Supplementary Material for
An Experimental Investigation of ‘Pledge and Review’ in
Climate Negotiations
Scott Barrett & Astrid Dannenberg
This file contains Supplementary Text, Supplementary Tables S1-S5, and additional
references.
1. Theory
Our underlying game-theoretic model assumes that there are N symmetric
countries, each i of which may reduce its emissions using a low-cost technology
denoted B for “Black” and a high-cost technology denoted R for “Red” (the reason for
B
R
these labels will become clear later), with qiB Î 0,1,..., qmax
and qiR Î 0,1,..., qmax
.
{
Aggregate abatement, denoted Q, is thus Q = å ( q
N
B
i
i =1
}
+q
R
i
{
), with Q £ N ( q
B
max
+q
R
max
}
).
The per-unit costs of reducing emissions are assumed to be constant, with
cR > cB > 0. Reductions in emissions lessen “gradual” climate change, yielding each
country a benefit, b, per unit of emission reduced, whether the reduction was
achieved using the Red or the Black technology. Reductions in emissions can also
decrease if not eliminate the chance of crossing a “dangerous” climate threshold. We
assume that the threshold, Q , is a random variable distributed uniformly over the
supports Qmin and Qmax such that the probability of avoiding danger is 0 for Q < Qmin ,
(Q -Q ) (Q
min
B
R
N ( qmax
+ qmax
)
)
-Qmin for Q Î Î
ÎQmin ,Qmax Î
Î, and 1 for Q > Qmax . We further assume
³ Qmax > Qmin ³ 0 and restrict parameters so that when countries
max
cooperate fully they abate Qmax collectively, eliminating the risk of crossing the
threshold, and when countries choose their abatement levels non-cooperatively,
they do nothing to limit their emissions, making it inevitable that the threshold will
be crossed. Our experiment assumes that the impact of crossing the threshold, X, is
certain. In a previous paper (S1) we showed that, consistent with theory (S2),
impact uncertainty has no effect on behavior.
Our experimental game was played by groups of five players (N = 5). At the
B
start of the game, every subject was given 5 black poker chips qmax
= 5 worth €.10
(c
B
(
)
(
)
R
= 15 worth €1.00 ( cR = 1.0 ) each. A
= 0.1) each and 15 red poker chips qmax
contribution of either type of chip by any player gave every player a benefit equal to
€.05 (that is, b = 0.05). These values imply c R > bN > c B > b > 0. We also assume
Qmin = 50, and Qmax = 100. In other words, to reduce the risk of “dangerous” climate
change, at least some players must contribute a sizable number of their expensive
chips. To eliminate the risk of “dangerous” climate change, every player must
contribute all of his or her chips.
To complete the model, we must also choose a value for X. In our experiment
we set X = €20. This ensures that the game of avoiding “catastrophic” climate change
is also a prisoners’ dilemma.
An important feature of this game is that cooperation promises a high
reward, if the other players cooperate and Nature chooses a value for Q that is less
than the total amount contributed. However, cooperation is also risky. If the other
players don’t cooperate, or Nature chooses a high value for Q , a cooperative player
could go home with very little money. Actual payouts in our experiment covered
almost the full range of feasible outcomes, from €1 to €37. This large range is
consistent with the view that climate change is a high-risk game. The smallest
payout in the first five groups was €0 (as is convention in experiments we cut the
payoffs at zero when a player had earned a negative profit). After increasing the
endowment fund, negative profits were no longer possible.
2. Choice of X
X must be neither “too small” nor “too large.” If X were too small, avoiding a
“catastrophic” outcome would not be optimal for the group. (Arguably, in this case,
exceeding the threshold would not be truly “catastrophic.”) If X were too big,
avoiding a “catastrophic” outcome would result in a coordination game—meaning
that avoiding the threshold would be a Nash equilibrium.
Under our assumptions, it will always pay the players collectively to
contribute all of their black chips. Once at least Qmin chips have been contributed, it
will also pay all of the players together to contribute all of their remaining red chips.
However, when fewer than Qmin chips have been contributed in total, contributing a
single red chip loses the group money. Hence, it will either pay a group to contribute
all of their red chips or none of them. If a group contributes all of their chips, each
B
R
B
R
member will get bN qmax
+ qmax
- c B qmax
- c Rqmax
. If a group contributes only its black
(
)
B
B
chips, each member will get bNqmax
- c B qmax
- X. Full cooperation thus requires
contributing
all
chips
if
and
only
if
B
R
B B
R R
B
B B
bN qmax + qmax - c qmax - c qmax > bNqmax - c qmax - X , which for our parameter values
(
)
implies X >11.25.
