ROYAL SOCIETY
OPEN SCIENCE
royalsocietypublishing.org/journal/rsos
3 ®
Cite this article: Lang M, Chvaja R, Grant
Purzycki B, Václavík D, Staněk R. 2022
Advertising cooperative phenotype through costly
signals facilitates collective action. /?. Soc. Open
5c/. 9: 202202.
https://doi.Org/10.1098/rsos.202202
Received: 3 December 2020
Accepted: 3 May 2022
Subject Category:
Psychology and cognitive neuroscience
Subject Areas:
psychology/behaviour
Keywords:
costly signalling theory, strategic choice model,
evolution of cooperation, public goods game
Author for correspondence:
Martin Lang
e-mail: martinlang@mail.muni.cz
Advertising cooperative
phenotype through costly
signals facilitates collective
action
Martin Lang1
, Radim Chvaja1,2
, Benjamin Grant
Purzycki3
, David Václavík4 , 6
and Rostislav Staněk5
1
LEVYNA, Masaryk University, Brno, Czech Republic
2
PRIGO Open Research, PRIGO University, Havířov, Czech Republic
department for the Study of Religion, Aarhus University, Aarhus, Denmark
department for the Study of Religions, and department of Economics, Masaryk University,
Brno, Czech Republic
department of Philosophy, Technical University of Liberec, Liberec, Czech Republic
ML, 0000-0002-2231-1059; BGP, 0000-0002-9595-7360
Around the world, people engage in practices that involve
self-inflicted pain and apparently wasted resources.
Researchers theorized that these practices help stabilize
within-group cooperation by assorting individuals committed
to collective action. While this proposition was previously
studied using existing religious practices, we provide a
controlled framework for an experimental investigation of
various predictions derived from this theory. We recruited
372 university students in the Czech Republic who were
randomly assigned into either a high-cost or low-cost
condition and then chose to play a public goods game (PGG)
either in a group that wastes money to signal commitment
to high contributions in the game or to play in the group
without such signals. We predicted that cooperators would
assort in the high-cost revealed group and that, despite these
costs, they would contribute more to the common pool and
earn larger individual rewards over five iterations of P G G
compared with the concealed group and participants in the
low-cost condition. The results showed that the assortment
of cooperators was more effective in the high-cost condition
and translated into larger contributions of the remaining
endowment to the common pool, but participants in the lowcost
revealed group earned the most. We conclude that costly
signals can serve as an imperfect assorting mechanism, but
the size of the costs needs to be carefully balanced with
potential benefits to be profitable.
Electronic supplementary material is available
online at https://d0i.0rg/l0.6084/m9.figshare.c.
5986008.
THE ROYAL SOCIETY
PUBLISHING
© 2022 The Authors. Published by the Royal Society under the terms of the Creative
Commons Attribution License http://creativecommons.0rg/licenses/by/4.O/, which permits
unrestricted use, provided the original author and source are credited.
1. Introduction
Finding reliable cooperative partners willing to commit to joint action is a crucial building block of
human societies. While many societies ease cooperative problems by instituting norms that guide
collective action and establish punitive mechanisms for norm transgression, people still vary i n their
willingness to obey these norms, especially when the short-term benefits of free-riding are temptingly
high [1]. Given that willingness to cooperate i n joint tasks is a hidden trait, it cannot be observed
directly and might be faked through relatively cheap verbal proclamations. The potential for
deception, therefore, presents a problem for the assortment of cooperative partners. Deceitful
proclamations may effectively break down collective action if uncommitted individuals verbally fake
their commitment and free-ride on the collective efforts. H o w can committed cooperators reliably
recognize each other?
One answer to this conundrum is offered by the strategic choice model [2-4] designed to explain nonhuman
animals' exaggerated phenotypes such as stotting i n Thomson's gazelles [5] or the elongated
upper tail coverts of the peacock's train [6]. The model asserts that the exaggeration of certain traits
reliably signals hidden genetic quality that is otherwise unobservable. Based on the conflict of interest
between the sender (who wishes to exaggerate the signal) and the receiver (who wishes to reliably
assess the quality of the sender; [7]), the strategic choice model predicts that high-quality signallers
benefit from honestly signalling their hidden quality through phenotypes that are exaggerated at a
specific cost ('handicap' or 'strategic cost'; [8]), which is not affordable to low-quality signallers. For
example, while the elongated tail feathers of male barn swallows handicap their flying ability, they
were shown to correlate with underlying genetic quality, increased mating opportunities and
reproductive success [9]. Whereas exaggerated phenotypes are not the only means to stabilize reliable
communication [10,11], the mathematical formalization of the strategic choice model suggests that the
differential fitness pay-offs of signalling through making phenotypes unnecessarily costly is
evolutionarily stable and separates signallers based on the quality of their hidden phenotype [4,12].
Using these models, researchers identified added strategic costs i n various human behavioural
patterns such as meat sharing [13,14], blood donations [15], or subsistence activity, which were
assessed using costly signalling theory (CST; [16-18]). Under the auspices of CST, behaviours that
ostensibly decrease individual fitness in the short term (e.g. meat sharing) reliably signal hidden
qualities (e.g. hunting skills), and advertisement of these qualities provides long-term fitness benefits
in the form of increased mating and cooperative opportunities [16,19].
Interestingly, the application of CST to the problem of communicating a commitment to cooperative
collective action—'a hidden cooperative phenotype' [1]—has been almost exclusively restricted to the
context of ritual behaviour [20-22]. Indeed, it has been long recognized that ritual practices such as
penile subincision of Aboriginal Australians [23] or Chukchi sacrifice of herd animals [24], together
with the cross-cultural omnipresence of regular ritual gatherings where people spend time and energy,
test the reliability of group members [25]. The CST of ritual (henceforth CSTR) suggests that ritual
practices may be understood as signals of commitment to cooperative norms that guide collective
action. The intensity of the signal may range from extreme signals such as self-mutilation to subtle
signals such as attending weekly ritual gatherings [26,27]. According to CSTR, these signals, alongside
other evolved mechanisms such as supernatural punishment [28-30], help mitigate problems of
cooperation, such as whom to trust, accountability and collective-action maintenance. Ritual practices
serve as a communication platform that offers individuals committed to collective action to truthfully
express their hidden cooperative phenotype (often through expressing commitment to a supernatural
deity or similar group symbols representing the group's cooperative norms), effectively separating
truly committed individuals from potential free-riders [20]. Collective rituals and similar religious
practices provide both a public arena and a shared code for communication of hidden cooperative
phenotype [30]. By binding specific material and energetic costs to ritual performance, the hidden
quality of commitment to cooperative norms materializes into physical signals that the receivers may
rely upon [31,32].
Several converging lines of empirical evidence support the basic premises of the CSTR model and
indicate that (i) sending costly signals (that is, performing costly rituals) correlates with hidden
qualities (i.e. a cooperative phenotype) and that (ii) signal receivers understand the signal and act
upon the received information. First, Sosis & Ruffle [33,34] found that self-reported participation in a
public ritual of religious kibbutz members in Israel predicted contributions to the common pool in the
public goods game (PGG), and Soler [35] observed a similar relationship i n her work with the
members of Brazilian Candomble groups. By analysing social support networks of two villages in
South India, Power [36] showed that participants who regularly worship in a local temple and carry out
public religious acts were more likely to be asked for help by other community members and more likely
to provide help. Moreover, Xygalatas et al. [37] found that charitable contributions to the local temple
after performing an extreme ritual of Thaipoosam Kavadi in Mauritius were predicted by the intensity
of participation as well as by self-perceived pain suffered during the ritual. Furthermore, in another
study in South India, Power [38] found that regular worship increased the chances of being
nominated as generous and devout and that performing costly religious activities was associated with
nominations for devoutness and for giving good advice. In her study of Brazilian Candomble, Soler
[35] also found that self-reported intensity of costly signalling predicted the reported number of
cooperative offers. Finally, using fictional characters varying on the performance of costly acts showed
that costly religious signallers are trusted more [39], even across religious traditions [40,41].
