[1,2,3]Eladio Montero-Porras

[1,2,3]Elias Fernández Domingos

1]Artificial Intelligence Laboratory, Vrije Universiteit Brussel, Pleinlaan 9,
Elsene, 1050, Brussels, Belgium

2]Machine Learning Group, Université Libre de Bruxelles, Boulevard du Triomphe
CP212, Elsene, 1050, Brussels, Belgium

3]FARI Institute, Universite Libre de Bruxelles-Vrije Universiteit Brussel,
Brussels, 1000, Belgium

4]Anthropo-Lab - ETHICS, Université Catholique de Lille, Maison des
chercheurs, 14 Bd Vauban, Lille, 59000, France

5]Center for Human-Compatible AI, University of California, Berkeley, 2121
Berkeley Way, Berkeley, 94720, CA, USA

# Defaults: a double-edged sword in governing common resources

<EMAIL_ADDRESS>Rémi Suchon<EMAIL_ADDRESS>Tom Lenaerts
<EMAIL_ADDRESS><EMAIL_ADDRESS>[  [  [  [  [

###### Abstract

Extracting from shared resources requires making choices to balance personal
profit and sustainability. We present the results of a behavioural experiment
wherein we manipulate the default extraction from a finite resource.
Participants were exposed to two treatments — pro-social or self-serving
extraction defaults — and a control without defaults. We examined the
persistence of these nudges by removing the default after five rounds. Results
reveal that a self-serving default increased the average extraction while
present, whereas a pro-social default only decreased extraction for the first
two rounds. Notably, the influence of defaults depended on individual
inclinations, with cooperative individuals extracting more under a self-
serving default, and selfish individuals less under a pro-social default.
After the removal of the default, we observed no significant differences with
the control treatment. Our research highlights the potential of defaults as
cost-effective tools for promoting sustainability, while also advocating for a
careful use to avoid adverse effects.

###### keywords:

common pool resource, defaults, personal preferences, nudging, experiments

##  1 Introduction

Modern life relies heavily on finite resources like water, electricity,
internet bandwidth or public roads. The over-consumption of these resources
may produce negative externalities on society and the environment. These pose
significant challenges and are difficult to overcome, as individual
rationality may easily lead to over-consumption, resulting thus in a “tragedy
of the commons” [1]. Resolving such social dilemmas require the design of
institutions and mechanisms to enforce rules. A central authority, e.g. the
state, can impose sanctions and rewards (such as taxes, or extraction rights)
to tame over-consumption. In opposition to such a top-down approach, Elinor
Ostrom’s seminal work [2] demonstrates the effectiveness of decentralised,
bottom-up arrangements in preserving exhaustible resources through self-
governance.

The consumption of finite resources often occurs through provider companies
(e.g., water and energy suppliers) or governmental institutions (e.g., natural
resource management agencies, environmental protection departments), to
enumerate some examples. These mediating entities can play a decisive role in
curbing over-consumption, by encouraging participants towards more desirable
consumption behaviours. For example, energy providers offer diverse
consumption plans tailored to their capacities and users’ schedules and
preferences, including selecting energy from environmentally friendly or cost-
effective sources. The same can be found for other resources, such as water or
internet access [3, 4].

As the number of provided options grows, intelligent automated systems become
useful to assist in making choices. In the context of energy consumption, for
example, automated systems can schedule when household appliances become
active or when hybrid cars should charge during off-peak hours, linking these
choices to when sustainable energy sources are providing more energy than non-
sustainable ones [5]. An important issue among these decision-support systems
is that their design is determined by the mediating entities mentioned
earlier. They can predefine a set of default consumption plans for users,
determined for instance by assumed users’ preferences or needs, their own
interest or broader prosocial goals, without reducing freedom of choice, while
also being easy to implement [6].

Users may respond differently to the available default setting, influenced by
their own inclinations and priorities [7]. In this line, Behlen et al. found
that defaults, while being effective, require a targeted approach to reach
individuals whose interests align with the policy-maker [8]. For instance, an
electricity provider can offer renewable energy for consumers by default,
promoting a course of action supported by policy or a prevailing social norm.
Yet, some consumers may prefer other sources of energy and adapt their
consumption habits to accommodate their individual preferences [9, 10]. For
instance, a person who is particularly insensitive to the collective issue of
energy over-consumption may be more likely to override a default directed
towards renewable energy sources. So far, no clear answers have been provided
experimentally on this association between personal preferences, default
settings and consumption of a finite resource. In this work, we aim to address
this gap in the literature by examining this question.

First, we want to assess whether a simple manipulation, like setting a default
extraction value, can curb collective (over-)consumption in a Common Pool
Resource dilemma (CPRD) [11, 2]. The CPRD is particularly well-suited to study
consumption of a finite resource: CPRD experiments have been used to study the
exploitation of water basins, lakes, irrigation of a community, fisheries or
timber, to name a few [12, 13, 14, 15]. The problem lies in the aggregate
behaviour of participants: without a system of governance, participants
excessively appropriate from the common resource, which may give rise to a
”tragedy of the commons” [16]. See Figure 1A for a visual representation of
the CPRD.

A meta-analysis by Mertens et al. demonstrated that choice architecture
strategies, particularly those on decision structure like default settings,
often surpass others focusing on decision information or assistance [17],
revealing the potential efficacy of such interventions. Fosgaard et al.
observed that in public goods games, presenting a conditional cooperation
strategy as the default option effectively nudged participants towards more
cooperative behaviour [18]. Similarly, Bynum et al. studied how default non-
participation in collective risk dilemmas (contributing zero by default) led
to participants more frequently failing to meet the required threshold in this
game[19]. Moreover, Ferguson et al. found in their dynamic organ donor game
that default opt-out decisions for non-cooperators significantly impact group
cooperation levels, more so than opt-in decisions for cooperators [20].
Furthermore, default settings significantly impact environmental choices.
Liebe et al. showed that when sustainable, or ’green’, energy options are set
as the default, their adoption rates increase, resulting in reduced energy
consumption [10]. Conversely, when ’grey’ energy options, which are less eco-
friendly, are defaulted, participants adopted these less sustainable sources
more often [21]. This study builds on prior research by evaluating defaults in
the CPRD management, contrasting a socially beneficial default with a socially
detrimental one and their impacts on overextraction.

Second, we aim to understand how default settings impact long-term consumption
habits, and what happens when the default is lifted. This includes assessing
the potential for both positive and negative spillovers. Positive spillover
refers to scenarios where a pro-social behaviour leads to more of such
behaviour, enhancing thus sustainability efforts. Conversely, negative
spillover, or backfire effects, occur when an initial pro-social action is
followed by opposing behaviours (see the work of Truelove et al. discussing
these spillover effects in detail [22]).