For contributing all red chips (in addition to all black chips) not to be a Nash
equilibrium, it must be the case that, if all other players contribute all of their chips,
the remaining player is better off contributing one fewer than all of his chips. Given
that the other players contribute all of their chips, the remaining player gets
B
R
B
R
if he contributes all of his remaining chips. If he
bN qmax
+ qmax
- c B qmax
- c Rqmax
(
)
contributes
one
fewer
red
chip,
he
gets
B
R
B B
R
R
bN qmax + qmax - b - c qmax - c qmax -1 - X Qmax -Qmin . For contributing all red
(
)
(
)
(
)
chips not to be a Nash equilibrium, it must therefore be the case that
X < c R - b Qmax -Qmin . Using our parameter values, this condition implies X < 47.5.
(
)(
)
Combining both results, to have a prisoners’ dilemma we must use a value of
X satisfying X Î 11.25,47.50 . Our chosen value of X = €20 clearly satisfies this
(
)
condition.
3. The effect of contributing in stages
In our previous experiments (S1, S3), players were allowed to choose their
contributions in a single stage. In this experiment, we allow the players to spread
their contributions over two stages. In theory, the difference shouldn’t matter; in
both cases, the game is “one shot.” However, in our game, there are at least two
reasons for believing that cooperation will be higher in the two-stage contribution
game than in the one-stage game. Other differences between this experiment and
our previous experiments are the number of players (N = 5 versus N = 10) and the
B
R
B
number of cheap and expensive chips ( qmax
= 5 and qmax
= 10 versus qmax
= 10 and
R
qmax
= 10 ).
First, in a two-stage game, conditional cooperators can condition their
second-stage contributions on the contributions they actually observe in the first
stage. By contrast, in a one-stage game, conditional cooperators can only condition
their contributions on the amounts they expect their co-players to contribute. In a
one-stage game, each conditional cooperator may hold back, fearing that her coplayers will contribute very little, whereas in a two-stage game, each such player
may contribute some red chips in the first stage, and then see how many their coplayers contribute before deciding whether to contribute any more red chips in the
second stage. This illustrates a basic insight (S4) that if players are able to break up
their contributions into smaller units, and contribute in stages, then they may be
more willing to contribute, as each player “can try the other’s good faith for a small
price,” and “no one ever may need risk more than one small contribution at a time.”
Second, in our game, the marginal (expected) private return to contributing a
chip increases once fifty chips have been (or are expected to be) contributed. When
only a “small” number of chips have been contributed, a player gains just €.05 for
each additional chip contributed, whereas when a “large” number of chips have
been contributed, a player gains €.05 + €20/(100 – 50) = €.45 in expected terms
for each additional chip contributed. Observing that a large number of chips have
been contributed in a first stage thus strengthens the motivation to contribute in the
second stage. Moreover, an expectation about this behavior may in turn increase the
incentive to contribute in the first stage. In a one-stage game, by contrast,
contributing chips seems more risky.
4. Experimental design
The games were played in stages. The stages were identical for each treatment, with
the exception of the grading stage. Ignoring grading, the stages were as follows:
1. Subjects proposed a collective target (the sum of contributions to be made over
the two stages by all players, a number between 0 and 100), after which every
player’s proposal was displayed to all the players in the group. The median value
was chosen as the group’s collective target. This target was non-binding.
2. Subjects pledged a total individual contribution for the game (the sum of the
own contributions to be made over the two stages, a number between 0 and 20),
after which every player’s pledge was displayed to all the players in the group.
Pledges were non-binding.
3. Subjects were asked to estimate the average contribution level of the other
group members. Players knew that they would get one euro for a correct guess
(that is, for guesses within 1 of the actual number). Guesses were not displayed
to the group.
4. Subjects played two contribution stages. In each stage they could contribute any
number of black chips and red chips in their possession. Over the two stages,
subjects could not contribute more chips in total than they had to start with—
five black and 15 red chips. Contribution decisions were binding. After each
contribution stage, the contributions made by every player and the group total
were displayed to the group. After the second stage, subjects were also shown
the probability of the loss and the payoffs they would get depending on whether
or not they avoided the loss.
This concluded play of the game.
The experiment just described is for the No-Review treatment. For the other
treatments, a grading stage was inserted in the above sequence. In this stage,
subjects were asked to assign grades to the other players and also to themselves (1
= very good, 2 = good, 3 = satisfactory, 4 = fair, 5 = poor, 6 = insufficient; this grading
scheme is used in German schools and is thus familiar to the students). Each player’s
average grade (excluding the grade which the player gave to him or herself) was
then displayed to the group. In the Ex-Ante-Review treatment, this grading round
was inserted between stages two and three above. In the Mid-Point-Review
treatment, the grading round was inserted between the first and second
contribution stage. In the Ex-Post-Review, the grading round was inserted after the
second and final contribution stage.
Decisions in every stage of the game were made simultaneously and independently.
All the rules of the game were common knowledge. Players also knew that, before
the real game started, there would be three trial rounds, which were not relevant for
their payoff. The groups were reshuffled after each trial round. After play of the
game was over, subjects completed a short questionnaire that elicited their
emotions and motivation while playing the game; see below.