However, while these studies provide valuable support for CSTR by harnessing existing religious
practices in various cultures, they usually cannot separate costly signals of commitment from other
tangled factors and motivations underlying participation in these rituals such as personal vows to
superhuman agents, anxiety management [42-44], or health improvement [27,45]. Nor can these
studies disentangle the complex causal chains of religious systems that may affect cooperation [46,47].
Thus, it is not clear whether participation in religious practices is the primary driver of cooperative
behaviour or whether it is the signalled cooperative phenotype driving the cooperative outputs. We
aim to study the latter. In comparison with field studies, two laboratory studies using P G G suggest
that simulated charity contribution and voluntary tax-paying may serve as a signal of prosocial
intentions [48,49], providing preliminary evidence for the existence of cooperative-intention signalling.
Nevertheless, these studies did not investigate how voluntarily undergoing self-harming (in terms of
resources) rather than prosocial acts may serve this function. Furthermore, there are important caveats
when applying the strategic choice model on cooperative signalling that previous studies failed to
consider.
Since performing a painful ritual or sacrificing livestock is not directly and immutably linked to
underlying genetic quality, the lack of commitment to collective action does not preclude ritual
performance. Even free-riders may sacrifice their resources if the benefit of subsequent interaction
with other ritual practitioners would offset these costs. To overcome this impasse, we suggest two
possible solutions. First, based on the model introduced by Roberts [50], we propose that costly
signalling of a cooperative phenotype would be stable only in iterative cooperative interactions such
that the cost could not be recovered after the first interaction. If a free-rider defects during the first
cooperative interaction, they would not compensate the cost of the signal but would be prohibited
from other interactions (or collective action of the whole group would fail). Costly signalling may,
therefore, be understood as signalling long-term cooperative intentions [50]. However, while Roberts
[50] models costly signalling on the example of unspecific helping, we argue that ritual behaviour
provides signals directed at cooperative norms, which crucially regulate collective action (as opposed
to simple helping). The second model accounting for the discrepancy between the non-human animal
and human signalling was proposed by Sosis [20], who argues that committed and uncommitted
individuals differ in the perception of costs associated with ritual practices. While committed members
discount the costs such that the cost/benefit ratio of participation in ritual activities appears positive,
the reverse is true for free-riders who differentially weigh alternative behavioural choices [51] (e.g.
individually pursuing monetary gain in an unconstrained group). The differential perception of costs
arises through socialization processes that, in interaction with genetically inherited traits, give rise to
the cooperative phenotype. According to Sosis' model [20], the differential perception of costs would
stabilize costly signals even for one-shot interactions (i.e. free-riders would perceive those as too costly).
In the current study, we test the relationship between the presence of a cooperative phenotype,
willingness to send costly signals to assort with other cooperators, and the resulting level of withingroup
cooperation. Hailing from the strategic choice model [4] and Roberts' [50] and Sosis' [20]
extensions of this model, we test four primary hypotheses. First, we test whether participants high on
the cooperative phenotype would elect to reveal their hidden cooperative phenotype by sacrificing a
substantial part of their resources to reliably signal their commitment to the group (HI). Second, we
assess whether participants low on the cooperative phenotype would perceive this signal as too costly
and refuse to send the signal (H2). Third, we investigate whether revealing the hidden cooperative
phenotype positively correlates with the quality of the phenotype. That is, we examine whether
participants who chose to send the costly signal would adhere to cooperative norms and contribute
more to the common pool in P G G compared with participants who did not send the signal (H3).
Finally, we assess whether the heightened adherence to cooperative norms and mutual assurance
I
I
5 iterations
each iteration starts with 40 CZK
cost at each iteration
Figure 1. Overview of the design. In the first part of the study, participants filled out a survey on demographic variables, trained on
PGG and selected their conditional choices in the pre-experiment PGG to assess their cooperative strategy. Next, they were randomly
assigned to either the low- or high-cost conditions and subsequently selected whether they wanted to play PGG in the revealed or
concealed group. In the second part of the study (approx. a week later), four participants in a given group were endowed with 40
CZK and played five PGG iterations.
through costly ritual signals would stabilize group cooperation such that individuals i n groups with
costly signals would earn larger monetary rewards compared with groups without signals (H4). (See
§2.5 for two additional assumption checks regarding the presence of a conflict of interest and forcing
uncommitted individualists to pay the signalling cost.)
To test these hypotheses, we designed a between-subjects study where we first obtained behavioural
data on the expression of the cooperative phenotype using an economic game designed by Fischbacher,
Gachter and Fehr (henceforth FGF) [52]. This procedure allowed us to categorize participants into three
types related to their cooperative strategy (selfish, tempted and cooperative). Next, participants were
randomly assigned to either a high-cost or low-cost condition. In both conditions, participants chose
whether to sacrifice part of their monetary endowment to play an iterated P G G in a group with other
costly signallers (the 'revealed' group) or whether to keep the total endowment and play an iterated
P G G with other players who decided to 'conceal' their phenotype. The description of both groups
stipulated that members of the group are expected to contribute as much as possible to the common
pool (a group norm). Choosing the revealed group i n the high-cost condition was associated with
sacrificing 15% of the monetary endowment before each P G G iteration to signal a commitment to this
norm, while only 2.5% of the endowment was sacrificed i n the low-cost condition (figure 1 for a
graphical overview of the design). We expected that our four main hypotheses would be supported
only in the high-cost scenario, pointing to the causal role of costly signals.
Before data collection, we surmised that if our results would not support H 1 - H 4 (i.e. no difference
between the revealed and concealed groups in the high-cost condition), it would suggest that the
effects of costly signals may be observed only in the context of group competition, which heightens
the need for within-group cooperation [53,54]. Alternatively detecting a difference between the
revealed and concealed groups i n both the high- and low-cost conditions would mean that even low
costs are sufficient to stabilize cooperation and that the CST needs to further investigate humanspecific
psychology [55]. We further assumed that if H I would not be supported, but H3-H4 would
be supported, then we would conclude that the assortment of cooperators does not depend on the
cooperative phenotype, and costly action is a method to induce cooperation in others by making one's
choices visible [56]. Likewise, not supporting H 2 but supporting H3-H4 would indicate that the
cooperative phenotype does not affect the perception of costs (per Sosis' model [20]). Conversely if
H1-H2 would be supported, but H3-H4 would not be supported, we presumed that the cooperative
phenotype might successfully separate signallers from non-signallers, but signals are not strong
enough to stabilize cooperation above the baseline levels. For more details, see table 1.
A pilot study testing the feasibility of this approach with hypothetical P G G scenarios and high costs
revealed that higher scores on a cooperative phenotype scale positively predicted the probability of
sending the costly signal (HI). In comparison, lower scores on this scale predicted the probability of
Table 1. Overview of planned analysis and interpretation.
