action and the risk of
ecosystem regime shifts: insights from a laboratory experiment. Ecology and Society
20(1):48.
Analysis
Why does the authors use median cooperation but mean extraction?
Because cooperation is not normally distributed and the center of its distribution
has a special meaning in the context of our study . For example, the median of cooperation
for the threshold treatment aligns almost perfectly with C = 1, an important reference
point in our study (where cooperation is at its maximum). Hence for the purpose of
our research question, magnitude of the effects are best described by the median rather
than the mean. The mean extraction is not normally distributed either. But its distribution
does not have an additional meaning in the context of our research question.
Check if this notation is “p = 0.1:0.9” is commonly used. Change to 0.1 < p < 0.9
instead?
We changed to the second choice as suggested.
L88 – L95. This should be in the method section.
We don’t understand this suggestion. L88-95 presents our first sets of results — that
fishing effort is reduced under threshold, risk and uncertainty treatments — It shows
that the result is consistent with different choices of correcting for robust standard
error estimations. It also interprets the result in the light of the literature introduced
earlier and cautious the reader about the confounding factors that the diff-in-diff
regression does not address, then motivating the next set of results.
L99 -L128: This should be in the method section
We have moved the text to the methods section as suggested.
L99-105: There is no need to discuss the different definitions of cooperation in the
literature. One sentence explaining cooperation and how it is defined in this study
is enough.
See comment below:
The measure of cooperation used lacks justification. This can lead readers to doubt
of the results on cooperation, which is problematic because this is the main result.
I understand the difficulty to create an index that take in account both the number
of fish taken and the situation of the fish stock (above or below the threshold).
I would advise to either split the index in two, with one index describing if individuals
take fish when the stock is below the threshold, and one index describing the amount
of fishes taken when above the threshold. Alternatively, the author needs to better
justify the index built.
In the broader literature, cooperation is often confounded as i) maintaining the resource,
versus ii) following agreements. For example, in the classical one-shot prisoner's
dilemma cooperation is taken as following an implicit agreement of non-defection.
But in our game that definition is limiting because, as you point out, there are multiple
dimensions to what cooperation means in a dynamic setting: when the choices of the
present changes dynamically the payoff functions of the future. In economics, there
is a handful of papers using dynamic games in common pool resource contexts; and most
of them operationalise cooperation at the group level (not crossing the threshold)
not at the individual one.
Calling for a more evolutionary perspective in our definition of cooperation allows
us to include the aspect of fitness (or fitness loss) in the long term, and control
for the scenario when people agree to collapse the resource. Would that be cooperation?
For some economists it is because agents are maximising their returns. But within
our framework it is not because by reducing the ability of the stock to recover, a
person is reducing her own profits in the future (reducing fitness) — regardless of
what the group do. So our way of measuring it allows us to speak of cooperators at
the individual level, distinguish from defectors, and contrast cooperation versus
mere coordination.
The option suggested is not feasible at the individual level because the fish taken
below the threshold is an attribute of the group, not the individual. For example
if the fish stock is 30 and all 4 players take 2 fishes (2*4 = 8) who should be made
responsible for taking the extra fish? Crossing the threshold is a group level feature,
not an individual one. It also changes the statistical analysis where the group is
the unit of analysis and the number of rounds above or below threshold is a response
variable. That is what we did on a separate paper for the group level analysis by
means of a logistic regression [pre-print available here: https://www.ssrn.com/abstract=3468677]. That analysis, however, cannot make use of the individual level information we
present in our manuscript e.g. the surveys.
Your questions, however, raises the issue that our measure and what motivates it does
not come sufficiently clear in the current text. We have added some clarifications
following your suggestions below as well as made some additional changes that should
improve our justifications.
o Provide the rationale behind the choice made to build the index:
▪ For instance, “We consider that cooperation is represented by individuals
maintaining the fish stock in its most productive/sustainable state. Thus, cooperation
happens when (i) individuals take a number of fishes that maintain the fish stock
above the threshold, or (ii) take no fishes when the fish stock is below the threshold”
We adapted the text following your suggestion (see line XXX):
“Here we operationalise these definitions by measuring cooperation as the ratio of
the individual extraction $x_{i,t}$ with respect to the optimal level for the group.
