New categories of conditional contribution strategies in the public goods game
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Schäffer, Klaudia; Král, Adrienn; Kun, Ádám Article New categories of conditional contribution strategies in the public goods game Games Provided in Cooperation with: MDPI – Multidisciplinary Digital Publishing Institute, Basel Suggested Citation: Schäffer, Klaudia; Král, Adrienn; Kun, Ádám (2025) : New categories of conditional contribution strategies in the public goods game, Games, ISSN 2073-4336, MDPI, Basel, Vol. 16, Iss. 3, pp. 1-21, https://doi.org/10.3390/g16030022 This Version is available at: https://hdl.handle.net/10419/330136 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may be saved and copied for your personal and scholarly purposes. You are not to copy documents for public or commercial purposes, to exhibit the documents publicly, to make them publicly available on the internet, or to distribute or otherwise use the documents in public. If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by/4.0/
Academic Editor: Ulrich Berger Received: 30 September 2024 Revised: 31 March 2025 Accepted: 16 April 2025 Published: 6 May 2025 Citation: Schäffer, K., Král, A., & Kun, Á. (2025). New Categories of Conditional Contribution Strategies in the Public Goods Game. Games,16(3), 22. https://doi.org/10.3390/ g16030022 Copyright: © 2025 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/ licenses/by/4.0/). Article New Categories of Conditional Contribution Strategies in the Public Goods Game Klaudia Schäffer 1, Adrienn Král 1,2 and Ádám Kun 1,2,3,* 1Department of Plant Systematics, Ecology and Theoretical Biology, Eötvös University, H1117 Budapest, Hungary 2Institute of Evolution, HUN-REN Centre for Ecological Research, H1121 Budapest, Hungary 3Parmenides Center for the Conceptual Foundations of Science, Parmenides Foundation, D82343 Pöcking, Germany *Correspondence: [email protected] Abstract: Human cooperation is ubiquitous and instinctive. We are among the most cooperative species on Earth. Still, research mostly focuses on why we cooperate, instead of understanding why some of us do not do so. The public goods game can be used to map human cooperation as well as to study free riding. We acquired data through an online, unincentivized questionnaire which prompted respondents to choose how much of an initial endowment to contribute to a common pool. The respondents contributed, on average, 54% of their initial endowment to the common pool. The usual categorization scheme of the elicited conditional contribution pattern discerns unconditional free riders who do not contribute irrespective of the contributions of others and calls everyone a conditional cooperator who correlates their contribution with that of the others. However, someone consistently offering less than the others should not be called a cooperator. Consequently, based on the conditional contribution patterns among our respondents, we suggest a recategorization of contribution patterns into the following categories: unconditional cooperator (1.5%), unconditional free rider (10.6%), perfect conditional cooperator (42.6%), hump-shaped contributor (0.7%), V-shaped contributor (0.4%), conditional cooperator (16.6%), conditional free rider (13.6%), conditional contributor (6.4%), negative conditional contributor (0%), and others (7.6%). We only call someone a cooperator if the respondent at least matches others’ contribution, and call everyone consistently offering less a free rider. Furthermore, we found no difference between the contributions of women and men. No correlation of contribution with age, educational attainment, and size of the residential settlement was found. Students’ contributions were not different from non-students’ contributions. We found a significant correlation of the contribution to the common pool with hypercompetitive orientation (negative correlation) and the self-assessed willingness to take risks in general (positive correlation). Keywords: public goods game; public goods; prisoner’s dilemma; tragedy of the commons; strategy method; cooperation; conditional cooperation; free rider; voluntary contribution mechanism 1. Introduction Cooperation is one of the defining characteristics of our species (Bowles & Gintis, 2003;Kaplan et al.,2009;Rand & Nowak,2013). We are still puzzled by this fact and try to understand why. Much ink has been spilled on why to cooperate at all. It stems from the roots of the evolutionary theory, which emphasizes selfishness, and also from Games 2025,16, 22 https://doi.org/10.3390/g16030022