(HI) hypothesis
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analytical
model
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The positive difference between selfish individuals and cooperators in the probability of choosing
the revealed group would be larger in the high-cost relative to the low-cost condition. We
remain agnostic about comparisons of selfish individuals with tempted individuals.
y, ~ Binomial(/?,, pi)
logWP/) = a
+ fi\ I! versus HC] + PlU versus TC] + versus; 5F] + * TC] ' Ps Hi • SF]
/i is individuals' (/') choice of the revealed group (/?,- = 1 since there is only one choice), p, is the
probability of choosing the revealed group, a is a fixed intercept, and $ is the parameter
for the effect of comparison between the low-cost and high-cost conditions for conditional
cooperators. fi2 and yS3 are the parameters for the effect of comparison between the
conditional cooperators and tempted individuals and between the conditional cooperators and
individuals with selfish strategy, respectively, in the low-cost condition. yS4 and fi5 are the
interaction terms comparing the effects of the three cooperative strategies between
conditions.
R model:
glm(group ~ coopjype * condition, family = 'binomial')
Pilot data suggest a semi-separating equilibrium whereby some cooperators may choose to hide
their phenotype. If no substantial effect would be detected, we would investigate whether
the separation process was convoluted by cooperators choosing the concealed group or by
selfish individuals choosing the revealed group. In combination with support for H3-H4, we
could conclude that the assortment of cooperators does not depend on the cooperative
phenotype, and costly action is a method to induce cooperation in others by making one's
choices visible.
The negative difference between individuals playing selfish and cooperative strategies in the
probability of stating that the costs in the revealed group were too high/unreasonable would
be larger in the high-cost relative to the low-cost condition. We remain agnostic about
comparisons of selfish strategies with tempted strategies.
y, ~ Binomial (/?/,/?,•)
logWP/) = a
+ A [ Z C versus HC] + fi> (( versus TC] + Pi[CC versus SF] ~ A « C « TC] + PbHC *SF]
y, is whether (= 1) or not (= 0) individuals (/') mention that costs are too high/unreasonable in
the revealed group (/?,• = 1 since there is only one choice), p, is the probability of mentioning
high costs, a is a fixed intercept, and $ is the parameter for the effect of comparison
between the low-cost and high-cost conditions for conditional cooperators. fi2 and yS3 are the
parameters for the effect of comparison between the conditional cooperators and tempted
individuals and between the conditional cooperators and individuals with selfish strategy,
respectively, in the low-cost condition. yS4 and fi5 are the interaction terms comparing the
effects of the three cooperative strategies between conditions.
R model:
glm(high_cost ~ contribution x condition, family = 'binomial')
If cooperators would separate based on their hidden phenotype, but individuals playing selfish
strategy would not be deterred by cost in the high-cost condition, we would interpret this
finding as possibly unconscious motivation for joining either of the two groups and reanalyse
the free-list data regarding the reasons for choosing the group. In combination with
support for H3-H4, we would conclude that the cooperative phenotype does not affect the
perception of costs.
(H3) hypothesis The positive difference between participants in the concealed group and participants in the
revealed group in the portion of their endowment contributed to the common pool would be
smaller in the low-cost compared with the high-cost condition.
analytical yri ~ 4>)
m d e l
'Ogi^/) <* 7 ^[mWl - versus IQ ~ & J C A ! versusM.Z..^MC
.'M
yri is the proportion of endowment contributed in PGG iteration r by an individual /'. a is a fixed
intercept, t»[m ( ,)] is a varying intercept for individual participants across multiple measures (m).
fii is the parameter for the effect of comparison between the low-cost and high-cost
conditions for the concealed group. f52 is the parameter for the effect of comparison between
the concealed and revealed groups in the low-cost condition. /?3 is the interaction term
between condition and group. The parameters of the assumed beta distribution comprise p,
representing location (i.e. proportion of send to kept endowment), and <f> denotes dispersion.
R model:
glmmTMB(proportion_contributed ~ group x condition + (1|ID), family = 'beta_family') If the
data would contain >1/3 of zeros and ones, we would also fit a zero-or-one inflated beta
(ZOIB) model.
interpretation If the 95% CIs for the interaction term would include zero and the assumed separation process
functional, we would investigate in a follow-up study whether this is due to the signal being
non-functional (no difference between the revealed and concealed groups) or the functional
assortment of cooperators in the low-cost condition. If the former would be true, we would
continue our investigation by designing an experimental procedure where two groups would
compete against each other (following the suggestion that costly signalling intensifies during
between-group conflict).
(H4) hypothesis Participants in the revealed group would earn more than participants in the concealed group in
the high-cost condition. This difference would not apply to the low-cost condition.
analytical y, ~ Poisson(A,)
model log(Ay) = a + P M M M H C ] + /32[CN versus RV] + PI\HC*RV]
XJ is the expected earned amount after five iterations by an individual /'. a is a fixed intercept.
fii is the parameter for the effect of comparison between the low-cost and high-cost
conditions for the concealed group. f52 is the parameter for the effect of comparison between
the concealed and revealed groups in the low-cost condition. yS3 is the interaction term
between condition and group.
R model:
glmmTMB (earned ~ group x condition, family = 'poisson') If the Poisson model would reveal
overdispersion, we would fit a negative binomial model instead. If the residuals would be
distributed normally, we would also fit an OLS model.
interpretation If the 95% CIs for the interaction term would include zero and the assumed separation process
functional, we would investigate the trends in earnings over individual iterations to estimate
how many iterations would be needed to support H4. If no trends would be detected, we
would proceed in the same steps as in the case of not supported H3.
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mentioning that the cost of the signal is too high (H2). Notably, participants who chose to send the costly
signal reported that they would send a higher portion of their remaining endowment to the common
pool in a hypothetical one-shot P G G (H3). However, comparing the hypothetical earnings between
the revealed and concealed groups indicated no substantial difference in their earnings (H4 not
supported). See §2.5. While generally supportive of the proposed framework, these results need to be
bolstered by an actual behavioural study on a high-powered sample, by an iterated P G G that better
reflects the dynamics of real-world collective action where cooperative interactions between specific
individuals are often repeated [57] and by manipulation of the costliness of the signal.
2. Methods
2.1. Ethics information
This study was approved by the Ethics Committee for Research at Masaryk University. Participants
provided informed consent and received at minimum 50 C Z K (1.7 GBP) as a show-up fee plus any
amount they earned in PGG.
2.2. Design
The study used a between-subjects and double-blinded design. Research assistants and participants were
blind to our hypotheses. However, note that we did not use deception, and participants knew that they
self-selected into one of the two groups. We offered participation i n this study to students from the
subject pool at Masaryk University, Czech Republic.
2.2.1. First part of the study (individual)
If interested, participants were first asked to fill out an online survey including basic demographic
information (age, sex, economic status; note that we did not plan to use these variables i n our preregistered
analyses due to the homogeneity of our population, but they may be used for further
exploration). Next, participants read instructions on playing a one-shot P G G with the following
parameters: an initial endowment of 100 C Z K , anonymously invested in an interval of 5 C Z K
simultaneously with the other three participants). The sum in the common pool was doubled, and the
earnings equally distributed among the players. Participants were provided with three examples of
how the game could evolve to affect players' earnings. We asked participants to fill out a fourth
hypothetical scenario to test their understanding of P G G rules. If they failed to pass the
understanding check, the rules of the game were explained again, and participants were offered to
answer once more. If they failed the second understanding check, they were not invited to participate
in the second portion of the study (but paid the show-up fee).