Upon completing the questionnaire, “Nature” chose the threshold in order for the
groups contributing 50 or more chips to know their payoff. For people to
understand the implications of uncertainty for their decision-making, probabilities
must be communicated very carefully (S5). In our experiment, the threshold was
determined by asking a student chosen at random within each session to activate a
spinning arrow on a computer wheel. The wheel represented a uniform distribution,
with 12 o’clock indicating the “ends” of the distribution ([50, 100]) and with
intermediate values being demarcated in 0.01 increments. Within this range, the
arrow could move freely. After being activated, the momentum of the arrow would
slow until the arrow finally came to rest at some point. This was the point chosen by
“Nature” from the distribution. All students could observe the arrow being spun and
learn their “fate” live on their own screen. To conclude the session, earnings were
paid out in cash at the end of the experiment.
Table S1 summarizes the key features of the experimental design.
5. Experimental instructions
The sample instructions reproduced below are from the Ex-Ante-Review treatment,
translated from German. The instructions for the other treatments are similar.
Instructions
Welcome to this experiment!
1. General information
In our experiment you can earn money. How much you earn depends on how you
and your co-players play the game. You will receive a lump sum participation fee of
€19. Note that a gain during the experiment will be added to this amount while a
loss will be deducted from that amount. For a successful run of this experiment, it is
essential that you do not talk to other participants. Now, read the following rules of
the game carefully. If you have any questions, please give us a hand signal.
2. Game rules
There are 5 players in the group, meaning you and four other players. Each player
faces the same decision problem. All decisions in the experiment are anonymous.
For the purpose of anonymity, you will be identified by a letter (between A and E),
which you will see later in the lower left corner of your display.
At the beginning of the game, you will receive 20 poker chips: 5 black chips and 15
red chips. During the game, you can use these poker chips to contribute to a joint
account or you can keep them. Black chips are cheap; they are worth €0.10 each.
Red chips are more expensive; they are worth €1.00 each. Overall you can
contribute any integer amount of chips between 0 and 20 to the joint account: at
most 5 black chips and at most 15 red chips.
Three rules determine your payoff:
First, you will receive the value of the chips you have not contributed to the
joint account. That is, you will get €0.10 for every black chip you keep and
€1.00 for every red chip you keep.
Second, you will get €0.05 for every poker chip contributed to the joint
account, irrespective of which player contributed the chip and whether it was
a black chip or a red chip.
Third, if the total number of chips contributed by your group is smaller than
a threshold, every player will lose €20. If the group contribution is equal to
or greater than the threshold, no player will lose any money. The threshold is
some number between 50 and 100, but you will not know the exact value of
the threshold until after the game is played. The exact value of the threshold
will be determined at the end of the experiment by the spinning wheel. The
wheel is programmed so that each value between 50 and 100 has the same
probability of being selected.
Players decide whether and by how much to contribute to the joint account in two
stages. A player’s overall contribution is the sum of his or her first-stage
contribution and his or her second-stage contribution. So, for example, if a player
contributes 3 chips in the first stage and 2 chips in the second stage, then his or her
overall contribution is 5 chips. After the first stage, the first-stage contributions
made by all players will be revealed to the group and after the second stage the
second-stage contributions as well as the overall contributions by all players will be
revealed. Players will see only the number of chips contributed, not whether those
chips were red or black.
Before choosing their contributions to the joint account, players will have the
opportunity to propose and announce a few things.
First, each player will make a proposal for how many chips he or she thinks
the group as a whole should contribute to the joint account. After that, all the
proposals made will be displayed to the group. The median of all proposals
will then become the final group target. So, for example, if the five players
propose 14, 45, 60, 77, and 98, then 60 chips will become the final group
target (since two of the proposals are above 60 and two below 60). The
group target is non-binding.
Second, each player will make a pledge for how many chips he or she intends
to contribute overall to the joint account (in both stages together). All
pledges will be displayed to the group. These pledges are also non-binding.
Third, after the pledges have been displayed, players will assess the decisions
made so far. In particular, every player will assign a grade from 1 (very good)
to 6 (insufficient) to the other co-players and also to himself or herself. The
grades given by each player will be private and will not be shown to the
group. However, players will learn the average grade given to them by their
co-players. These average values, one for each player, will also be revealed to
the group.
To summarize, the experiment involves the following steps:
-
Proposals for the group target
Pledges for intended contributions
Grading of decisions
Choice of first-stage contributions
Choice of second-stage contributions
Determination of the threshold by the spinning wheel
Payment
3. Determining the threshold with the spinning wheel
Whether or not the loss occurs depends on the overall group contribution and the
threshold which will be determined by the spinning wheel. If the group as a whole
contributes less than 50 chips, the loss occurs with certainty. Recall that the
threshold will be between 50 and 100. But what happens if the group contributes
more than 50 chips? Consider the following numerical examples.