Thus, cooperation happens when (i) individuals take a number of fishes that maintain
the fish stock at the optimal level (i.e. above the threshold in the treatments),
or when (ii) take no fishes when the fish stock is below the optimal level (i.e. below
the threshold in the treatments)..”
▪ Using biological terms rather than mathematical terms helps readers understand
the choice made to built the index. For instance: “To avoid division by zero or negative
values, if the denominator is < 1 and x_i,t = 0 cooperation is set to C = 1 (212/4096
observations), [...]” can be replaced by “When the fish stock is below the threshold
(denominator < 1) and fishers do not take any fish (x_i,t = 0), we consider that they
cooperate C = 1”.
Change made
o The authors consider that fishers taking fish while the stock is below the threshold
results in a cooperation value of 1.5. This value is arbitrary so what does happen
when a different value is used?
This was an error in the text, the text should read “if the denominator is zero and
x_i,t = 1, C = 1.5”. We introduced this rule to avoid division by zero. This seemingly
arbitrary choice of value does not affect results in any way because it concerns only
17 / 4096 observations, i.e. 0.004% of the data. The important decision to follow
here was to choose a value between 1 (maximum cooperation) and 2 (non-cooperative
behaviour that could lead to the group crossing the threshold in one of the threshold
treatments). An obvious choice for a value between 1 and 2 is 1.5. The error is corrected.
o It is confusing that a higher value of the cooperation index means lower cooperation.
Change the index to (1 – C_i,t) or change the name of the index.
I don’t think a change of name or scale would do the trick because the underlying
function has a concave shape with a maximum in 1. Transforming 1-C centres the distribution
to zero, but the magnitude of the scores loses interpretability. C = 2 means people
took twice of what was fair, C = 1 means they took 100% of what was fair, and C =
0.5 means they took 50% of what was fair favouring the common good over maximising
individual earnings. That numeric interpretation is lost with negative and positive
values (-1 is not a negative equivalent of +1).
We have also emphasised that singular points in time were not good indicators of cooperation,
but rather the distribution across time. This is because rotation schemes could emerge
when an individual in a round is allowed to take more than what is fair, if she allows
others to do the same in the future. So it is the shape of the distribution (and its
median because the observations are not normally distributed) rather than C_i, which
is interpreted as cooperation in our study.
o Why does the replenishment rate is not taken in account in the cooperation index?
It is taken into account indirectly in the sign of the denominator for stock size
values around the threshold. If the denominator is positive the replenishment rate
is high. When the threshold has been crossed and the replenishment rate jumps to a
lower value, the denominator is negative. Low values of the replenishment rate at
high stock sizes are not taken into consideration in the cooperation index because
these are not situations of scarcity or risk.
L120-123. It is not clear why the authors justify the choice of describing coordination
this way. If the authors use the average cooperation across different rounds, deviation
from cooperation for a single round should not be a problem. I would remove this part.
Simply introduce coordination in a way to measure coordination.
We did not fully understand the comment. Our measure of coordination is simply to
measure coordination, it is a distance measure on the fish extraction decisions (x_i,t).
It does not take into account cooperation. There is a weak negative correlation between
the two (shown in SFig 1), and as we argue above they measure different things. People
can coordinate to collapse the resource or to maintain it above the threshold. Both
strategies will score high on coordination, but cooperation will be low in the first
case while high on the second. We introduced both measures to be able to distinguish
between cases.
L120-123 introduces the reader to the case when coordination is high but not 1 (a
rotation scheme emerged making choices among players similar), and cooperation is
high on average (close to 1) but sometimes higher than 1 because of the rotation agreement
(one or two players take more than what is fair while keeping the stock as a group
above the threshold). The game does not allow people to fish non-discrete numbers
of fish forcing sometimes such rotation agreements.
L128: Present the results of the effects of treatments on cooperation and coordination
before starting to explain these effects. So far, the results section seems to lack
the main result (no effect of treatments on cooperation)
We adapted the results section according to your suggestion regarding cooperation.