After passing the understanding check, participants were asked to make unconditional and
conditional decisions i n a one-shot P G G per the FGF [52] procedure. Specifically, participants made
one decision on contributing to P G G out of 100 C Z K endowment (in an interval of 5 C Z K ) without
knowing how much the other three players contributed (unconditional). Then, participants made 21
conditional decisions based on the average contribution of the other three players (rounded to the
nearest multiple of five; i.e. for an average contribution of 0, 5, 10... 100). After the end of the first
part of the study, participants were randomly paired with three other players, and one participant
from each group was randomly selected as the relevant person for the conditional decision. P G G payoffs
were calculated based on the unconditional contributions of the remaining three players and the
respective conditional contribution of the selected player. A s such, participants were motivated to
make genuine decisions because these decisions impacted their earnings. The earnings were known to
participants and paid only after the second part of the study. For more details, see FGF [52]. Using
the conditional choices, we categorized participants into three different cooperative strategies that we
assumed reflect their hidden cooperative phenotype (see below). For the complete survey, see
materials at the Open Science Framework (OSF) repository.
After making their choices in the FGF procedure, participants were introduced to the second part of
the study conducted approximately one week later. Specifically, participants were told that they will be
endowed with 40 C Z K and play P G G simultaneously with three other individuals. Participants were
informed that they will decide how much of their endowment to send into the common pool while
not knowing how much the others will send. After making individual contributions, money i n the
common pool will be multiplied by two and evenly distributed among the four group members,
irrespective of their contributions. Next, they were told that they will again receive 40 C Z K and play
the second round of P G G with the same group members and likewise in the third, fourth and fifth
round of P G G .
Crucially, participants were presented with a choice of two groups for the actual P G G play in the
second portion of the study (participants played all five iterations in the same group of their choice).
We call these groups a 'revealed' group and a 'concealed' group; however, participants decided
between Groups X and Y.
The instructions for the X group (the 'concealed' group) were as follows:
In Group X, money invested into the common pool is multiplied by two and equally distributed among group
members. It is expected that every member should contribute as much as possible to the common pool to
increase the welfare of all group members; however, all contributions are anonymous. Choosing this group is
not associated with a cost, and it is not necessary to demonstrate intentions regarding the size of the
contribution to the common pool.
The instructions for the Y group in the high-cost condition (the 'revealed' group) were as follows:
In Group Y, money invested into the common pool is multiplied by two and equally distributed among
group members. It is expected that every member should contribute as much as possible to the common
pool to increase the welfare of all group members; however, all contributions are anonymous. Choosing
this group is associated with a monetary cost that no one will benefit from. Specifically members of this
group will sacrifice 15% [or 2.5% i n the low-cost condition] of their endowment before each P G G round
(6 C Z K [1 C Z K i n low-cost]) to demonstrate their intentions regarding the size of the contribution to the
common pool.
The order of the group presentation (X or Y first) was randomized. Upon choosing either the Y or X
group, participants were prompted to provide a short rationale for choosing their group and invited
to participate in the second part of the study one week later. Participants were invited to the second
part of the study i n groups of four to interact with members of the same group (revealed or
concealed). We invited participants in such a way as to approximately balance the number of women
and men for each condition.
2.2.2. Second part of the study (group interaction)
For the second part, we invited at least one extra participant for each session to ensure that each session
had four participants. If not needed, these extra participants were paid a show-up fee of 100 C Z K plus
any earning from the FGF played online before the experiment. If we had fewer than four participants in
one session, we did not run the session. Upon joining the online testing session, participants were
welcomed by a research assistant through a virtual chat platform, individually read an informed
consent and reminded of the rules of P G G specific for their group.
Next, participants were introduced to a software (oTree) programmed to facilitate the multi-player
iterated P G G . On a computer screen, they saw their actual earnings, and for each P G G iteration, they
inputted the percentage of their endowment they wanted to contribute to the common pool. After each
PGG iteration, the software summed all players' contributions, multiplied them by two, and equally
distributed this product between the group members, updating their earnings. Specifically, i n the
high-cost condition, participants in both groups started each P G G round with an initial endowment
of 40 C Z K (approx. 1.3 GBP), and participants i n the revealed group immediately lost 15% of their
endowment, i.e. 6 C Z K . Using their remaining endowment, participants i n both groups made first
iteration P G G decisions and learned about others players' contributions and their current earnings.
Before the second P G G round, each participant in the revealed group again lost 6 C Z K from their 40
C Z K endowment for the second round, and the same procedure was repeated for the third, fourth
and fifth P G G iteration (after each iteration the participant would see other players' anonymous
contributions). Upon finishing the gameplay, participants were paid out their earned sum after five
iterations plus a show-up fee and earnings from FGF. The maximum earning for full cooperation in
the revealed group was set at 408 C Z K , while for the concealed group at 480 C Z K in the high-cost
condition. The maximum earning for playing the selfish strategy while the other three players
would unconditionally cooperate was set at 425 C Z K i n the revealed group and 500 C Z K i n the
concealed group.
In the low-cost condition, this procedure was identical except that participants chose between a
concealed group without any signal and a revealed group that would sacrifice 2.5% of their
endowment, that is, 1 C Z K . The maximum earning for full cooperation in the revealed group was set
at 468 C Z K , while for the concealed group at 480 C Z K . The maximum earning for playing the selfish
strategy while the other three players would unconditionally cooperate was set at 488 C Z K i n the
revealed group and 500 C Z K in the concealed group (see OSF materials for these calculations).
2.3. Sampling
Participants were recruited from a student participant pool at Masaryk University, Czech Republic.
Expectedly sampling from this pool in our previous studies [46,47] revealed a young (mean age = 24)
and secular sample where the modal answer on religiosity was 'not religious', and the modal answer
on ritual participation was 'never/not often'. Hence, testing our hypotheses on a population largely
unengaged with costly religious signals should present a strong test of our hypothesis.
For both conditions, we invited participants separately for the revealed- and concealed-group
sessions to balance the ratio between the revealed and concealed groups and the ratio of women and
men i n each group. We planned to recruit 160 participants for each condition: approximately 80 per
group and four per session (for a grand total of 320 participants). Participants who filled out the first
portion of the study but did not take part i n the second part of the study were paid a show-up fee
and FGF earnings. The planned sample size was based on the cost/benefit ratio of power analyses for
our four hypotheses.
To assess the expected power of the main planned statistical tests for H1-H4, we specified three
estimated effect sizes for the interaction between cooperative strategy and condition (H1-H2) and for
the interaction between chosen group and condition (H3-H4). Specifically for each hypothesis, we
expected no effects of the main predictors (strategy/group) i n the low-cost condition and varied the
effect sizes for the high-cost condition based on pilot data and theoretical expectations (see electronic
supplementary material, figure SI for expected effects). Next, we used the command powerSim from
the simr package [58] i n R to simulate the planned statistical models for various sample sizes, simr
uses Monte Carlo simulation with pre-specified effect size and variance explained by varying
intercepts (and other relevant parameters for other distributions) to re-fit the planned statistical model
a specified number of times, assessing the binomial ratio of models with significant/non-significant
results (at significance level a = 0.05). We used 1000 Monte Carlo simulations to simulate the expected
differences i n slopes between conditions for each hypothesis for sample sizes ranging from 40 per
condition to 240 per condition (in the steps of 20). The results of these simulations (with 95% CIs) are
plotted in electronic supplementary material, figure SI, suggesting that 160 participants per condition
should allow us to detect moderate effect sizes of the specific interactions with greater than 80%
power for all four hypotheses.
Since most of the questionnaire data were collected online, we did not expect missing data. Since our
primary outcome and predictor variables are bounded, we did not expect to detect any outliers, and we
used appropriate statistical techniques to account for participants scoring on the boundaries of possible
data distribution (see Analysis). Finally, we planned to exclude participants who did not pass an
understanding check (specified above) but this was not the case for any participant in the second
round. Likewise, we planned to screen participants' reasons for choosing either of the groups and
exclude those whose responses indicating a misunderstanding of the group definitions. We did not
exclude any participant on this basis. There were no additional exclusion criteria.