Suppose the group contributes 63 chips. Then the loss occurs if the
threshold exceeds 63 (the red area in the pie chart shown on the
right). The loss does not occur if the threshold is 63 or less (the blue
area). You can see that the loss occurs with probability 74% (= (100 −
63)/(100 − 50)).
Suppose the group contributes 87 chips. Then the loss occurs if the
threshold exceeds 87 (the red area in the pie chart shown on the
right). The loss does not occur if the threshold is 87 or less (the blue
area). You can see that the loss occurs with probability 26% (= (100 −
87)/(100 − 50)).
4. Payoffs
The following hypothetical examples show how the payoff in the game is calculated.
Recall that positive payoffs in the game are added, and negative payoffs deducted,
from the €19 participation fee.
Assume you have contributed 5 black chips and no red chips. The group as a whole
has contributed 40 chips. What is your payoff? You will get €0.05 for every chip
contributed (40 × €0.05 = €2). You have kept 0 black chips (0 × €0.10 = €0) and 15
red chips (15 × €1 = €15). The loss occurs with probability 100%. Therefore your
payoff in the game is €2 + €0 + €15 − €20 = − €3.
Assume you have contributed 5 black chips and 10 red chips. The group as a whole
has contributed 70 chips. What is your payoff? You will get €0.05 for every chip
contributed (70 × €0.05 = €3.50). You have kept 0 black chips (0 × €0.10 = €0) and
5 red chips (5 × €1 = €5). The loss occurs with probability 60%. If the loss occurs,
your payoff in the game will be €3.50 + €0 + €5 – €20 = − €11.50. With probability
40% the loss doesn’t occur. If the loss doesn’t occur, your payoff will be €3.50 + €0 +
€5 = €8.50. Your expected payoff is thus − €3.50 (= 0.6 × (− €11.50) + 0.4 × €8.50).
5. Trial rounds
The game will be played and paid out only once. You should think carefully about
how to decide in the game. Before playing “for real,” three trial rounds will be
played so that you and the other players can become familiar with the game. The
trial rounds are not relevant for the payoff. Also, the people you will play with in the
trial rounds and the real round will always change, so that you will never play more
than one round with the same group of people.
6. Control questions
Please answer the following control questions.
a. Assume the group as a whole has contributed 45 chips. What is the probability
that the loss occurs?
O 0%
O 20%
O 40%
O 60%
O 80%
O 100%
b. Assume the group as a whole has contributed 80 chips. What is the probability
that the loss occurs?
O 0%
O 20%
O 40%
O 60%
O 80%
O 100%
c. Assume you have contributed no chips. The group as a whole has contributed 70
chips. What is the probability that the loss occurs? __________ Ignoring the
participation fee, what is your payoff if the loss occurs? __________ What is your payoff
if the loss doesn’t occur? __________ What is your expected payoff? __________
d. Assume you have contributed 5 black chips and 15 red chips. The group as a
whole has contributed 70 chips. Ignoring the participation fee, what is your payoff if
the loss occurs? __________ What is your payoff if the loss doesn’t occur? __________
What is your expected payoff? __________
e. Assume that the five players have made the following proposals for the group
target: 0, 97, 66, 78, 25. What is the final group target? __________
f. Right or wrong? Before the players choose their actual contributions they make
pledges for their intended contributions. The pledges are non-binding.
Right
Wrong
g. Right or wrong? After the group target and the pledges have been published to the
group, players have the opportunity to assign grades to each other. Grading is
private but the average grade players have received from their co-players will be
published.
Right
Wrong
h. Right or wrong? There will be three trial rounds. These trial rounds will not be
relevant for the payment. The group composition will differ in every round,
including the real round.
Right
Wrong
i. Right or wrong? A player’s overall contribution is the total of his or her first-stage
contribution and his or her second-stage contribution.
Right
Wrong
Give us a hand signal after you have answered all the control questions. We will
come to you and check that you have answered all the questions. The game will
begin after we have checked the answers of all the players and answered any
questions you may have. Good luck!
6. Literature
Naming and shaming
The idea that social feedback could affect cooperation—or pro-social behavior, in
general—is not new in the experimental literature. Psychologists and economists
have done experiments in the lab and in the field, and found evidence that humans
are sensitive to approval or disapproval by their peers. We can distinguish between
two different forms of investigation.
The first form of investigation is to reveal the players’ identity after they have
made their decision. For example, in (S6), after the participants had chosen their
contributions in a public goods game, each participant had to stand up and write his
or her contribution on a blackboard in front of the others. In another experiment of
a public goods game (S7), after the players had chosen their contributions, the
identity of each individual was revealed to the group by displaying a picture and the
first name along with his or her contribution. These experiments typically do not
include an explicit mechanism for feedback but rather assume that the revelation of
a player’s identity and the “unspoken” approval or disapproval by the co-players
change behavior. In a field experiment, (S8) show that residential customers in
California were more likely to take part in a demand response program that helps
prevent or shorten power interruptions by curbing demand from central air
conditioners on days with unusually high demand, or in the case of an unexpected
plant or transmission failure, when their participation could be observed by others.