In this regard, the experimental findings are mixed. Cappelletti et al. found
a decline in choice of the default contribution following the removal of
defaults in a public goods game, highlighting the challenges in sustaining
behaviours when the default is removed [23]. Fosgaard et al. found that after
participants saw a free-rider strategy by default, they were significantly
more defective in subsequent public goods game without defaults [18]. However,
contrasting these findings, Ghesla et al. found that encouraging pro-social
decisions through choice defaults, with or without significant opt-out costs,
does not affect unrelated subsequent pro-social behaviour [24] and they might
be effective for subsequent tasks [25]. Albeit these soft interventions are
very popular for policymaking, their long-term efficacy has been questioned
[26]. Our work expands on this current understanding by testing the presence
and nature of spillover effects when default values are lifted.

It remains unclear how default settings, known to limit individualistic
behaviour, might also have negative social impacts. Prior studies show that
consumers often select products with costly, preselected add-ons by default,
rather than customising basic products with their preferred options [27]. This
pattern, evident across various shopping platforms and devices, leads to
unintended purchases or non-consensual sharing of personal data due to default
settings [28]. Our study examines the dual nature of default effects by
introducing both pro-social and self-serving defaults, to assess their
influence on group decisions towards either beneficial or harmful outcomes.

Therefore, the third and final goal is to explore how the impact of defaults
on (over-) consumption is mediated by (the heterogeneity of) individual
preferences. We introduce two different default values, which might encourage
pro-social individuals towards increased extraction and individualistic ones
towards reduction. Understanding the heterogeneous effect of nudges could help
tailor nudge interventions to individual characteristics and make them (more)
effective [29, 8]. However, mismatches between these two can lead to
backfiring, surpassing the impact of transparent information or modes of
thinking [30]. Guido et al.’s experiment showed that rule-followers responded
more to nudges with persuasive, socially conscious messages than rule-
breakers, but no average effect was noted when social preferences were ignored
[31]. Additionally, Ghesla et al. found in the context of energy consumption
that politically left-leaning individuals or those prioritising environmental
concerns are likelier to opt out of default gray energy contracts [32].

To achieve our 3 goals, we introduce defaults in the CPRD, and we also collect
data on participants’ social preferences. Importantly, behaviour in such
experimental social dilemmas predicts real-life behaviour, which ensures the
external validity of our approach and results [33, 34].

Figure 1: Visual representation of the experiment designed for this work. We
use the Common Pool Resource dilemma (CPRD) [11] to understand collective
resource management. In this game, individuals extract resources (as tokens)
and receive payoffs (in experimental units, or ECUs) proportionate to their
extraction levels. Panel A shows four individuals who request 45 tokens in
total. Panel B transforms these requests into a collective payoff of 52.87
ECUs, determined by a payoff function curve shown in panel C. (more details in
the Methods section). D:  Experiment flow. the experiment consists of three
tasks: In task 1 (brown box), participants complete an incentivised Social
Value Orientation task (SVO) [35], allowing us to identify participants’
resource allocation preferences. Task 2 (green box), assessed participants’
risk aversion (also incentivised) [36, 37]. Finally, in task 3, participants
engage in the CPRD as part of one of three treatments, which cover 2 different
types of defaults and one treatment without a default for comparison (panel
E): Pro-social (default = 11 tokens, optimal group extraction yielding 52.8
ECUs), Self-serving (default = 23, excessive extraction yielding no returns),
and a Control with no preset extraction. The green dots represent the rounds,
where the darker green represent the first five rounds with default values,
and the lighter green the rounds with no default. More details on these
treatments are provided in the Methods section.

In the CPRD experiment, as represented in Figure 1, participants in groups of
four have to coordinate their consumption of a finite resource, which offers
benefits to consumers based on their proportional usage. They repeat this task
for 10 rounds. Two default scenarios are presented: i) the _Self-serving_
default, while enticing since it leads to higher payoff if the rest extract
reasonably, selecting this value results in zero benefits if it is chosen by
everyone in the group; and ii) the _Pro-social_ default, which, if
collectively adopted, yields the social optimum, maximizing the resource’s
potential benefits (see Methods for details). Although the default value in
the CPRD suggest a course of action, participants can override it and choose
another consumption level (opt-out). This preserves the participants’ autonomy
over the shared resource. To assess the ability of a default to build lasting
consumption habits, our second goal, we provide the default only during the
first five rounds of the experiment, and remove it in the last five.

Before the actual CPRD experiment (see Figure 1), we use a Social Value
Orientation (SVO) test [38] to classify participants into four social-
preference types: altruistic, pro-social, individualistic and competitive
individuals. Pro-social individuals, identified by their SVO, have been shown
to exhibit heightened concern for environmental causes and collective welfare
[39, 40, 41]. Research has demonstrated that individuals classified as
individualistic and competitive tend to extract significantly more than those
classified as altruistic or prosocial in resource dilemmas [42]. Moreover,
certain decisions can pose greater challenges for specific individuals, such
as the relatively slower evidence collection among equality seekers compared
to categorical decision-makers [43]. Lastly, we also measure the level of
risk-aversion of participants and correlate it with default adoption, as the
default option is often perceived as the safe and risk-free option [44].
Moreover, we want to test the relationship between risk perception and
consumption, since risk-averse individuals have shown to consume less in CPRD
experiments [45].

##  2 Results

###  2.1 While defaults influence participants, the effect is asymmetrical

In the experiment flow (see Figure 1), participants were randomly assigned to
one of three treatments in the third stage (see Methods for details): In the
_Self-serving_ treatment ($n=156$ participants, 39 groups), the default
extraction shown to participants in the first five rounds corresponds to an
individually beneficial extraction (i.e. extraction value $x=23$). This
default could potentially yield a high individual payoff, but if collectively
chosen, results in all participants obtaining zero payoff. In the _Pro-social_
treatment ($n=156$ participants, 39 groups), the default was set to an
extraction value beneficial for resource and society (i.e. extraction value
$x=11$). This choice is a mutually optimal one, which, if selected by
everyone, leads to an individual payoff of $132$ ECU and maximises collective
surplus. Lastly, in the _Control_ treatment ($n=100$ participants, 25 groups),
no default value was shown, and thus each participant had to select how much
to consume in each round. In CPRD theory, rational, self-interested
participants extract the symmetric Nash equilibrium ($x=18$, depicted as the
blue dashed line in Figure 2), leading to resource overexploitation and a
suboptimal equilibrium [16].