2.4. Analysis
Analyses were conducted in R [59] (R version for the presented analyses: 3.6.3). First, we categorized
participants into three cooperative strategies based on their play of the FGF version of P G G . Namely,
participants playing a cooperative strategy (corresponding to the cooperative phenotype), tempted
individuals (cooperate if the temptation to free-ride is low but free-ride if benefits are high), and
individuals playing a selfish strategy (always free-ride). To this end, we fitted a finite mixture model
to our FGF data using the function flexmix from the flexmix package [60]. This function estimates
distributional parameters for each of the three cooperative strategies and then classifies participants
into one of those strategies (for an example, see Chen & Fischbacher [61]). We also coded participants'
responses to the open question on the reasons for choosing their particular group, searching for words
such as 'waste', 'loss' or 'unnecessary' concerning the signal cost, which would indicate that the signal
was perceived as too costly (see electronic supplementary material, section S2.2 for examples from the
pilot data). Two independent coders blind to our hypotheses coded participants' answers with 87%
agreement. The first author of this study arbitrated the 13% of responses on which the two coders did
not agree.
To analyse the mean contribution to the common pool in each PGG, we first calculated the percentage
contributed to the common pool from the remaining endowment, accounting for various costs between
groups and conditions and the fact that there was a limit on the minimum and maximum contribution.
The overall earning in P G G for each participant was calculated as a sum of individual earnings in every
PGG iteration.
Next, we tested our hypotheses using a generalized linear mixed model (GLMM) framework,
accounting for the specific data-generation process and hierarchical structure tailored to each
hypothesis. The first hypothesis was assessed using logistic regression with the probability of
choosing the revealed group as the outcome variable, and cooperative strategy (selfish versus tempted
versus cooperators) interacted with condition (low-cost versus high-cost) as the predictor variables.
The second hypothesis was assessed using a binomial regression where the outcome variable was the
probability of mentioning that costs were too high in the revealed group. The predictors comprised
cooperative strategies (selfish versus tempted versus cooperators) interacted with condition (high-cost
versus low-cost). The third hypothesis was planned to be assessed using a beta regression to account
for the typical structure of percentage data [62,63], where the proportion of the endowment
contributed to the common pool across the five P G G iterations would comprise the outcome variable
and group (concealed versus revealed) interacted with condition (low-cost versus high-cost) the main
predictor variable. However, we also planned that if more than 1/3 of the P G G contributions would
contain 0 or 1, we would fit a zero-or-one-inflated beta model. Since this was the case (see Results),
we fitted the zero-or-one inflated beta (ZOIB) model using the gamlss package [64]. We adjusted the
model estimates for the fact that individuals were nested within the five P G G iterations. Finally, H4
was assessed b y a structurally similar model as H 3 ; only the dependent variable was the sum
individual earnings in C Z K after all five P G G iterations. We planned to use Poisson regression to
account for the fact that our data were bounded by minimum and maximum earnings. However, we
also planned that if the Poisson model would display overdispersion (as suggested by pilot data), we
would opt for a negative binomial model instead and that if the data would be approximately
normally distributed, we would consider using an ordinary least-square regression (OLS) for a more
straightforward result presentation. A s we detected overdispersion, we fitted a negative binomial
model. A detailed overview of the statistical tests assessing each hypothesis can be found in table 1
and the electronic supplementary material, R code.
2.5. Pilot data
To assess the feasibility of the planned procedure, we conducted two online pilot studies (henceforth
Pilot 1 and Pilot 2) with the Czech student population. Participants for the pilot studies were
recruited through advertisement at various student groups on Facebook and asked for help testing a
new study. N o compensation was offered for participation. For Pilot 1, we recruited 89 participants
(63 women; M a g e = 23.9) and for Pilot 2, we recruited 91 participants (68 women; M a g e = 24.5).
2.5.1. Pilot design
Since this is was an online study, we assessed the cooperative phenotype using a cooperative values scale
adapted from Peysakhovich et al. [1] rather than the cooperative strategy planned for the actual
experiment (see electronic supplementary material, section S2.1 for the specific items and reliability
analysis). Note that we did not plan to use this scale as a predictor in the actual experiment. Next, we
explained the rules of P G G and tested participants' understanding of the P G G rules (see §2.2).
Participants who failed the second understanding check were excluded from the analysis (three
participants in Pilot 1 and five participants in Pilot 2). We also excluded participants who did not
finish the survey (three participants in Pilot 2), and one participant who reported being 96 years old.
After explaining the rules of P G G , participants were asked to imagine three hypothetical P G G
scenarios played with three other players:
2.5.1.1. First scenario
In the first scenario, participants were asked to imagine receiving an endowment of 200 C Z K and playing
one-shot P G G as the last player, that is, after knowing how much other hypothetical players contributed
to the common pool. This scenario aimed to test an assumption of the signalling theory that people vary
in cooperative affordances (conditional cooperators versus selfish individuals). That is, we tested
Assumption Check 1 (AC1), stating that selfish individuals often defect collective action for personal
benefits while conditional cooperators mainly contribute to collective action for their mutual benefit.
We varied the contributions of other hypothetical players such that the remaining three players
concealed revealed
1 2 3 4 5 1 2 3 4 5 1 2 3 4 5
cooperative values cooperative values cooperative values
concealed revealed concealed revealed 2 3
group group scenario
Figure 2. Overview of pilot data. Reporting higher cooperative values increased reported contributions to the common pool in PGG
Scenario 1 (a) as well as increased the probability of choosing the revealed group (b). Lower reported cooperative values positively
predicted mentioning costly entrance fee in the revealed group as too high (c). Participants in the revealed group reported that they
would send a higher percentage of their endowment to the common pool in PGG Scenario 2 (d), but this would not lead to higher
earnings (e). Finally, forcing participants in the concealed group to make the costly signal would decrease their earnings (f). Black
lines are regression estimates with 95% CIs. Figures d-f also contain density plots for the respective comparisons.
contributed either their entire endowment (i.e. 200 CZK), part of their endowment (80 CZK), or variable
sums (200, 0 and 20 CZK).
2.5.1.2. Second scenario
In the second scenario, participants were presented with two hypothetical groups they could join for yet
another P G G in which they would again receive 200 C Z K endowment and contribute simultaneously
with the other three players to the common pool. These hypothetical groups afforded either to reveal
participants' commitment to contribute to the common pool at a cost (20% of their endowment in
Pilot 1 and 10% of their endowment in Pilot 2) or to save the money and play in a group that
conceals intentions (see §2.2 for definitions of the two groups). Given the assumed variation of the
cooperative phenotype in the population [1,65], we expected that participants would self-select
roughly 50/50 in the concealed and revealed groups (Assumption Check 2; AC2). After choosing
either of the two groups, we asked participants how much they would contribute to the common
pool and to give a reason for choosing the specific group, testing H1-H4.
2.5.1.3. Third scenario
Finally to test another assumption of the signalling model in these hypothetical scenarios, we included a
third scenario in Pilot 1 where we asked participants who played in the revealed group to imagine
playing in the concealed group and vice versa. The purpose of this manipulation was to examine
whether the costly signal would indeed be too costly for the uncommitted individualists,
hypothetically present in the concealed group. Thus, the third Assumption Check (AC3) stated that
participants who chose the concealed group in the second P G G scenario should earn less when forced
to signal norm commitment in the revealed group in the third P G G scenario. The results of the pilot
test are described in verbatim below and plotted in figure 2. Note that we used G L M M in the pilotdata
analysis analogically to models in table 1 (see also electronic supplementary material, R code).