The results of these experiments show that the revelation of players’ identities has a
positive and significant effect on cooperation. This indicates that the revelation of an
individual identity and the mere suspicion that others may like or dislike this
person’s behavior constitutes an incentive for people to behave in a more socially
oriented way.
The second form of investigation is to keep the players’ identity and
contribution level confidential but to provide them with an explicit feedback
mechanism. Many public goods experiments have shown that giving players the
opportunity to punish each other after contributions have been displayed to the
group increases contributions significantly (see, e.g., (S9); for a review, see (S10)).
The use of punishment is costly for both the punisher and the player who is
punished. More relevant to our study, non-monetary feedback also affects behavior.
For instance, (S11) used a repeated public goods game in which, at the end of every
period, each subject got to know the contributions of the other group members and
could then assign “disapproval points” to the other group members. These
disapproval points were costless to assign and had no direct effect on payoffs.
Nevertheless, giving players this opportunity to signal disapproval increased
contributions. Over time, however, the non-monetary sanctions were less effective
than monetary sanctions. In (S12), the players played a one-shot prisoners’ dilemma
and were then given the opportunity to send one out of three messages (“Your
choice was . . . good, . . . neither good nor bad, . . . bad”) to their co-player. The results
show that this feedback opportunity increased cooperation compared to a control
treatment without feedback. Another paper (S13) compared a non-monetary
reward option (sending a smiley ) and a non-monetary punishment option
(sending a frowny ) in a repeated public goods game. They found that these
options had no effect in a stranger matching design but a small positive effect in a
partner matching design. In a similar experiment, (S14) tested the effects of sending
smiley or frowny emoticons in a framed downstream water pollution game. They
found that expressing negative emotional feedback (frowny) led to more
environmentally friendly behavior whereas expressing positive emotional feedback
was rather counterproductive. (S15) analyzed behavior in a one-shot dictator game
where the recipient could send an unrestricted anonymous message to the dictator
after observing his or her choice. They found that this option increased donations as
compared to a control treatment without feedback messages. (S16) report the same
finding even when dictators were not required to read the message.
Taken together, these experiments suggest that social feedback can lead to
more socially oriented behavior. The question is, will the ability to give social
feedback be enough to avoid “catastrophe?” In our experiment, we have chosen the
second approach where players’ identities remain anonymous and they are
provided with an explicit feedback mechanism. We believe that this approach is
more suitable for several reasons. First, Paris isn’t changing the “naming” part of
“naming and shaming.” Second, even though the negotiators’ personal identities are
known, these individuals do not “play” for themselves but on behalf of their
country’s citizens which makes the game rather anonymous. Finally, the pledge-andreview scheme being envisaged for Paris constitutes an explicit feedback
mechanism.
Conditional Cooperation
A number of experiments have shown that many people are conditional
cooperators—being willing to cooperate when they know or expect that others will
cooperate, too. For example, (S17) use the strategy method to measure the share of
conditional cooperators. Every participant in their experiment has to decide how
much he or she wants to contribute to a public good given the average contribution
of the other players in the group. They find that half of the individuals in their
sample are conditional cooperators—people who increase their contribution as the
average of the other players’ contributions increases.
Building on this finding, it has been shown that cooperation is higher and
more stable when conditional cooperators are grouped together. Here we can
distinguish between settings in which subjects are sorted into groups by the
experimenter (assortative matching) and ones in which subjects are allowed to form
groups endogenously (partner selection). Looking first at the former approach,
(S18), in a public goods experiment, separate high contributing subjects from low
contributing subjects and then place them into four-person groups (without their
knowledge and after they have chosen their contributions to the public good). They
find that the usual decay of contributions is much slower when the conditional
cooperators play with free riders less often. (S19) use subjects’ contributions in a
one-shot public goods game to sort them into three-person groups of like-minded
(high or low) contributors. They find that the groups whose members know they are
composed of high contributors are able to maintain higher cooperation levels than
the groups whose members know they are composed of low contributors or the
groups that are formed randomly.
The literature on partner selection has analyzed cooperation in situations in
which the players can choose the people with whom they play. For example, (S20)
employ a four-person public goods game over 20 periods with endogenous
regrouping after every three periods. Based on information about everyone’s
previous contributions, each player can provide a costly ranking to show which
players he or she would prefer to interact with in the future. Groups are then
formed according to the mutual preferences expressed by the players. The
mechanism perfectly sorted the groups in the order of their average contributions
and significantly increased both contributions and efficiency compared to a control
treatment without regrouping and a comparison treatment with monetary
punishment. (S21) allowed their subjects to choose between two group types before
playing a repeated three-person public goods game within their group. In blue
groups, subjects received a fixed extra payoff; in red groups, this extra payoff was
donated to the Red Cross. The results show that contributions in red groups were
initially higher and stayed high, while contributions in blue groups displayed the
well-known pattern of declining contributions. (S22) let their subjects play a
repeated public goods game with initially 16 individuals in one group. After each
round, players were allowed to vote on whether to expel individual group members.