The second sentence in the results section now reads as follows: “We also find that
contrary to theoretical expectations, cooperation does not break down.” The result
regarding coordination we have to report later (with the second set of regressions)
as we cannot perform the DID random effects panel model with the variable coordination
(because the similarity score is calculated over the rounds 1-6 for the first phase
and 7-16 for the second).
L141: Not clear and this choice looks arbitrary. Add justification or reference.
The justification is that our experimental design focuses on the impacts of tipping
points in natural resource dynamics, so for us it is more important how it affects
the livelihood of fishers rather than their income per se. Our survey provides info
on income as well as the frequency of bad days (or days without income); and of course
they are correlated. We’ve chosen the second because it is closely related to the
exposure of fishers to regime shift dynamics. Income per se might be compensated by
other economic activities or alternative sources of income such as pension or remittances.
The justification is in L288-92.
L149. Split the sentence for clarity. First part is about all treatments having an
effect and second part is about a single treatment having an effect.
Modification added.
L157: But do individuals that reach agreement are explained by socio-economic effects?
Thanks for the suggestion, really good idea that we have not checked before. We tested
it now and the only socio-economic factor that explains the proportion of agreements
is unsurprisingly education. The p-value is 0.002, but the size of the effect is rather
minimal 0.01. It means that for every additional year of education, the subject is
likely to reach agreements in 0.01 rounds. The proportion of agreements is measured
between 0-1 and corresponds to the number of rounds in which the group made agreements
in the treatment stage (10 rounds max). Because the effect is so little, we don’t
think it is worth including in the main text. If the editor and reviewer deem it necessary,
we are however happy to include the respective regression table in the SM. Below a
raw summary:
Call:
lm_robust(formula = prop_ag ~ Treatment + Place + education_yr +
BD_how_often + fishing_children + Risk + Amb, data = ind_coop %>%
filter(part == T) %>% ungroup(), clusters = group, se_type = "stata")
Standard error type: stata
Coefficients:
Estimate Std. Error t value Pr(>|t|) CI Lower CI Upper DF
(Intercept) 0.509674 0.127783 3.98859 0.0001781 0.254239 0.76511 62
TreatmentThreshold 0.109000 0.099416 1.09640 0.2771433 -0.089730 0.30773 62
TreatmentRisk 0.011077 0.123237 0.08988 0.9286704 -0.235271 0.25742 62
TreatmentUncertainty 0.104112 0.108432 0.96016 0.3407063 -0.112641 0.32086 62
PlaceB -0.180979 0.118071 -1.53280 0.1304129 -0.417000 0.05504 62
PlaceC 0.095775 0.087121 1.09934 0.2758723 -0.078377 0.26993 62
PlaceD -0.003950 0.120360 -0.03282 0.9739244 -0.244546 0.23665 62
education_yr 0.016855 0.007177 2.34840 0.0220580 0.002508 0.03120 62
BD_how_often -0.001341 0.012102 -0.11084 0.9120992 -0.025533 0.02285 62
fishing_children 0.025059 0.044248 0.56635 0.5732031 -0.063390 0.11351 62
Risk 0.004053 0.012261 0.33058 0.7420790 -0.020457 0.02856 62
Amb -0.010571 0.014910 -0.70897 0.4809979 -0.040377 0.01923 62
Multiple R-squared: 0.2235 , Adjusted R-squared: 0.1871
F-statistic: 2.083 on 11 and 62 DF, p-value: 0.03487
The results section ends without having the main result (no effect of treatment on
cooperation) being clearly presented. It appears that the result section starts by
describing the effect of treatments on the number/proportion of fishes taken and then
jumps directly to how these effects can be explained (socio-economic factors, coordination
and agreement).
As explained above, to another of your comments, the second sentence in the results
section now reads as follows: “We also find that contrary to theoretical expectations,
cooperation does not break down..” Furthermore, we clearly repeat this result now
at the beginning of the third paragraph of the results section: “Besides the effects
of treatments on the reduction of fishing effort, we find that cooperation does not
break down .” This aligns with the caption used in Fig 2 to describe the main results
of our paper.