2.5.2. Pilot results
The results of the first P G G scenario collapsed across both pilots, and three contribution schemas suggest
that participants scoring higher on the cooperative values scale reported that they would contribute a
larger portion of their endowment to the common pool (/J=0.40, 95% CI = [0.11, 0.69]; supporting
AC1). Scoring 'one' on the cooperative values scale was associated with a reported contribution of
30% of the endowment, while scoring 'five' was predicted to yield contributions at 68% of the
endowment. Furthermore, signalling strategies were roughly equally represented (n revealed = 94,
n concealed = 74; supporting AC2), and higher scores on the cooperative values scales positively
predicted the probability of choosing the revealed group (supporting HI), albeit this effect was not
precise and 95% CIs contained zero (0=0.27, 95% CI = [-0.20, 0.74]). The lowest score on the
cooperative values scale predicted a 41% probability of choosing the revealed group, while the
maximum score was associated with 67% probability. This imperfect separation is further explored in
the electronic supplementary material, section S2.3. Supporting H2, higher scores on the cooperative
values scale negatively predicted the probability of mentioning that the cost of the revealed group
was too high (J3= -1.24, 95% CI = [-2.04, -0.44]) when prompted to explain why they chose to play in
the concealed group (estimated 68% probability for cooperative values score of 'one').
Participants in the concealed group reported that they would contribute a smaller proportion of their
remaining endowment compared with participants in the revealed group (60% versus 72%), supporting
H3 (yS = 0.52, 95% CI = [0.14, 0.90]). However, when assessing how much players in each group would
earn after summing contributions in hypothetical sessions with other players, overall estimated
earnings were higher in the concealed (315) compared with the revealed (302) group (/?=-0.04, 95%
CI = [-0.10, 0.02]). While this result does not support H4, the difference between groups was not
precisely estimated, and we expected that using real monetary incentives in iterated P G G would
support H4 (there would be a steady decline in mean contributions in the concealed group as more
members choose to free-ride in subsequent iterations, as shown by other P G G experiments [66]).
Finally, we compared the potential earnings of participants who chose the concealed group in the
second scenario with their hypothetical earnings in the third scenario, where they were forced to play
in the other group. Participants in the concealed group would, on average, earn less in the third
scenario (321 versus 257), supporting A C 3 (0 = -0.22, 95% CI = [-0.28, -0.16]). Further details on the
pilot procedures and additional analyses are reported in the electronic supplementary material.
3. Results
3.1. Classification of cooperative strategies
To account for dropouts between the two stages of the study and have sufficient substitutes, we initially
recruited 458 participants for the first phase of the study who were randomly assigned to the high-cost
and low-cost conditions. From this pool of participants, 372 (197 women; 1 non-binary; M a g e = 23.6,
s.d.a g e = 3.1) finished the first phase and were interested in taking part in the second phase of the
study (we aimed for a final sample of 320 participants, 80 per each combination of group and
condition). Of the 372 participants, 90 participants chose the revealed group and 99 participants chose
the concealed group in the high-cost condition. In the low-cost condition, 122 participants chose the
revealed group and 61 participants chose the concealed group.
We classified participants into three different cooperative types based on the strategies they played in
the FGF version of P G G : cooperators, tempted cooperators and individuals playing a selfish strategy
(figure 3). We assumed that these strategies should approximate the underlying cooperative
phenotype. The model classified 171 participants as cooperators, 107 as tempted cooperators and 94
as playing selfishly. The ratio of prior and posterior probabilities for all three categories was greater
than 0.994, suggesting a non-overlapping classification of participants [60].
3.2. Choosing the revealed group (H1)
We used this classification to predict the selection of concealed and revealed groups in the high- and lowcost
conditions, hypothesizing that individuals playing selfishly will be less likely to choose the revealed
group in the high-cost condition. The results of our binomial regression model lent support to this
hypothesis, showing that compared with cooperative behaviour, selfish behaviour in the conditional
P G G was associated with a lower probability of choosing the revealed group in the high-cost condition
(j5= -1.05, 95% CI= [-1.78, -0.32]). As predicted, this difference was smaller in the low-cost condition,
although the 95% confidence intervals of this interaction included zero (interaction = 0.80, 95% CI = [-0.25,
1.85]). Since most of the probability mass was positive, we interpret this difference as a preliminary
support for H I . Looking at the high-cost condition, cooperators had a 57% chance of choosing the
revealed group while this probability dropped to 46% for tempted cooperators and only to 32% for
H cooperators (46%) H tempted (29%) H selfish (25%)
0 25 50 75 100
others' average contribution
Figure 3. Classification of participants into three cooperative strategies. The thick lines plot the predicted values for each of the
cooperative strategies, while the thin lines represent raw data colour-coded based on the specific strategies. We used a cubic spline
interpolation on the raw data for easier visual reading.
Table 2. Beta-estimates from logistic regressions with 95% CI from testing hypothesis 1 (probability of selecting the revealed
group) and hypothesis 2 (probability of mentioning high costs). The reference category is 'cooperators' for the strategy factor and
'high cost' for the condition factor. The estimates are logged odds.
hypothesis 1 hypothesis 2
intercept 0.29 -1.89
(-0.13, 0.71) (-2.53, -1.26)
strategy: tempted -0.45 -0.05
(-1.15, 0.24) (-1.12, 1.01)
strategy: selfish -1.05 1.07
(-1.78, -0.32) (0.17, 1.96)
condition: low-cost 0.42 0.23
(-0.21, 1.04) (-0.65, 1.12)
low-cost x tempted 0.60 0.08
(-0.41, 1.61) (-1.37, 1.52)
low-cost x selfish 0.80 -1.44
(-0.25, 1.85) (-2.87, -0.01)
N participants 372 345
individuals with selfish strategy. By contrast, these probabilities were estimated at 67%, 70% and 61% in the
low-cost condition. See table 2 for all estimates, figure 4« for illustration, and electronic supplementary
material, R code for re-analysis of this data using raw conditional contributions for each type as predictors.
3.3. Differential perception of costs (H2)
We further used the classification into cooperative strategies to predict whether participants mentioned
wasted resources when verbally explaining their choice of the group for the second phase. From 345
(a)
1.0
> 0.8
S 0.6
I 0.4
o
" 0.2
OH
0
choosing costly signal (HI)
r t-T
--
(b)
cost -•- high low
c
CD
s
u
OH
selfish cooperative selfish cooperative
strategy strategy
concealed revealed concealed revealed
group group
Figure 4. Estimated means with 95% CI plotted over raw data for the four core hypotheses. The density plots represent the
distribution of raw data for each group/condition combination. Note that the estimated lines in plot) C are from a beta
regression rather than ZOIB regression to include the full spectrum of the data modelled by the mixture of separate regressions
in the main text (table 3). Specifically, in this graph, the 0 and 1 contributions were converted using the formula
(y' = (y(« - 1) + 0.5)//?) where y is the transformed variable and n is the sample size, such that the data could be analysed
with the beta regression (this correction has negligible effects on inference). See electronic supplementary material, R code for
precise estimates from this model.
participants who answered this question, 56 participants mentioned that the signal is a waste of
resources. Using a binomial regression model, we found a difference in mentioning waste between
individuals playing cooperative and selfish strategies in the high-cost condition (5=1.07, 95%
CI = [0.17, 1.96]) and this difference was smaller in the low-cost condition (/Weractkm = -
1 -44, 95%
CI = [-2.87, -0.01]). The estimated probabilities of seeing the costly signal as inefficient were 14% for
cooperators, 13% for tempted and 30% for individuals playing selfishly in the high-cost condition and
16%, 16% and 12% in the low-cost condition. See table 2 for all estimates and figure 4b for illustration.