Individuals being voted against by more than half of the members were irreversibly
banished to another group, which played a public-goods game with a lower
endowment and no voting. The threat of expulsion increased contributions close to
the efficient level with significantly higher efficiency compared with a no-expulsion
baseline. These results demonstrate that punishment in form of exclusion can
greatly enhance cooperation, though it doesn’t allow players to develop trust,
causing cooperation to collapse in the final period when the threat of expulsion is
removed.
Another paper (S23) tested if gossip could foster cooperation by facilitating
partner selection. Groups of four individuals played a repeated public goods game in
a stranger design (i.e. groups were re-shuffled after each round). The experiment
involved a control treatment with no gossip and two gossip treatments. In the
gossip treatments, after learning the results of each round, the players could send a
note to the members of each player’s future group. In the gossip-with-ostracism
treatment, these members, after receiving the gossip note at the beginning of each
round, could vote to exclude one player from playing the next round. The players in
the experiment often used the opportunity to send gossip notes (notes were sent
over 80% of the time). Unsurprisingly, free riders were most often the subject of the
gossip note while cooperators often sent a note. Individuals who were negatively
portrayed in the notes were more likely to be expelled by the new partners, even
though expulsion came at the cost of losing potential contributions. Overall,
contributions were larger in the gossip treatments than in the control and they were
largest in the gossip-with-ostracism treatment. One reason for this was that the
individuals who were ostracized later increased their contributions.
These results show that people differ in their inclinations to cooperate and
that many people are conditionally cooperative. These individuals often manage to
cooperate at a high level and to sustain high cooperation over time, when able to
exclude free riders. However, it is difficult for conditional cooperators to establish
and sustain cooperation when sorting is imperfect and free riders cannot be
excluded. Since we are interested in the provision of a public good rather than a club
good, we use fixed groups and do not allow for sorting or expulsion. As is
conventional practice in the literature, our experiment involved students as
participants (all but one of the above studies used students). The external validity
cannot be taken for granted but the experiments nevertheless provide valuable
insights into the timing and effectiveness of a review process.
7. Results
Table S1 gives an overview of the four different experimental treatments.
Table S2 shows the group averages and standard deviations for targets, pledges, and
contributions as well as the range of group contributions. Table 3 shows the
significance of treatment differences in targets, pledges, and contributions. Table S4
presents the results of some correlation tests across all treatments. Table S5 shows
additional regression analyses.
Table S6 presents the responses to the ex-post questionnaire, separating out
the responses for the No-Review treatment and all three of the review treatments
combined. The responses are generally quite similar between these two groups.
This is true in particular for the general questions about trust, risk aversion,
estimation of the threshold, and the corresponding confidence level (see questions
9-12). The median estimated value of the threshold is 75, which suggests that our
participants understood the probability distribution and that the treatment variable
did not bias their uncertainty perception. The percentage of risk-averse subjects in
the two different groups is 78% and 79%. The analysis within each treatment shows
that there is no significant correlation between individual risk aversion and
individual contributions or between the number of risk-averse members in a group
and group contributions (Pearson correlation test, P > .10 each). Thus, we cannot
reject the hypothesis that risk aversion and behavior in the game are independent.
Overall, participants in the review treatments were slightly happier with the
outcome of their game and found the collective target and the exchange of pledges a
little more useful, but these differences were small. Only a minority of players in the
review treatments found the review useful (see question 7). What is more, a
substantial majority (85%) said that the review had little or no effect on their
decisions (question 8).
Table S1. Treatments
Treatment
Target
Pledge
Grading
Number of players
No-Review
Yes
Yes
No
5 per group × 10 groups
Ex-Ante-Review
Yes
Yes
Mid-Point-Review
Yes
Yes
Ex-Post-Review
Yes
Yes
After pledges and before
contribution stages
After first but before second
contribution stage
After second contribution stage
5 per group × 10 groups
5 per group × 9 groups
5 per group × 10 groups
Table S2. Summary statistics
Treatment
Mean target
Mean pledge
Mean group
contribution
Min / max group
contribution
No-Review
84
(8.43)
74.7
(11.64)
58.1
(14.36)
35 / 78
Ex-Ante-Review
95.2
(6.36)
90
(5.33)
64.2
(9.46)
54 / 85
Mid-Point-Review
88.22
(8.44)
83.55
(10.27)
63.56
(20.01)
30 / 92
Ex-Post-Review
96.7
(6.67)
91.5
(15.53)
69
(19.46)
25 / 95
Mean values across groups per treatment; standard deviations in parentheses. The rightmost column
shows the range of group contributions.