Figures
• Figure 1:
What is before and after? I do not find explanations in the text. Does that mean that
the cooperation presented is averaged on the rounds before and after the round 7?
Indeed, before and after corresponds to the introduction of the treatment in round
7. We included that information in the caption of the figure. The technical explanation
and formulas to calculate the diff-in-diff regression are introduced in the Regressions
section under the Methods. We added the number of observations to the caption.
I would advise to start the caption by a sentence presenting the plots, and then have
a sentence describing more formally the analysis. For instance, “Effect of treatment
(risk, threshold, uncertainty) on the individual extraction (top), proportion of stock
(middle) and cooperation (bottom). The effects of the treatment are tested using ...”
We appreciate the suggestion but given that our main message seemed lost in your previous
comments, we prefer to keep the start of the caption as is. It encapsulates our main
result: fishers fish less but cooperation does not change. However, we do see the
benefit of clearly referring to the three treatments versus baseline in the caption.
We adapted the caption accordingly.
Replace “counterfactual” by “baseline” in the line type (or explain in the caption).
The counterfactual is not the baseline per se, it is what people in the treatment
would have done if they would have played the baseline instead of the treatment. It
relies on the parallel assumption of the diff-in-diff identification strategy. The
counterfactual is not actually observed, it is inferred (see table with formulas in
the methods). For more details we recommend:
Angrist and Pischke. 2009. Mostly harmless econometrics. Princeton Press
We have amended the caption with the clarification as suggested.
• Figure 2 is not clear at all.
First, it can be improved in term of appearance, e.g. the quality is low, the number
of different plots is too high, the size of the plots change.
Second, a plot needs to support one or two conclusions rather than providing an exhaustive
presentation of the results (this goes into supplementary materials). Split this figure
in different figures.
Thanks for your comments and suggestions. We improved and simplified the figure accordingly.
• Figure 3
o If possible, colour the points as a function of their p-values, in the same way
than Figure 1.
Suggestion implemented.
Discussion
• L175: First sentence is not clear.
L175: “Fishers under uncertain thresholds maintained higher levels of cooperation
than when the risk of thresholds was known, but risk had a stronger effect at reducing
individual fishing effort than uncertainty.” L207: “However, cooperation as measured
in our study was not affected by our treatments.”. These two statements seem to contradict
each other.
Indeed, there was a mistake. We have rephrased the first sentence as follows: “Fishers
under uncertain thresholds showed lower levels of extraction than when the threshold
was known. Risk had a stronger effect at reducing individual fishing effort than uncertainty.”
The second part of the statement was left unchanged.
L180: The authors state that uncertainty increase cooperation, but I thought that
uncertainty did not affect the level of cooperation.
L180 reads: “Our findings supports the hypothesis that uncertainty can increase cooperative
behaviour in public good settings when the value of the public good is sufficiently
high”.
What we report is that cooperation does not decrease — does not break down. And it
can increase, as suggested previously under certain circumstances, when it matters
a lot to people e.g. their livelihood depends on it. We observe signals of increasing
cooperation in the form of reduction of fishing effort as uncertainty increases. We
observe both displacement of the distribution to C values 0-1 in Figure 2, and effects
on reduction of variance in extraction (Figs 2 and 3). Cooperation increased but the
differences to the counterfactual were not significant (Fig 1). Our main point is
that cooperation does not break down. The studies on public goods measure cooperation
differently (the size of contribution to the public good). Here they are compared
with the size of reduction in use to the CPR.
L211: The author could cite Elinor Ostrom, e.g. Governing the commons (1990).
Reference added
Typo
A comma is often missing “,”: L316: “For risk the chances [...]”, L360: “As response
variables we used […]”.
Commas added
Fig 1 caption: “contorl”. Corrected
L184 “effots”. Corrected
Fig2 caption: Add “Figure” before “A) and B)”. Added
- Attachments
- Attachment
Submitted filename: Response_to_reviewers.pdf
https://orcid.org/0000-0003-2322-5459