3.4. Contributions to the common pool (H3)
From 372 participants who proceeded to the second phase of the study, 284 actually participated
(146 women; 1 non-binary; M a g e = 23.5, s.d.a g e = 3.0). The remaining participants were either
substitutes on a given experimental session or did not show up for a session. Note that we succeeded
to collect data from 80 participants in the high-cost concealed group and low-cost revealed group as
planned, but we missed data from four participants in the high-cost revealed group because not
enough participants showed up for an experimental session. Moreover, only 61 participants chose the
concealed group in the low-cost condition, and when accounting for participants who were selected
as substitutes, this group comprised 48 participants instead of 80. Nevertheless, the a priori analysis
plotted in electronic supplementary material, figure SI suggests that 284 participants should be
sufficient to detect the expected effects with 80% power for H3 and 75% power for H4.
Looking at the raw contributions, participants allocated 54% of their remaining endowment on average.
The average allocations were highest in the first round (62%) and lowest in the last round (36%). Figure 5
provides an illustration of raw data. Since 45% of the allocations were either 0% or 100% of the endowment,
we used the zero-or-one inflated beta regression (ZOIB) that allows to infer the probability of contributing
zero or one as well as the size of the mean contribution (for technical details see [67]).
group — concealed • • • revealed cost — high — low
1.00
Table 3. Beta-estimates from GLMM with 95% CI from testing hypotheses 3 (highest contributions in the high-cost revealed
group) and 4 (highest earnings in the high-cost revealed group). Note. The reference category is 'concealed' for the group factor
and 'high cost' for the condition factor. The estimates are untransformed.
hypothesis 3 hypothesis 3 hypothesis 3 hypothesis 4
% sent pr. sending 0 pr. sending 1
intercept -0.23 -0.94 -1.57 5.66
(-0.33, -0.13) (-1.23, -0.64) (-1.92, -1.23) (5.62, 5.67)
group: revealed 0.55 -1.44 1.02 -0.003
(0.40, 0.69) (-1.96, -0.93) (0.57, 1.46) (-0.06, 0.06)
condition: low-cost -0.02 -0.63 -0.71 -0.01
(-0.18, 0.13) (-1.11, -0.15) (-1.29, -0.13) (-0.08, 0.06)
low cost x revealed -0.21 0.93 0.31 0.10
(-0.42, 0.004) (0.19, 1.68) (-0.39, 1.02) (0.004, 0.19)
N participants 284 284 284 284
For average contributions excluding zeros and ones across the five rounds of PGG, the model showed
that participants i n the high-cost revealed group contributed larger portions of their endowment
compared with participants i n the high-cost concealed group (J3= 0.55, 95% CI = [0.40, 0.69]). This
difference was smaller i n the low-cost condition (Afteraction = -0.21, 95% CI = [-0.42, 0.004]).
Furthermore, the parameter modelling the probability of contributing zero was smaller i n the highcost
revealed group compared with the high-cost concealed group (/?= -1.44, 95% CI = [-1.96, -0.93])
and this difference was again smaller in the low-cost condition (Afteraction = 0-93, 95% CI = [0.19, 1.68]).
The estimated probabilities of contributing zero were 6% for the high-cost revealed group, 25% for the
high-cost concealed group, 8% for the low-cost revealed group, and 16% for the low-cost concealed
group. Finally, the parameter modelling the probability of contributing the full remaining endowment
(conditioned on the probability of contributing zero) was higher in the high-cost revealed group
compared with the high-cost concealed group (fi= 1.02, 95% CI= [0.57, 1.46]). However, this difference
was larger, albeit not reliable, in the low-cost condition (Ainteraction = 0.31, 95% CI = [-0.39, 1.02]). While
the probability of sending everything was the highest in the high-cost revealed group (34% compared
with 26% i n the low-cost revealed group), it was low i n the low-cost concealed group (8% compared
with 13% in the high-cost concealed group). Refer to table 3 for all estimates and figure 4c for illustration.
3.5. PGG earnings (H4)
For our final hypothesis test, we compared participants' earnings across conditions. Participants, on
average, earned 294 C Z K in P G G . Using a negative binomial regression to model count data (Poisson
distribution was disqualified due to overdispersion), we found that contra our predictions there was
no difference in earnings between the high-cost revealed group and the high-cost concealed group
(J3= -0.003, 95% CI =[-0.06, 0.06]). However, a larger difference was detected in the low-cost
condition ( / W a c t i o n = 0.10, 95% CI = [0.004, 0.19]). Refer to table 3 for all estimates and figure 4d for
illustration.
4. Discussion
In this registered report, we investigated whether participants with 'a cooperative phenotype' [1] (as
indexed by a cooperative strategy in conditional PGG) would choose to reveal the quality of their
phenotype using a costly signal and whether this signal would be associated with contributions to a
group cooperative effort. Furthermore, we examined whether this relationship would hold only in the
case of a highly costly signal. We found that the groups with costly signals mostly deterred
participants with selfish strategies and that costlier signals were more effective (HI). However, the
contrast in signal cost was not reliably estimated and needs further testing. We also found that
participants with selfish intentions were more likely to mention unreasonable costs as a reason for not
choosing the revealed group, and this probability increased with increasing signal cost (H2).
Furthermore, groups with costly signals contributed larger portions of their remaining endowments to
the common pool compared with the concealed groups, and these differences increased with
increasing signal costs (H3). However, these larger contributions in the high-cost revealed group did
not translate into larger earnings (H4). In summary, the results provide general support for the
positive effects of costly signals on assorting cooperators and subsequent cooperation in a joint
cooperative task but suggest that frequent high costs would not be evolutionarily stable. There are
several important caveats to this conclusion that warrant discussion.
Whereas the separation mechanism worked rather well in the high-cost condition by driving most of
the individuals playing selfishly into the concealed group and the majority of the cooperators into the
revealed group, the mechanism still allowed for a semi-separating equilibrium where participants
playing a selfish strategy chose the revealed group. Even more importantly, high cost deterred many
cooperators from choosing the revealed group, suggesting that while increasing cost may better filter
out selfish strategies, it also filters out many cooperators to the potential detriment of the joint action
(as indicated by the wide 95% CIs of interaction between the group and cost variables in the statistical
model testing HI). This result suggests that the mapping of cooperative phenotype on the costly
signal is not a simple proportional process as envisioned by the strategic choice model [4], at least not
for humans. Humans exhibit substantial communicative flexibility that can be situationally detached
from the underlying phenotype. Hence, applying the strategic choice model to humans necessitates an
amendment of additional parameters covering this flexibility.
One of these parameters should relate to the cost/benefit perception as suggested by Sosis [20]. We
found support for his assertion that the differential perception of the cost size deters individuals playing
selfishly from choosing the revealed group (H2). According to Sosis, this perception is facilitated by the
socialization process whereby individuals regularly partake in costly actions (e.g. collective rituals)
associated with their group's normative system, effectively discounting the perceived costs of future
participation. While our data cannot attest to the role of the socialization process, we speculate that at
least in our study, cooperative phenotype affected not only the perception of costs but also benefits.