Target
Pledge
Contribution
Target
Pledge
Contribution
Ex-Post-Review
Contribution
Mid-Point-Review
Pledge
Ex-Ante-Review
Target
Table S3. Significance of treatment differences
.009
(.394)
.262
(.941)
.004
(.242)
.001
0.125)
.060
(.770)
.002
(.942)
.325
(.174)
.512
(.413)
.112
(.533)
.055
(.317)
.594
(.492)
.153
(.188)
.048
(.284)
.838
(.069)
.211
(.108)
.030
(.215)
.008
(.782)
.513
(.874)
No-Review
Ex-Ante-review
Mid-Point-Review
P-values from a Mann-Whitney Wilcoxon rank-sum test of treatment differences in mean values; in
parentheses P-values from a Levene test of treatment differences in variances.
Table S4. Correlations across treatments
Correlation
coefficient
P-value
Number of
observations
Group target and group contribution
.30
.06
39
Group pledge and group contribution
.51
.00
39
Group target and individual pledges
.50
.00
195
Individual target proposal and individual contribution
.24
.00
195
Individual pledge and individual contribution
.31
.00
195
Other’s average pledge and own belief
.44
.00
195
Belief and individual contribution
.56
.00
195
Variables
P-values from a Pearson correlation test. Results are qualitatively the same when a Spearman
correlation test is used.
Table S5. Linear regressions of individual proposals, pledges, beliefs, and
contributions
Variables
Treatment dummies
(Baseline: No-Review)
Ex-Ante-Review
Mid-Point-Review
Ex-Post-Review
Proposal
Pledge
Belief
Contribution
12.94**
(3.11)
3.06**
(0.79)
0.72
(0.79)
2.84** 0.73
(0.99) (0.89)
1.22
(1.06)
-0.94
(1.25)
5.92
(4.79)
1.77
(0.97)
0.89
(0.73)
1.02
-0.09
(1.16) (0.92)
1.09
(1.56)
0.10
(1.31)
13.14**
(4.04)
3.36**
(1.19)
0.70
(1.24)
3.42** 1.09
(1.07) (0.83)
2.18
(1.48)
-0.38
(1.396)
0.21**
(0.05)
0.05
(0.06)
-0.10
(0.06)
0.51**
(0.18)
0.04
(0.25)
Target
Others average pledge
Own pledge
0.31**
(0.11)
Belief
0.77**
(0.11)
Constant
79.10**
(2.76)
14.94** -2.63
(0.71) (4.58)
13**
1.27
(0.69) (2.89)
11.62**
(0.88)
4.68
(3.92)
Observations
195
195
195
195
195
195
195
R-squared
0.08**
0.11** 0.25**
0.11** 0.21**
0.02** 0.36**
Numbers show coefficients from Ordinary-Least-Squares regression models. Numbers in
parentheses are robust standard errors clustered at the group level. Levels of significance: ** P < .01,
* P < .05. Definitions of variables: Proposal = individuals’ proposals for collective contribution target,
Target = groups’ collective contribution target, Pledge = individuals’ announced contributions, Belief
= individuals’ expectations of others’ contributions.
Table S6. Responses to the ex-post questionnaire (in % of subjects)
Question
1) Were you generally satisfied with the game's outcome?
2) Knowing how the game was played, with the benefit of hindsight, do
you wish you had made a different contribution?
3) Knowing how the game was played, with the benefit of hindsight, do
you feel that some of the other players betrayed your trust in them?
4) Knowing how the game was played, with the benefit of hindsight, do
you feel that you betrayed other players’ trust in you?
5) Do you agree with the statement that the collective target was
helpful?
6) Do you agree with the statement that the exchange of pledges was
helpful?
7) Do you agree with the statement that the grading was helpful?
8) Did the knowledge that you would be graded by your co-players
affect your decisions?
9) Generally speaking, do you trust other people?
10) Please imagine the following situation in another unrelated
experiment: You have an initial endowment of €40. There is a 50%
possibility that you will lose your €40. However, you can avoid this loss
by paying €20 up front. Would you rather pay this amount and get €20
for certain or would you rather accept the risk of losing the €40 with
probability 50%?
11) For the groups that contributed more than 50, the contribution
threshold will soon be determined by the “spinning wheel.” What single
value do you estimate will come closest to the threshold value
determined by the “spinning wheel”?
12) How confident are you about your estimation in the previous
question?