Games 2025,16, 22 2 of 21 the games we model cooperation with. The public goods game (PGG), a formalization of the tragedy of the commons (Hardin,1968), is a commonly employed framework. In this game’s theoretical situation, N individuals independently and simultaneously decide on contributing to a common pool. Contributions come from their initial endowment of, for example, 10,000 monetary units (or other quantifiable resource). Whatever they retain for themselves is theirs. The monetary units in the common pool yield a return proportional to the invested amount. The amount in the common pool is multiplied by r (1 <r≤N ), and the resulting sum is divided equally among the N individuals. A monetary unit retained is still one monetary unit at the end of the day, but a monetary unit contributed to the common pool yields r/N monetary units (mean per capita return, MPCR). However, others’ contributions also yield the same for every other individual. Mutual cooperation, i.e., contribution of the whole initial endowment to the common pool, is the Pareto efficient outcome yielding the highest total payoff to the whole group. If r>N , a contribution is also the individually optimal behavior, but we focus on the case (1 <r≤N ) where there is a social dilemma. In this case, the yield is r/N< 1, and thus every individual can maximize their own payoff by not contributing, hence, no contribution (no cooperation) is the Nash equilibrium of this situation. Still, if human subjects face such a situation, they usually contribute between 40–60% of their initial endowment to the common pool (Ledyard,1995). A one-shot endowment offers some glimpse into why people cooperate. Some of the differences between our tendencies to cooperate have a genetic underpinning (Hiraishi et al.,2015;Mertins et al.,2011;Schroeder et al.,2013). This manifests directly or through other personality traits that influence cooperation (Guilfoos & Kurtz,2017;Schroeder et al.,2015;Volk et al.,2012). There are also extrinsic factors influencing cooperation. Both broad culture and individual economic reality modify cooperative tendencies. One study (Lamba & Mace,2011) argues that it is individual economic realities that determine how much people are willing to contribute to the public good: individuals experiencing economic hardship contribute less. However, culture (cultural norms) can elevate levels of cooperation even in the face of hardship (Ostrom,1990). An individualist worldview increases the prevalence of free-riding, whereas individuals with a more communitarian worldview are more often (conditional) cooperators (Cherry et al.,2017). A larger household reduces the contribution to the public good in India (Kumar & Kant,2016) and in Thailand (Carpenter et al.,2004), but increases it in Vietnam (Carpenter et al.,2004), Colombia, and Kenya (Cardenas et al.,2010). Culture seems to have an effect on cooperation (Gächter et al.,2010). The seminal paper by Herrmann et al. (2008) focused the spotlight on the potential of cultural differences in cooperative behavior. There are cultural comparisons that find some differences (Ahmed & Salas,2009;Cadsby et al.,2007;Carpenter et al.,2004; Chaudhuri et al.,2006;Herrmann et al.,2008;Ishii & Kurzban,2008;Nishi et al.,2017), and there are others that find none (Herrmann et al.,2008;Leibbrandt et al.,2015). On the other hand, there could be differences even within a country (Bigoni et al.,2016;Eckel Catherine, 2015;Kamei,2012). The strategy method (Selten,1967) offers more insight into cooperative behavior. There, experimenters ask participants how much they would contribute to the public good if they knew the average contributions of the other participants. The strategy method is a good estimator of people’s behavior given their beliefs about others’ contributions (Brandts & Charness,2011;Fischbacher et al.,2012). The behavioral types are stable over time (Gächter et al.,2022;Volk et al.,2012) (but see (Andreozzi et al.,2020)). The contribution schedules resulting from the strategy method questions are put into categories. The commonly used ruleset for categorization (Fischbacher et al.,2001) is as follows: •Afree rider is the one who always contributes 0, irrespective of others’ contributions.