In the first five rounds of the CPRD (see Figure 1), where participants of the
Self-serving and Pro-social treatments were shown a default value, the mean
extraction did not start exactly from the default option but was effectively
nudged to more or less extraction levels depending on the default value
presented to them, as shown in Figure 2A. The pink markers in Figure 2A show
that participants in the Self-serving treatment extracted more
($\overline{x}=18.7756$, 95% CI = $[18.3171,19.2342]$) in the first rounds
than those in the control ($\overline{x}=15.9280$, 95% CI =
$[15.3137,16.5423]$) and Pro-social ($\overline{x}=15.1192$, 95% CI =
$[14.7122,15.5263]$) treatments. An analysis of variance (ANOVA) shows for the
first five rounds that the average extraction over time is significantly
different between treatments ($F(2)=9.7317$, p-value$=<0.0001$). The Self-
serving default nudged participants towards the Nash equilibrium, particularly
in rounds 3 to 5, with a mean extraction of $\overline{x}=18.6859$ and a 95%
CI of $[18.0816,19.2902]$, not significantly different from the Nash
equilibrium (Wilcoxon signed-rank test, V $=24780$, $p=0.1734$).

As long as the default value was shown, the participants in the Self-serving
treatment extracted significantly more than the in control treatment
($F(1)=54.872$, p-value$=<0.0001$). For the Pro-social treatment, this
difference extended until round 3, but thereafter the difference was no longer
significant ($F(1)=1.0671$, p-value$=0.3017$).

To visualise these differences, Figure 2B, C and D show the estimated
differences in the extraction over rounds using a mixed-effects model (see
Methods for more details on this model). This model can identify the time
periods where the extraction is significantly different from zero. The area in
pink between the red vertical lines represents the area where differences
between treatments are significant at the 5% level. The fit between the model
and the experimental data can be seen in Figure 11 in the Appendix.

Figure 2B shows that the participants extracted less (below the zero line) in
the control treatment than in the Self-serving treatment in the first five
rounds, i.e. where the default value was shown. Figure 2C shows how
participants extracted more (above the zero line) in rounds 1 and 2, and then
the mean extraction remained the same on average in the remaining rounds.
Figure 2D shows the mean difference in extraction between the Pro-social and
Self-serving treatments.

In this regard, the default effect showed an asymmetrical duration: the effect
of showing a selfish default value lasted for longer, compared to showing a
pro-social default value. Indeed, if the effect was symmetrical, participants
in the Pro-social treatment would extract significantly less (compared to
showing no default) for the same duration as they did in the Self-serving
treatment. The selfish default was more effective to anchor participants to
over-extract than the pro-social default was to nudge participants toward
sustainable levels of extraction.

Figure 2: Mean extraction per treatment. A) Mean extraction by round and by
treatment: Pro-social $n=156$, Self-serving $n=156$ and Control $n=100$. The
blue dotted line represents the Nash Equilibrium of the game, while the dotted
lines on both extremes represent the default values presented to participants.
Vertical lines represent $95\%$ confidence interval. (B, C and D) Estimated
difference of mean extraction between treatments the red is the estimated
difference, as given by the mixed-effect model, while the vertical lines
represent the round where this significant difference can be found. The colour
shaded areas represent the $95\%$ confidence interval from the model.

###  2.2 The effect of all defaults disappear as soon as they are lifted

After round 6, where participants must choose an extraction without a default
as in the Control treatment, the participants in the three treatments had
similar mean extractions, as shown in the gray shaded areas of Figures 2B, C
and D. Actually, in the last five rounds, the mean extractions of the Self-
serving ($\overline{x}=16.9051$, 95% CI = $[16.4246,17.3857]$) and Pro-social
($\overline{x}=16.3256$, 95% CI = $[15.8844,16.7668]$) treatments are very
similar to the mean extraction in the Control treatment for all rounds
($\overline{x}=16.7180$, 95% CI = $[16.1161,17.3199]$). An analysis of
variance (ANOVA) further confirms this, as extractions are not significantly
different between the three treatments after round 6 ($F(2)=1.5333$,
p-value$=0.2161$). Note that the mean extraction in all treatments is closer
to the symmetric Nash equilibrium (18 tokens, shown in the blue dotted line in
Figure 2A) than to the default values provided in the treatments. Therefore,
the effect of defaults fades away as soon as the defaults are lifted, which
contradicts the “stickiness” hypothesis.

###  2.3 Cooperatives can be nudged to extract more and selfish participants
to extract less.

We hypothesised that extractions are affected not only by the defaults but
also by personal preferences (which were measured in Task 1 and 2) and that
there could be interesting interactions between the default value and both SVO
and Risk preferences.

The results of Tasks 1 and 2 allows us to study the personal preferences of
the participants and to link them with the behaviour in the third task. Figure
8 in the Appendix presents the distributions of SVO, measuring social
preferences, and gambles choices, measuring risk preferences. Most
participants across all treatments fall under the “cooperative” spectrum
($n=275,\approx 67\%,22.45^{\circ}<SVO^{\circ}<57.15^{\circ}$) and another
share under the “individualistic” ($n=132,\approx
32\%,12.04^{\circ}<SVO^{\circ}<22.45^{\circ}$) trait in this task. Three
participants can be classified as “altruistic” ($\approx
0.7\%,SVO^{\circ}>57.15^{\circ}$) and two as “competitive” ($\approx
0.4\%,SVO^{\circ}<12.04^{\circ}$). Moreover, 283 participants (69%) picked the
three least risky gambles (the lower, the safest) in the Risk Assessment task.
Figures 8 and 9 in the Appendix show the distribution of extraction by SVO
scores and gamble choices.

To link the individual data from the first two tasks with the data of Task 3,
we fitted a mixed-effects model (see Methods section for the details on the
fitting). The results of the regression model are detailed in Table 3 in the
Appendix, there is a significant interaction term between SVO score and the
treatments, which means that the extraction participants made depended on both
the default value presented and their SVO score.

The model also reveals a difference in extraction based on SVO and CPRD round,
which we visualise in the form of a heatmap in Figure 3. This figure shows the
extraction difference between two treatments, and where a significant
difference was found. In panel A, the difference shown is negative, meaning
that the participants in the Self-serving treatment extracted more than in the
Control treatment, for the first five rounds and mostly on the upper bounds of
the SVO spectrum, i.e. where Cooperative and Altruistic preferences reside.
This means that the Self-serving default presented led cooperative and
altruistic individuals to extract more on average ($F(1)=44.662$, p-value
$<0.0001$) than what they would do in the Control, as also shown in Figure 3C.
In panel B, where the Pro-social treatment is compared to the Control, this
difference is mostly in the first three rounds for the lower bounds of the SVO
spectrum, i.e. Individualistic and Competitive participants. Similar to the
previous finding, the Pro-social default makes selfish participants extract
less, with respect to the Control treatment ($F(1)=7.6922$, p-value$=0.0059$).
This difference can be seen in Figure 3D where the highlighted markers show
the mean extraction in treatments Control and Pro-social.