Response
Very much
Somewhat
Little
Not at all
Very much
Somewhat
Little
Not at all
Very much
Somewhat
Little
Not at all
Very much
Somewhat
Little
Not at all
Very much
Somewhat
Little
Not at all
Very much
Somewhat
Little
Not at all
Very much
Somewhat
Little
Not at all
Very much
Somewhat
Little
Not at all
Very much
Somewhat
Little
Not at all
€40 uncertain
Indifferent
€20 certain
No review
8
24
30
38
10
32
18
40
36
32
12
20
12
20
18
50
20
30
34
16
12
40
30
18
-
28
44
22
6
8
14
78
With review
14
33
30
23
9
26
28
37
38
28
19
14
14
23
21
42
34
32
21
12
36
29
23
12
12
21
32
36
2
12
21
64
22
51
23
3
8
13
79
Median
Mean
75
72.06
75
72.26
Very much
Somewhat
Little
Not at all
10
36
40
14
10
40
34
15
-
Supplementary References
S1. S. Barrett, A. Dannenberg, Climate Negotiations Under Scientific Uncertainty.
Proc. Natl. Acad. Sci. USA 109, 17372-17376 (2012).
S2. S. Barrett, Climate Treaties and Approaching Catastrophes, Journal of
Environmental Economics and Management 66, 235-250 (2013).
S3. S. Barrett, A. Dannenberg, Sensitivity of Collective Action to Uncertainty about
Climate Tipping Points. Nature Climate Change 4, 36-39 (2014).
S4. T. C. Schelling, The Strategy of Conflict (Harvard University Press, Cambridge,
MA, 1960).
S5. D. Spiegelhalter, M. Pearson, I. Short, Visualizing Uncertainty about the Future.
Science 333, 1393-1400 (2011).
S6. M. Rege, K. Telle, The impact of social approval and framing on cooperation in
public good situations. Journal of Public Economics 88, 1625-1644 (2004).
S7. A. Savikhin Samek, R. M. Sheremeta, Recognizing contributors: an experiment on
public goods. Experimental Economics 17, 673-690 (2014).
S8. E. Yoeli, M. Hoffman, D. G. Rand, M. A. Nowak, Powering up with indirect
reciprocity in a large-scale field experiment. Proc. Natl. Acad. Sci. USA 110, 1042410429 (2013).
S9. E. Fehr, S. Gächter, Cooperation and Punishment in Public Goods Experiments.
The American Economic Review 90, 980-994 (2000).
S10. A. Chaudhuri, Sustaining cooperation in laboratory public goods experiments: a
selective survey of the literature. Experimental Economics 14, 47-83 (2011).
S11. D. Masclet, C. Noussair, S. Tucker, M. C. Villeval, Monetary and Nonmonetary
Punishment in the Voluntary Contributions Mechanism. American Economic Review
93, 366-380 (2003).
S12. R. López-Pérez, M. Vorsatz, On approval and Disapproval: Theory and
Experiments. Journal of Economic Psychology 31, 527-541 (2010).
S13. R. Peeters, M. Vorsatz, Immaterial rewards and sanctions in a voluntary
contribution experiment. Economic Inquiry 51, 1442-1456 (2013).
S14. N. V. Czap, H. J. Czap, M. Khachaturyan, M. E. Burbach, G. D. Lynne, Smiley or
Frowney: The Effect of Emotions and Empathy Framing in a Downstream Water
Pollution Game. International Journal of Economics and Finance 5, (2013).
S15. T. Ellingsen, M. Johannesson, Anticipated verbal feedback induces pro-social
behavior. Evolution and Human Behavior 29, 100-105 (2008).
S16. E. Xiao, D. Houser, Avoiding the sharp tongue: Anticipated written messages
promote fair economic exchange. Journal of Economic Psychology 30, 393–404
(2009).
S17. U. Fischbacher, S. Gächter, E. Fehr, Are People Conditionally Cooperative?
Evidence from a Public Goods Experiment. Economic Letters 71, 397-404 (2001).
S18. A. Gunnthorsdöttir, D. Houser, K. McCabe, Disposition, history and
contributions in public goods experiments. Journal of Economic Behavior &
Organization 62, 304-315 (2007).
S19. S. Gächter, C. Thöni, Social Learning and Voluntary Cooperation Among LikeMinded People. Journal of the European Economic Association 3, 303-314 (2005).
S20. T. Page, L. Putterman, B. Unel, Voluntary association in public goods
experiments: reciprocity, mimicry, and efficiency. Economic Journal 115, 1032-1053
(2005).
S21. K. A. Brekke, K. E. Hauge, J. T. Lind, K. Nyborg, Playing with the good guys. A
public good game with endogenous group formation. Journal of Public Economics 95,
1111–1118 (2011).
S22. M. Cinyabuguma, T. Page, L. Putterman, Cooperation under the threat of
expulsion in a public goods experiment. Journal of Public Economics 89, 1421–1435
(2005).
S23. M. Feinberg, R. Willer, M. Schultz, Gossip and Ostracism Promote Cooperation
in Groups. Psychological Science 25, 656-664 (2014).