Games 2025,16, 22 3 of 21 • Aconditional cooperator is one with a positive and significant (at 1% significance level) Spearman correlation with the investments of others. • Ahump-shaped or triangular (Fischbacher et al.,2012) contribution is the one that increases to about 50% of the others’ contributions; then, the contribution decreases. • If an outcome does not fall into any of the above categories, then it is considered “other” . This categorization, however, was based on a sample of just 44 contribution schedules collected in a single study (Fischbacher et al.,2001). While the definition of free riders and conditional cooperators was exact from the beginning, the definition of hump-shaped cooperators was less clear. Fischbacher et al. (2012) made the definition more precise by also requiring the Spearman correlation to be significant for both the upward trend and the downward trend. Many patterns that have surfaced over the years in other studies cannot be found among those original categories. For example, while hump-shaped cooperators were included, the opposite—someone contributing much in the beginning, reducing their contribution for a while, and then increasing it again (a V-shaped contribution profile)—has not been considered. Such a pattern was reported by (Muller et al.,2008) (1 instance) and (Grandjean et al.,2022) (1 instance). Another new category is that of negative cooperators (Burton-Chellew et al.,2016) or counter-conditional cooperators (Bergantino et al.,2023) who, similarly to conditional cooperators, change their contribution based on the contributions of others, but for whom the correlation is negative, i.e., they contribute much when others do not, and then decrease their contribution. They found 6 (out of 36) (Bergantino et al.,2023) and 2 (out of 72) (Burton-Chellew et al.,2016) subjects exhibiting such patterns. Other experiments have also found examples of such contribution patterns: 2 instances in (Muller et al.,2008), 1 instance in (Kamei,2012), and one or two instances in (Grandjean et al.,2022). Unconditional cooperators as a separate category have been proposed many times (Burton-Chellew et al.,2016;Katušˇcák & Miklánek,2023;Thöni & Volk,2018). It was defined as a non-zero contribution that does not change with others’ contributions. The problem with this definition is that an individual always investing 10% would be labeled as an unconditional cooperator as well as someone always investing the maximum amount. Grandjean et al. (2022) increased the bar slightly. They only considered someone an unconditional cooperator if their mean contribution was above 10% and the contributions were within the 5% standard deviation range from the mean contribution. Still, someone consistently contributing 20% would be called an unconditional cooperator. One study (Rustagi et al.,2010) only considered someone an unconditional cooperator (altruist) if it always contributed the maximum amount. Another study (Bigoni et al.,2019) was a bit more permissive and included in its altruist category anyone who always contributed more than 75%, irrespective of others’ contributions. At the lower bound of unconditionally investing 80%, such individuals would offer more than others with a low-to-medium average investment and would only fall behind others with high investments. As seen above, the established definition of free riders is too restrictive. We speculate on the reason in the discussion. Here, we just mention that people do not generally consider a low investment to be fair (Baumard,2011;Fehr & Schmidt,1999). Some authors allowed 1 monetary unit out of 20 to be contributed over all choices and still considered it to be free-riding (Makowsky et al.,2014;Rustagi et al.,2010). While there can be potentially more individuals categorized as free riders, it still does not solve the problem of consistently low contributions. One study (Grandjean et al.,2022) considered someone a free rider if their contribution was on average below 10%, while another study (Bergantino et al.,2023) used the cutoff value of 20%. Nagatsu et al. (2018), based on the study by (de Oliveira et al., 2015), on the other hand, considered everyone a selfish player whose contribution never