Regarding risk preferences, we classified the subjects who picked gambles 1 to
3 as ”risk-averse” and those who picked gambles 4 to 6 as ”risk-seekers” (see
Methods for details about the gambles). We found that in the Self-serving
treatment, risk-seekers extracted less on average ($\overline{x}=17.8809$, 95%
CI = $[16.9825,18.7792]$) than risk-averse subjects ($\overline{x}=19.1615$,
95% CI = $[18.6331,19.6899]$), and this difference is significant (KS-
statistic $=0.1181$, p-value $=0.0001$). Conversely, risk-seeking subjects
extracted more in the Pro-social treatment ($\overline{x}=16.3915$, 95% CI =
$[15.5705,17.2124]$) than risk-averse ($\overline{x}=14.5706$, 95% CI =
$[14.1138,15.0275]$), and the difference between these two means is
significant (KS Statistic $=0.1450$, p-value$=0.001$), see Figure 10. With
this finding, we could observe how the risk-averse participants conform with
the proposed default more often, resulting in more average extraction in the
Self-serving treatment and less extraction in the Pro-social, with respect to
their risk-seeking counterparts.

Figure 3: Difference in extraction depending on participants’ SVO over time. A
and B: Estimated difference given by the mixed-effects model, where non-white
parts show a significant difference between two treatments. The horizontal
lines show the SVO categories for reference and the colours the difference in
extraction. Negative (or positive) differences show a larger (or smaller)
extraction than the results in the Control treatment. C and D: Mean extraction
over time given by the experimental data, where the most pro-social categories
of SVO (cooperative and altruist) are grouped in panel C and the most selfish
categories of SVO (individualistic and competitive) are grouped in panel D.
The highlighted points in both panels are the ones given by the model in
panels A and B. Vertical bars show the 95% confidence interval.

##  3 Discussion

Our experiments show that defaults impact over-extraction in a CPRD. In our
case, we found an asymmetrical persistence of the influence of the default,
with respect to the Control treatment. Specifically, participants in the Self-
serving treatment extracted more on average over five rounds, while those in
the Pro-social group extracted less only in the initial two rounds. Notably,
our findings indicate that this effect persists even when players are
repeatedly prompted with the same decision, as shown in previous research
[25].

Previous literature has shown that individuals often underestimate the
influence of default choices on their decisions [46]. Echoing this, in our
study, nearly half of the participants (161 out of 312) across both Self-
serving and Pro-social treatments reported feeling unaffected by the default
values presented. Nonetheless, our analysis showed the default value
significantly influenced average extractions in each treatment. However, our
analysis showed that the extractions of those who self-assessed as
“unaffected” are significantly different from the mean extraction in the
Control (lower for the Pro-social treatment and higher for the Self-serving
treatment) indicating a disconnect between perceived and actual influence of
defaults.

In the CPRD, participants are incentivised to extract more than their peers.
Although their extractions decreased with respect to the control, in the first
five rounds of the Pro-social treatment, participants still extracted more
than the presented default. In contrast, in the Self-serving default,
participants extracted significantly more than in the control, and converged
towards an average extraction which coincides with the Nash equilibrium of the
game. Additionally, in both Pro-social and Self-serving treatments, there is a
symmetrical trend of converging towards the average extraction observed in the
control, once the default nudge is removed. However, the time it takes for the
population of each treatment to converge is asymmetrical, that is, the effect
of the selfish default lasted longer than the effect of the pro-social one.

Nevertheless, our results show that if the participants play the CPRD game
with high values by default (Self-serving treatment), it is expected for them
to extract significantly more than showing a low default (Pro-social
treatment). Since our experiment intended to reflect real scenarios of
resource consumption, this result is highly important. For example, in
contexts such as energy consumption, individuals often face the choice of
selecting a consumption plan, with one option frequently set as the default.
This design decision can ultimately influence both individual payoffs and
resource consumption patterns.

In rounds 6-10, participants had to pick their extraction in every round
without a default, regardless of the treatment. One of our hypotheses was that
we might observe a persistence effect of the default, such as participants
continuing to extract at a higher rate if they were initially shown a selfish
default in the first five rounds. However, our results did not support this
hypothesis. We found no difference in mean extraction once the default was
lifted. Participants in all treatments extracted around 16 tokens per round in
all treatments. This quantity is closer to the symmetrical Nash equilibrium
[2] than to the default values provided in the treatments, which is still
inefficient from the resource management point of view [47].

Another important finding relates to how individual preferences (as measured
by the SVO) determine resource allocation. We wanted to understand the effect
of the (mis)alignment of the default value and the participants’ SVO: i.e.
what happens if a cooperative person is confronted with a selfish default and
vice-versa. Previous research suggests that individuals with higher SVO scores
typically exhibit more pro-social behaviour, while those with lower scores
tend toward more self-interested behaviour. [48, 40] However, our results show
that cooperative individuals extracted more when shown a selfish default than
in the absence of default. Moreover, defaults worked as a nudge to make
selfish participants extract less when confronted with a low default as in the
Pro-social treatment, confirming the use of default values as a valuable tool
in fostering sustainable behaviour.

The results presented in this paper shed light on some of the factors -
besides economic incentive - that play a role in how we make decisions in
common pool resource dilemmas. We show that participants can be nudged into a
certain behaviour by pre-setting an extraction value. This has implications on
the way we consume finite shared resources and how we interact in such a
social context. We found that selfish participants (as measured by the SVO)
were induced to extract less by a default, suggesting a sustainable course of
action. In the case of systems where a default value has to be enforced by
design, setting up the ”best practices” as defaults, may be an effective
strategy to mitigate over-consumption. On the other hand, setting the ”wrong”
default can have even stronger (negative) consequences, and spoil the
decisions of previously pro-social participants [49]. While good defaults can
nudge otherwise selfish people, bad defaults have the potential to do the
inverse to a greater extent.

This last point is critical for policy-making, for example with laws aimed at
mitigating dark patterns in digital services and markets [50], enhancing data
privacy [51], and improving products’ environmental performance [52] through
the use of defaults. Policies should adopt evidence-based approaches to ensure
defaults align with individual and societal welfare, emphasising ethical
considerations and autonomy preservation of the individuals.