That is, rather than differently perceiving costs due to engaging in costly behaviours during the
socialization process, it is the differential perception of potential benefits that affected the assessment
of cost size as appropriate or wasteful. Looking at the pilot data—where we asked participants about
their expected earnings—indicated that participants in the revealed group (compared with the
concealed group) had a higher probability of saying they expect to receive the maximum amount
from full cooperation (/? = 1.55, 95% CI = [0.52, 1.03]). However, this finding may not apply in real life,
where ritual participation does not typically precede any specific cooperative dilemma but rather a
host of cooperative opportunities. In such situations, differential cost perception appears as a more
likely driver of decisions to partake in costly signalling.
Notwithstanding this evidence, a stronger test of Sosis' proposition [20] would be a modification of
our current design into a one-shot P G G . Although free-riders would probably invade the high-cost
revealed group more often in the one-round set-up, showing that the assorting mechanism related to
cost perception is functional, albeit limited, even in such a set-up would provide robust support for
Sosis' proposition [20] (contra to [50]).
Regarding the effects of the separation mechanism on subsequent behaviour in PGG, we observed that
participants in the high-cost revealed group invested the largest proportion of their remaining endowment
(H3). Compared with participants in the low-cost revealed group, the high-cost revealed group also had
lower probability of contributing nothing. Although the high-cost revealed group had the highest
probability of contributing everything to the common pool, the predicted interaction effect between
group and condition was not reliably estimated due to a relatively high probability of contributing
everything in the high-cost concealed group, probably resulting from the large number of participants
who played the cooperative strategy but refused joining the revealed group. While we did not
statistically assess the difference between the revealed and concealed groups in the low-cost condition,
raw data suggests that participants in the low-cost revealed group also invested larger proportions of
their remaining endowment compared with participants in the concealed group. One possible
explanation for this result is that despite a higher probability that a particular session in the low-cost
revealed group would contain individuals playing selfishly the low-cost signal still allowed many
groups to establish a cooperative exchange. Crucially due to a lower signal cost, the relatively successful
assortment of cooperators translated into the highest earnings for this group (contra H4). This result has
a plethora of interesting implications for real-life signalling contexts such as human ritual behaviour.
Since high-cost rituals often involve pain, physical effort and the expenditure of material resources,
they are usually performed only on special occasions during one's lifetime (such as various rites of
passage) or only occasionally during the liturgical year. In our study, the high-cost signal was sent in
each P G G round, which turned out to be counterproductive in terms of the overall earnings. Having
the high cost only during the first P G G round (such as an initiation ritual) or appearing only in some
cyclical intervals would perhaps better simulate the real-world signalling behaviours. Indeed, for
everyday mundane cooperative exchanges, low-cost regular signalling may be sufficient to stabilize a
profitable level of trustworthy interactions. This conclusion is in accord with a signalling study by
Chvaja et al. [68] that contrasted the trustworthiness of foot pilgrims to Santiago de Compostela
(religious pilgrimage) with the trustworthiness resulting from participation in a Christian mass and in
a secular activity. While pilgrims were rated as most trustworthy the difference between pilgrimage
and mass participation was smaller than the difference between mass participation and secular
activity. Rather than a linear effect of cost, the difference between no signal and a low-cost signal is
probably more important than the difference between low-cost and high-cost signal. Furthermore, in
the study of two Indian villages, Power [36,38] showed that regular low-cost signals are more
predictive of reputation for being trustworthy because high-cost signals may sometimes be seen as
means to individual aggrandizement. While this would not be the case in our study because
participants in the low-cost condition did not know about the high-cost condition, a direct comparison
of high- versus low-cost choice could shed light on the perception of high-cost signals.
A preliminary inference from the current results could be that cultural evolutionary processes would
pressure signal costs to be in equilibrium with expected benefits. For example, regular high-cost signals
may be stable only in high-stake contexts such as combats or risky hunts where assorting cooperators
without free-riders would be a crucial factor determining a group's success. In support of this
conjecture, a survey of ethnographies describing ritual practices in 60 small-scale societies [54]
revealed that ritual cost is positively predicted by the frequency of warfare the society experiences.
Whereas the imperfect sorting mechanism in the low-cost condition afforded a profitable level of
cooperative exchange in our study, the presence of free-riders would presumably disintegrate the
group's cooperative effort in high-stake contexts. Our design might be easily modified to test this
prediction by pitting various signalling groups against each other and comparing how the competitive
context affects the workings of the sorting mechanism and subsequent cooperation.
Other important modifications to the design of the current study could alter the currency of signals
and benefits. Signal costs and cooperative benefits are often disassociated in real-life settings such as
costly rituals where signallers may, for example, use suffering and pain as the currency of the signal
while getting helped in the future as the currency of the benefit. To provide a stronger test of CST, we
decided to keep the currency of costs and benefits identical, but it could be speculated that if the cost
would be, for instance, time spent on a boring task, participants in the high-cost revealed group
might earn the most (due to the possibility to turn their endowment into larger investments rather
than waste them as signals). Furthermore, while having the currency of signals and benefits identical
allowed us to assess the role of cooperative phenotype i n signalling within the specific context of
P G G , it could be speculated that cooperative phenotype would manifest differently i n different
cooperative contexts. To indicate this uncertainty we talk about different cooperative strategies specific
to P G G throughout the paper rather than hard-coded cooperative types [cf., [1].
In summary this registered report provides an experimental framework that can be easily amended to
examine particular extensions of CST. In our OSF repository we provide all materials used i n the current
study which can be used to replicate this study in different populations or to extend the protocol in order to
further empirically develop the strategic choice model. Since cooperative communication is the cornerstone
of human group living, understanding factors affecting the reliability of such communication may help us
better appreciate the cooperative peculiarity of humankind.
Ethics. The research was approved by the Research Ethics Committee at Masaryk University.
Data accessibility. Data, materials and analytical code are publicly available at OSF: https://osf.io/vsjcp/. The Stage 1
manuscript associated with this Registered Report was granted in-principle acceptance on 11 June 2021 prior to
data collection and analysis. The accepted Stage 1 manuscript, unchanged from the point of in-principle
acceptance, may be viewed at https://osf.io/c63xk.
The data are provided in electronic supplementary material [69].
Authors' contributions. M . L . : conceptualization, data curation, formal analysis, funding acquisition, investigation,
methodology, project administration, supervision, visualization, writing—original draft, writing—review and
editing; R.C.: conceptualization, data curation, investigation, methodology, project administration; B.G.P.:
conceptualization, methodology, supervision; D.V.: conceptualization, methodology, supervision; R.S.:
conceptualization, investigation, methodology, resources, supervision.
All authors gave final approval for publication and agreed to be held accountable for the work performed therein.
Conflict of interest declaration. The authors declare no competing interests.
Funding. M.L. acknowledges the generous support from the MSCAfellow3@MUNI project [CZ.02.2.69/0.0/0.0/19_074/
0012727].
Acknowledgements. We would like to thank our colleagues at the Department for the Study of Religion and Laboratory for
the Experimental Study of Religion (LEVYNA) at Masaryk University, as well as colleagues at the Department for the
Study of Religion at Aarhus University for helpful feedback during the development of the idea for the current study. We
are grateful to Connor Wood and Dimitris Xygalatas for providing comments on an earlier draft of this registered report
and Adam Kenny and two anonymous reviewers for helpful comments on Stage-1 and Stage-2 manuscripts. We further
thank Jana Zuzaňáková and Katarína Cellárová for help with the preparation of the data-collection procedure, Matěj
Troup for help with data collection and processing, Martin Both and Jana Zuzaňáková for preparation of the datacollection
software, Theiss Bendixen for statistical advice and Markéta Poledníková for help with data processing. We
would also like to thank Petra Koudelková and Dagmar Navrátilová for administrative support.
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