Games 2025,16, 22 4 of 21 exceeded 25%. There is a subtle difference between these two approaches. The definition requiring an average contribution of not more than 10% or 20% also includes a pattern in which all contributions are 0, except when everyone else’s contribution is the maximum amount, in which case this contribution is matched. This can still be considered selfish, but it is different from the case where one always gives 20%. Free riders (Burlando & Guala,2005) and subpar conditional cooperators (Neugebauer et al.,2009) drive repeated cooperation downward. This behavior is selfish, as they contribute less than they expect others to contribute. Lumping most of these together hides important differences between the strategies of individuals. The issue is not really the use of the Spearman correlation vs. the Pearson correlation (Thöni & Volk,2018), the numerical value of the correlation (Grandjean et al.,2022), or the significance level of the said correlation (Rustagi et al.,2010). All contribution patterns in Figure 1have both the Pearson correlation and the Spearman correlation above 0.89, and all are highly significant at p< 0.001. One study (Andreozzi et al.,2020) distinguished between perfect conditional cooperators and imperfect conditional cooperators. Perfect conditional cooperators match others’ contributions exactly, whereas imperfect cooperators include all other conditional cooperators. However, there should be a distinction made between those not matching others’ contributions and those that contribute even more (compare top right and top center in Figure 1and bottom left and center with bottom right). Burlando and Guala (2005) defined conditional cooperation as that where “conditional contribution functions approximate the ‘perfect reciprocation function’, with a margin of variation of ± 10%”. By that definition, the patterns/profiles in the top row in Figure 1would be considered as conditional cooperators while the contribution patterns in the bottom row would not. Fischbacher et al. (2001) called the strategy of not matching others’ contributions as conditional cooperation with a self-serving bias.Teyssier (2012) called them low reciprocators, who match the first mover’s contribution only if it is not too high. Games2025,16,xFORPEERREVIEW4of23 studyby(deOliveiraetal.,2015),ontheotherhand,consideredeveryoneaselfishplayer whosecontributionneverexceeded25%.Thereisasubtledifferencebetweenthesetwo approaches.Thedefinitionrequiringanaveragecontributionofnotmorethan10%or20% alsoincludesapatterninwhichallcontributionsare0,exceptwheneveryoneelse’s contributionisthemaximumamount,inwhichcasethiscontributionismatched.Thiscan stillbeconsideredselfish,butitisdifferentfromthecasewhereonealwaysgives20%. Freeriders(Burlando&Guala,2005)andsubparconditionalcooperators (Neugebaueretal.,2009)driverepeatedcooperationdownward.Thisbehaviorisselfish, astheycontributelessthantheyexpectotherstocontribute.Lumpingmostofthese togetherhidesimportantdifferencesbetweenthestrategiesofindividuals.Theissueis notreallytheuseoftheSpearmancorrelationvs.thePearsoncorrelation(Thöni&Volk, 2018),thenumericalvalueofthecorrelation(Grandjeanetal.,2022),orthesignificance levelofthesaidcorrelation(Rustagietal.,2010).AllcontributionpatternsinFigure1have boththePearsoncorrelationandtheSpearmancorrelationabove0.89,andallarehighly significantatp<0.001.Onestudy(Andreozzietal.,2020)distinguishedbetweenperfect conditionalcooperatorsandimperfectconditionalcooperators.Perfectconditionalcooperators matchothers’contributionsexactly,whereasimperfectcooperatorsincludeallother conditionalcooperators.However,thereshouldbeadistinctionmadebetweenthosenot matchingothers’contributionsandthosethatcontributeevenmore(comparetopright andtopcenterinFigure1andbottomleftandcenterwithbottomright).Burlandoand Guala(2005)definedconditionalcooperationasthatwhere“conditionalcontribution functionsapproximatethe‘perfectreciprocationfunction’,withamarginofvariationof ±10%”.Bythatdefinition,thepatterns/profilesinthetoprowinFigure1wouldbe consideredasconditionalcooperatorswhilethecontributionpatternsinthebottomrow wouldnot.Fischbacheretal.(2001)calledthestrategyofnotmatchingothers’ contributionsasconditionalcooperationwithaself‐servingbias.Teyssier(2012)calledthem lowreciprocators,whomatchthefirstmover’scontributiononlyifitisnottoohigh. Figure1.Differentconditionalcooperators.Thetopleftpanelshowsaperfectconditional cooperator.Thenextpanelshowsacontributionpatterninwhichcontributionsareconsistently10% Figure 1. Different conditional cooperators. The top left panel shows a perfect conditional cooperator. The next panel shows a contribution pattern in which contributions are consistently 10% less (top center) or 10% more (top right) compared to the perfect conditional cooperator. In the bottom row, the first two panels show conditional free riders, and the rightmost one shows a conditional cooperator.