##  4 Limitations

Our experiment uses an abstract game as a proxy for real-world resource
consumption. To improve the generalisation of our results, we avoided using
loaded language or contextual instructions. While this allows for a greater
control and interpretability of participants’ behaviour, this also sidesteps
important dimensions that are present in many (politicised) real-world
settings, such as emotional involvement in the preservation of the
environment, notions of fairness or the idea of global responsibility. Thus,
future use of our findings may require further testing to account for
contextual specificity of the desired application setting.

Moreover, our study did not account for the long-term behavioural changes of
participants, which suggests the need for longitudinal studies to observe the
durability of the observed behaviours in the long term.

##  5 Conclusions

Our experiment reveals that exposing participants to a default extraction
value in a CPRD significantly affects their extraction patterns. Specifically,
we found that participants in the Self-serving treatment extracted
significantly more resources than those not exposed to any default values.
Additionally, its impact varies based on the participant’s SVO. Cooperative
individuals exhibited selfish behaviour by extracting more when faced with a
Self-serving default, while, notably, selfish individuals extracted less when
confronted with a Pro-social default. Furthermore, the default effect is non-
persistent, and its impact on participants’ decisions diminishes rapidly once
the default is removed.

Our findings have substantial implications for designing systems and policies
aimed at the sustainable management of common resources. They highlight the
importance of accounting for individual heterogeneity and demonstrate the
potential of simple, low-cost interventions like defaults in nudging groups
towards more socially beneficial outcomes.

##  6 Methods

###  6.1 Study design

The data used in this paper was collected through a behavioural experiment,
performed on the online platform Prolific (www.prolific.com). Participants had
to complete three tasks (see Figure 1). Task 1 is the Social Value Orientation
test (SVO) from Murphy et al. [53], and task 2 is the Risk-attitude
elicitation task developed by Eckel and Grossman [37] with the values used by
Dave and Eckel [36]. In task 3, participants play a CPRD in a group of 4. We
designed the experiment so we can link extraction behaviour in the CPRD in
task 3 with participants’ social preferences and risk attitudes elicited in
tasks 1 and 2. Additionally, our experimental design, hypotheses, analyses and
sample size were pre-registered in OSF: https://osf.io/jg2sa

####  6.1.1 Common Pool Resource Dilemma

In the main task, task 3, participants played a version of the Common Pool
Resource Dilemma (CPRD). This dilemma captures the tension that emerges in a
group exploiting a common finite resource. The group payoff is determined by
the sum of extractions of the group members: over-extraction depletes the
resource, leading to a payoff of zero to everyone, while a sustainable
management of the resource yields the highest collective payoff. Individual
payoff is proportional to individual extraction: one gets a higher share of
the group payoff if one extracts a bigger share of the group extraction.
Hence, narrow self-interest dictates to appropriate the resource as much as
possible, however, if everyone does so, depletion ensues (tragedy of the
commons), which is the worst collective outcome.

We propose a variant of the game where participants have to extract a minimum
of 1 and maximum 30 units (or tokens, as they are called in the experiment)
from the resource, which participants can select from a drop-down menu in each
round. The extraction variable is discrete, that is, participants were able to
extract any natural number in the interval $[1..30]$. Participants can aim to
maximise their individual payoffs by extracting more from the resource, or
they can aim to have a group maximum by coordinating their strategies to do
so.

The amount extracted by each player $i$ from the resource is $x_{i}$, and the
amount extracted by the group is $X=\sum_{i=1}^{N}x_{i}$. Extraction of the
resource earns each player $a$ times every unit extracted personally, minus
$b$ for every unit extracted by the group regardless of who extracts it. We
adjusted the parameters used by Walker et al. [11] to obtain similar payoffs
among the different tasks ($a=2.3$ and $b=0.025$). The payoff of extracting
$x_{i}$ and the group extraction $X$ from the CPRD is then:

$\pi_{i}=(x_{i}/X)(aX-bX^{2})$ (1)

Participants have the following information at all times (see Figure 4):

  1. 1.

The round number.

  2. 2.

A two-minutes timer.

  3. 3.

The participant’s extraction and payoff in the previous round

  4. 4.

The total group extraction in the previous round

  5. 5.

The participant’s extraction for the round (this is where the default was
shown)

  6. 6.

An interactive sandbox where they can simulate their and others’ payoffs and a
table with all the possible group extractions, and the ECU’s produced.

Figure 4: Screenshot of the third task. In this task, participants had to
choose their desired extraction for ten rounds. At the top, the platform
showed the round number and the time left to make their decision. The
participants had their previous extraction and the extraction of the other
members of the group, and their payoff, as shown on the left side of the
figure. At the bottom, participants had a sandbox at their disposal to
calculate their potential earnings depending on theirs and others’ extraction.

Additionally, the participants knew that they are interacting in groups of
$4$, that games is played over $10$ rounds, and that there is a maximum of $2$
minutes to make a decision. Participants were instructed to make their
decisions within this time, otherwise they will be considered as dropouts from
the experiment. Also, after every round, the participants know how much the
other three participants extracted in the previous round, and they are
notified if a co-player dropped out of the experiment, in which case they
continued playing in a smaller group, and got paid. Dropouts, totalling 21
instances ($2.8\%$ of the total participants) due to Timeout or Lost focus
(see Table 1), led to the exclusion of data from those completing the ten
rounds. Table 2 indicates that previous tasks’ results, demographic
information, or approval numbers do not predict individual drop-out,
discarding selective attrition concerns.

All participants had to complete a comprehension test for task 3, in which
they were given five attempts to get the five questions correct. If they could
not complete this test, they were paid for the earnings in the previous two
tasks, but they were excluded from playing the CPRD game. All the instructions
and captions can be found in the supplementary documents.

####  6.1.2 Experimental treatments

The treatments consist in the introduction of default extractions. We
implemented defaults by pre-setting a token extraction value. Participants had
the possibility to override this value. We also include a Control treatment
with no default values, i.e., participants always had to choose their own
extraction. Both in the Control treatment and the last five rounds of the Pro-
social and Self-serving treatments, this was enforced by making participants
choose a value between 1 and 30, before proceeding to the next round. In this
case, what they saw in the interface then was a drop-down menu, with two
dashes (–) meaning that they had to pick an amount. We compare the effect of
the manipulation done in the two default value treatments with this control.

The values were chosen based on the social optimum and the individualistic
extraction:

  * •

Social optimum: $x_{f}=\frac{a}{2bn}$ where n is the group size.

  * •

Individualistic extraction: $x_{h}=\frac{a}{bn}$

Given the parameters we chose ($a=2.3$ and $b=0.025$, see previous section),
$x_{f}=11.5$ and $x_{h}=23$. We rounded $x_{f}$ to $11$ because participants
can only pick an integer from the user interface. If in any given round,
$x_{f}$ is collectively chosen, i.e. the group extraction is 44, the resource
will yield its maximum. This also means that participants can get more if they
stick with this extraction. However, players will be enticed to pick a higher
extraction to get a higher share of the group extraction. When the group
extraction reaches 92, or $x_{h}$ is chosen by everyone, the group and
individual payoffs are zero. The Nash equilibrium in this game is defined as
$x^{*}=\frac{a}{b(n+1)}$, in which, if all players are self-interested and
rational, they will pick this reaching a suboptimal equilibrium [47, 54], as
shown in Figure 5 in the Appendix.

The group payoff depending on the total of extraction can be found in Figure 5
in the Appendix. The coloured dashed lines in the figure indicate the amount
that is given back to the players if all members of a group selected a certain
default value.

Participants are subjected to one of the 3 treatments:

  * •

Control - No default value, $n=100$: in this control treatment, participants
play the CPRD without default extraction proposed for 10 rounds.

  * •

Pro-social treatment (Pro-social), $n=156$: in this treatment, participants
are shown a default value representing the social optimum value $x_{f}$ with a
label that reads: Your extraction this round: $11$. At each round, each
participant has the option to override this value, and choose another
extraction for themselves. The wording is neutral, and no notion of “fairness”
or “fair extraction” is communicated to the participants.

  * •

Self-serving treatment (Self-serving), $n=156$: in this treatment,
participants are shown a default value representing the individualistic value
$x_{h}$ with a label that reads: Your extraction this round: $23$. At each
round, each participant has the option to override this value, and choose
another extraction for themselves. The wording is neutral, and no notion of
“individualistic” or “selfish extraction” is communicated to the participants.

To change the default extraction, participants have to click a button below
the extraction and pick a value from a drop-down menu. To measure persistence,
in both treatments (Pro-social and Self-serving) participants are subjected to
the default value manipulation for 5 rounds, while in the subsequent 5 rounds,
no default option is presented, i.e., participants have to manually pick the
extraction they desire. Our experimental manipulation is “between-subject”:
participants could not take part in more than one treatment.

The currency used in this experiment is ECU (Experimental Currency Unit). Each
ECU is converted to U.K. Pounds (£) with an exchange rate of or 100 ECUs = £1,
or 1 ECU = £0.01. Participants were recruited using Prolific
(www.prolific.com). In Prolific, we recruited participants who indicated they
were fluent in English, had a high approval rate ($+99\%)$ and had more than
$20$ submissions on the site. These filters were applied to filter out
possible dropouts. Participants received £3 as a fixed participation fee plus
£6 bonus depending on the decisions they made in the game. The average total
earnings were £5.05 for a duration of roughly 30 minutes.

We excluded participants who did not sign the Informed Consent Form, dropped
out, failed the comprehension test, or did not act within the time limit for
each round. Participants with group drop-outs are also excluded, even if they
finished the experiment themselves. Additionally, participants who were
excluded or dropped out from the experiment were only paid for the tasks they
completed. This design choice aimed at motivating participants to finish all
tasks, while rightfully paying them for their time and for the completed
tasks. Therefore, the experimental data used in this paper are from
participants in groups of four who completed all ten rounds, passed the
comprehension test, and successfully submitted their work on Prolific.

The raw experimental data, instructions with screenshots included, is attached
to the Supplementary Information. All experiments described in this paper
followed the guidelines and regulations of data protection and experiments
with human participants, and they were approved by the Ethical Commission for
Human Sciences at the Vrije Universiteit Brussel in Brussels, Belgium
(ECHW_361.02). Also, all participants who took part in the experiment signed
an Informed Consent form for the use of the data collected in the experiment,
including decisions and background information, including gender and age.
Without signing this form, they could not proceed with the experiment.

####  6.1.3 Personal preferences

For the first task of the experiment, we assessed participants’ social
preferences using the Social Value Orientation measure (SVO) [55] and the
Slider measure by Murphy et al. [53, 35] with a modification to include
incentives (see Figure 6 for a sample of the decisions shown to participants).
Participants made six allocation decisions. Participants were informed that
they would be matched with another participant at the end of the experiment.
In each match, the allocation decisions of one of the participants would be
played out (described as Group A), with the other one being paid as a receiver
(described as Group B). When decisions are made, one of the six choices was
randomly selected as the final allocation between a participant from Group A
and another from Group B. Participants in Group B will receive an allocation
determined by a member of Group A. Their resulting SVO were represented as an
angle from the origin, where a higher angle means greater cooperativeness, and
lower angles indicated individualistic or competitive allocations. For an
easier analysis, we grouped subjects with SVO angles $<22.45^{\circ}$ as
”Individualistic+Competitive” and SVO $>=22.45^{\circ}$ as
”Cooperative+Altruistic” (as done in other works [42, 56]) in some sections of
the document instead of using the continuous angle.

In the second task, we implemented a risk-attitude elicitation task as done by
Eckel and Grossman [37], with the values from Dave et al. [36] Participants
have to decide between six different gambles, from the least risky to the most
risky, of an event happening with 50% chance. A coin was flipped to pick which
of the events will pay them and that was their payoff for their task. The
resulting measure is a discrete range from 1 to 6 where 1 is the safest and 6
is the riskiest (see Figure 7 for a sample of the options shown to
participants).

####  6.1.4 Mixed models

We fitted a generalized additive (mixed) regression model (GAM) for the panel
data using the mgcv _R_ package for _GAM_ estimation [57, 58]. We used this to
test the interactions of the variables over time and by treatment. The
variables we want to study to understand the extraction behaviour were:

  * •

Treatment (or the default value presented, if any)

  * •

Round number

  * •

SVO score in task 1

  * •

Gamble choice in task 2

  * •

Player’s extraction in the last round

  * •

Others’ extraction in the last round

Our aim is to test the hypothesis that the default value presented in the Pro-
social and Self-serving treatments will have different effects in function of
the social and risk preferences of different subjects. Specifically, depending
on their SVO score in task 1 and gambling choice in task 2. The reason behind
this is that we hypothesised, for example, that cooperative individuals will
react to a high default differently compared with an individualistic person.
Also, we assumed random intercepts for each individual as a random effect,
that accounts for individual-level variability in our subject pool, not
captured by the fixed effects we included. Hence, our lme4 formula looked like
this:

$x_{i,r}\sim T+T\times\text{SVO}+T\times
r+T\times\text{gamble}+x_{i,r-1}+X_{-i,r-1}+(1|i)$ (2)

Where $x_{i,r}$ is the extraction of the player $i$ in round $r$ where they
were in treatment $T$, also $X_{-i,r-1}$ represents the extraction of the
three other group members, and the last term $(1|i)$ in the equation
represents the random effects for player variability.

We also show the difference in extraction between two levels of a categorical
variable, in this case we use this model to show the time window where the
extraction between two treatments is significantly different according to the
model. A significant time window is given by the estimated difference in
extraction, where the confidence intervals of the prediction do not include
zero. This is useful to show the evolution of the default manipulation and how
it affects individuals with different SVO scores.

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##  7 Acknowledgements

E.M. and T.L benefit from the support by the Flemish Government through the AI
Research Program and by TAILOR, a project funded by the EU Horizon 2020
research and innovation program under GA No 952215. T.L. is furthermore
supported by the F.N.R.S. projects with grant number 31257234 and 40007793,
the F.W.O. project with grant no. G.0391.13N, and the Service Public de
Wallonie Recherche under grant n° 2010235–ARIAC by DigitalWallonia4.ai. E.F.D.
is supported by an F.N.R.S Chargé de Recherche position, grant number
40005955.

##  8 Author information

###  8.1 Contributions

E.M.P., R.S. and E.F.D. designed the study and wrote the paper; E.M.P.
implemented the experimental platform, collected data, and performed the
analysis. T.L. wrote and reviewed the paper. All authors edited and approved
the final version.

###  8.2 Corresponding authors

Eladio Montero-Porras Elias Fernández Domingos

## Ethics declarations

###  8.3 Competing interests

The authors declare no competing interests.

##  9 Source data

The source dataset, the code used for the analysis and to reproduce the
figures can be found in Zenodo

##  Appendix A Experimental design

###  A.1 Deviations from pre-registration

The pre-registered experiment, shown in this paper (https://osf.io/jg2sa), was
performed from May 2023 until August 2023.

We made the last changes to the pre-registration in March 2023. In these
changes, we clarified the experimental hypotheses and uploaded the latest
documents before starting the experiments. Here are some updates we did after
that:

  * •

Sample size rationale: Our initial power analysis was based on the work by
Pichert and Katsikopoulos [21] on default adoption of green energy options,
this was done in July 2022. However, in later iterations, we adapted our
calculations and effect size based on a meta-analysis done by Jachimowicz et
al. [6]. This meta-analysis included the effect size of 58 studies, which we
found was more robust. However, by mistake, we did not upload the updated file
to OSF, where we estimated a required sample size of about 69 participants per
treatment, instead of the 54 needed according to the initial analysis. This
new power analysis was performed on January 2023, before the experiments took
place. The correct file was updated and uploaded in OSF in February 2024.
Moreover, we adapted the effect size to $F=0.25$, $\alpha=0.05$ and
$1-\beta=0.95$. Additionally, we assumed a low correlation among repeated
measures ($0.1$). In every treatment, we chose a significantly larger sample
size than the minimum required, to account for estimation errors and ensure
that we have sufficient power.

  * •

Repeated Measures ANOVA: We switched from repeated measures ANOVA (RMANOVA) to
Generalised Additive Mixed Regression models due to the non-normal
distribution in time periods, violating RMANOVA assumptions.

  * •

Treatment names: Changed from ’High or Fair Extraction’ (HE/FE) to ’Self-
serving or Prosocial’, for clarity.

##  Appendix B Experiment metadata

Table 1 shows the distribution of the participants according to their final
status in the experiment. _Completed_ refers to the participants who reached
the end of the experiment, while _incomplete_ refers to the people who left
before the end of the experiment, without cashing any payoff (normally people
that withdrew consent or just did not finish the first two tasks). _Failed
test_ were participants who completed the first two tasks but did not pass the
comprehension test for task 3. Status of _ungrouped_ means that they completed
the first two tasks and the comprehension test, but were waiting for 15
minutes or more for a group of 4 to be formed. _Lost focus_ is all
participants who were waiting to be grouped but either left or lost the focus
of their browser tab when they were being grouped. _Timeout_ refers to people
who were excluded because they did not make a decision within 2 minutes in a
given round of task 3. All participants except for the ones with status
_incomplete_ were paid for their time (6 pounds per hour) and a bonus for each
task they managed to complete.

Of the participants who completed the experiment, some groups had to be
removed, specifically those who had a group member who was timed-out. Thus,
our final sample size used in the results shown in this manuscript is 412
participants across all treatments. In the Self-serving treatment: 156, Pro-
social: 156 and Control: 100. 50% of them were Female. The mean age of
participants was 28.77 years old (SD = 9.02 years). The average time taken for
the experiment was 28 min (SD = 9.10 minutes). Main nationalities are South
African = 21%, Portuguese = 16% and Polish = 15%. Moreover, 30% of them were
employed full-time, 13% part-time employees and 15% unemployed. All
participants were fluent in English, had at least 10 successful submissions on
Prolific and had a 99-100% success rate in their submissions. None of them
could participate more than once in the experiment as past sessions’
participants were filtered out.

Status | No. participants | %
---|---|---
Completed | 494 | 70%
Failed test | 74 | 10.4%
Incomplete | 71 | 10.0%
Ungrouped | 49 | 7%
Timeout | 19 | 2.6%
Lost focus | 2 | 0.2%
| 709 | 100%
Table 1: Number of participants per status in the experiment.

| Estimate | Std. Error | z value | Pr($>$—z—)
---|---|---|---|---
(Intercept) | -43.9800 | 60860 | -0.0010 | 0.9990
svo_score | -0.0126 | 0.0320 | -0.3930 | 0.6940
gamble_choice | 0.3874 | 0.2460 | 1.5750 | 0.1150
Nationality∗∗∗ | -3.8309 | 60957 | 0.0000 | 1.0000
Age_x | -0.0010 | 0.0466 | -0.0220 | 0.9820
Sex_xFemale | 17.1400 | 31200 | 0.0010 | 1.0000
Sex_xMale | -1.3440 | 31320 | 0.0000 | 1.0000
Sex_xPrefer not to say | 15.0400 | 57900 | 0.0000 | 1.0000
Ethnicity_simplified_xBlack | 20.7300 | 15670 | 0.0010 | 0.9990
Ethnicity_simplified_xDATA_EXPIRED | 1.8900 | 50680 | 0.0000 | 1.0000
Ethnicity_simplified_xMixed | 3.6620 | 17890 | 0.0000 | 1.0000
Ethnicity_simplified_xOther | 3.0780 | 20190 | 0.0000 | 1.0000
Ethnicity_simplified_xWhite | 19.8500 | 15670 | 0.0010 | 0.9990
Total_approvals_x | 0.0018 | 0.0017 | 1.0850 | 0.2780
Table 2: Results of the logistic regression made to test if the 21
participants who dropped out did so because of their results in previous tasks
(variables svo_score and gamble_choice) or their demographic information.
$***$: due to the number of options, the Nationality variable was grouped as a
single variable and the estimates were averaged. Figure 5: Group payoff as a
result of a given group extraction. As shown in the green line, the maximum
return the CPRD can provide is when participants extract 46 tokens as a group
(average 11.5 tokens per player), which is shown with the yellow dashed line.
If participants extract more or less than that quantity as a group, they will
be under or over extracting the resource, respectively. The pink line shows
that if participants extract 92 tokens as a group (average 23 tokens per
player) they will all receive zero ECUs.

###  B.1 Default picking and self-assessment

At the end of the experiment, we asked participants to self-assess the
influence the default value had on their extractions, this question was open-
ended and was only shown to participants in the Self-serving and Pro-social
treatments. The question was: “Did the presence of a default value in the
first 5 rounds affected your desired extraction?”.

As this question was open-ended, we manually formatted each participant’s
response and classified “Not affected” those who responded either “No”, “Not
really” or something similar the denoted a clear negative response to the
question. We did not label as “Not affected” those who responded a more vague
reaction, such as: “I don’t think so, only in the first one” or “Only
slightly”. We were this strict in the negative responses because prior work
has showed that individuals often underestimate the influence of default
choices on their decisions [46], and we wanted to test this new hypothesis. In
total, we classified $161$ participants as “Not affected” and $151$ as
“Affected”.

We analysed the extractions of the self-assessed “Not affected” with the
extractions of both the “Affected” and the participants in the Control
treatment, where no default value was displayed.

Comparing the mean extraction in the Control treatment $\overline{x}=15.9280$,
95% CI = $[15.3137,16.5423]$, with those who self-assessed as “Not affected”
is significantly different in both cases, in the Pro-social treatment (KS test
$=0.097398,$ p-value $=0.02707$) and in the Self-serving treatment (KS test
$=0.19523$, p-value $<0.0001$).

The mean extraction of the “Not affected” participants in the Pro-social
treatment was $\overline{x}=15.3855$, 95% CI = $[14.7947,15.9763]$ while the
“Affected” was $\overline{x}=14.8164$, 95% CI = $[14.2624,15.3704]$. This
difference is not significant (KS test: $=0.080607$, p-value $=0.1603$). In
the Self-serving treatment, “Not affected” extracted $\overline{x}=18.1462$,
95% CI = $[17.4712,18.8211]$ and the “Affected” $\overline{x}=19.4051$, 95% CI
= $[18.7876,20.0227]$ and this difference is significant (KS test:
$=0.14359,p-value=0.0006$).

###  B.2 Tasks 1 and 2 supplementary material

Figure 6: Sample of three out of six decisions participants had to make in the
first task. Each decision was shown individually, to not crowd the user’s
interface. The decisions were taken from Murphy’s et al. Slider Measure, with
the six main measures [53]. Figure 7: Sample of three out of six options
participants had for the second task. In this case, all options were shown in
the same table for comparison. The options were taken from the measure
developed by Dave et al [36].  Figure 8: Left: Distribution of participants
according to their SVO Score (task 1). This test measures a participant’s
resource allocation preferences. Values near 0 represent more individualistic
preferences, while values towards 90 represent more altruistic preferences.
Right: Distribution of participants in the Task 2 (Risk assessment). In this
task, participants had to choose between 6 gambles, where 1 was the less risky
and 6 was the riskiest one. Figure 9: A: relationship between participant’s
SVO score in task 1 and their mean extraction in all rounds. The line across
represents the linear fit and the shades the 95% confidence interval. B: Mean
extraction of the participants according to their gamble choices in Task 2 of
the experiment.

Figure 10 shows the gamble choice of those who picked the approximate default
in task 3 and those who picked another value. As shown in the figure, the
gamble choice of default extractors is lower in both Pro-social (KS: 0.1224,
p-value: 0.0177) and Self-serving treatment (KS: 0.1266, p-value: 0.0048).
This means that risk-averse individuals picked the default more often than
risk-seekers.

Figure 10: Gamble choice and extracting the default option. We divided
participants who extracted exactly the default value provided (marked as True)
and those who did not (marked as False), in any round, so they could have
picked the default in one round and change their extraction in the next one.
In the Pro-social treatment, 19% ($147$ out of $780$ decisions) of the
extractions were the default option in the first five rounds, compared to 24%
($184$ out of $780$ decisions) in the Self-serving treatment.

###  B.3 Results from the Mixed effects model

Parametric coefficients |  |  |  |  |
---|---|---|---|---|---
| Estimate | Std. Error | t value | Pr(<—t—) |
(Intercept) | 7.7650 | 0.3655 | 21.2470 | <2e-16 | ***
Treatment:Pro-social | -0.7952 | 0.5307 | -1.4980 | 0.1341 |
Treatment:Self-serving | 1.1464 | 0.5318 | 2.1560 | 0.0312 | *
extraction_last_round | 0.0823 | 0.0148 | 5.5640 | 0.0001 | ***
others_extraction_last_round | 0.0064 | 0.0086 | 0.7470 | 0.4549 |
svo_score | 0.2927 | 0.0136 | 21.4500 | <2e-16 | ***
gamble_choice | -0.1215 | 0.1162 | -1.0460 | 0.2958 |
Approximate significance of smooth terms |  |  |  |  |
---|---|---|---|---|---
| edf | Ref.df | F | p-value |
round*Treatment:Control | 1 | 1 | 1.971 | 0.16045 |
round*Treatment:Pro-social | 2.1844 | 2.7316 | 5.1910 | 0.00238 | **
round*Treatment:Self-serving | 6.7837 | 7.9327 | 9.8370 | <2e-16 | ***
svo_score*Treatment:Control | 0.8471 | 0.8471 | 193.7410 | <2e-16 | ***
svo_score*Treatment:Pro-social | 0.8470 | 0.8471 | 216.9680 | <2e-16 | ***
svo_score*Treatment:Self-serving | 0.8470 | 0.8470 | 206.5900 | <2e-16 | ***
player_id | 333.0459 | 405.0000 | 2.6550 | ¡ | ***
Table 3: Results from the Mixed-effects linear model of the variable
extraction. The upper table indicates the parametric coefficients which are
the fixed effects of the model. The table below shows the smoothing terms,
which assumes a non-linear interaction between two variables, and the last row
indicates the random effects we included by player, to account for individual
heterogeneity and other effects that might not be captured by our model.

Figure 11: Mean extraction by treatment, with the fit given by the Mixed-
effects regression model. For more information about this model, see the
Methods in section 6.1.4. We accounted for multiple intercepts and effect of
the round depending on the Treatment, SVO and risk assessment, plus a random
effect for individual heterogeneity.