Games 2025,16, 22 5 of 21 We need to mention the reclassification of categories by Fallucchi et al. (2019). They made a classification based on hierarchical clustering of contribution vectors. Their new categories included own-maximisers,strong conditional cooperators,weak conditional cooperators, unconditional cooperators, and various (which is basically the “others” category). Ownmaximizers contribute zero or few tokens (which is in line with the definition of free riders). Strong conditional cooperators match the contributions of others. Weak conditional cooperators, on the other hand, match others’ contributions to at most half the level. Unconditional cooperators contribute the maximum amount (or close to it) to the public goods. Strategies of players can be inferred from the behavior observed in repeated games. While the strategy space of the public goods game is vast, the comparable strategy space of the prisoner’s dilemma (a two-player version of the PGG) is more manageable. The strategy frequency estimation method (Dal Bó & Fréchette,2011) can be employed to discern strategies. Interestingly, simple strategies such as “always defect” (comparable to unconditional free riders), “tit-for-tat” (start by cooperating and then do what the others did in the previous round, analogous to the perfect conditional cooperation), and “grim” (cooperate as long as the others cooperate, then switch to free riding) come out frequently (Dal Bó & Fréchette,2019;Romero & Rosokha,2023). Even if mixed strategies are allowed, players converge on these simple strategies (Romero & Rosokha,2023). Here, we offer a new classification scheme of the outcome of the strategy method (Fischbacher etal.,2001;Selten,1967). We measured the cooperative tendencies in Hungary, a high-income, former socialist bloc country in Central–Eastern Europe. While unconditional contribution in the PGG has already been reported (Czibor & Bereczkei,2010;Romano et al.,2021), conditional contribution remains so far unexplored in the Hungarian context. Actually, studies of this sort are currently available only from very few countries (Table 1), as most such research has so far been limited to the USA, UK, Switzerland, and Germany. From the wider Central–Eastern European regional context, data involving conditional contributions has so far only been collected from the Czech Republic (Katušˇcák & Miklánek, 2023). Consequently, our study also has the potential to add valuable data to the wider question of how culture affects cooperative tendencies. Table 1. Distribution of contribution types from the literature. Conditional Free Rider HumpShaped Unc. Cooperator Number of Participants Country Ref. 50 29.5 13.6 - 44 Switzerland (Fischbacher et al.,2001) 80.6 8.3 - - 36 USA (Kocher et al.,2008) 41.7 36.1 11.1 - 36 Japan (Kocher et al.,2008) 44.4 22.2 11.1 - 36 Austria (Kocher et al.,2008) 38 35 15 1.6 60 UK (Muller et al.,2008) 58.3 14.6 8.3 - 96 Colombia (Martinsson et al.,2009) 55.5 6.3 7.5 - 160 Russia (Herrmann & Thöni,2009) 55 23 12 - 140 Switzerland (Fischbacher & Gächter,2010) 34.0 11.5 2.95 2.2 679 Ethiopia (Rustagi et al.,2010) 58.3 25.0 13.9 - 72 4(Volk et al.,2012) 55.0 22.9 12.1 1.4 140 Switzerland (Fischbacher et al.,2012) 69 15 - - 1488 Denmark (Thöni et al.,2012) 50.0 25.7 14.0 - 350 USA (Kamei,2012) 47.8 23.3 15.1 - 272 USA (Aimone et al.,2013) 62.5 4.2 8.3 - 48 Colombia (Martinsson et al.,2013) 50.0 4.2 8.3 - 48 Vietnam (Martinsson et al.,2013) 63.2 22.8 9.6 - 228 Germany (Fischbacher et al.,2014)
Games 2025,16, 22 6 of 21 Table 1. Cont. Conditional Free Rider HumpShaped Unc. Cooperator Number of Participants Country Ref. 66.7 2- - 48 The Netherlands and Switzerland (Dariel & Nikiforakis,2014) 68 15 - - 1366 Denmark (Fosgaard et al.,2014;Nielsen et al.,2014) 51 13.5 17.7 - 96 USA (Makowsky et al.,2014) 71.0 6.5 3.2 - 31 UK (Cartwright & Lovett,2014) 63 24 - - 128 Germany (Hartig et al.,2015) 43.6 24.8 - - 296 Japan (Hiraishi et al.,2015) 58.13 20.16 11.63 - 144 Germany (Kocher et al.,2015) 67. 8 15.5 4.0 - 174 UK (Abeler & Nosenzo,2015) 54.4 6.5 6.5 15.2 46 Denmark (Fosgaard & Piovesan,2016) 50 21 10 - 72 UK (Burton-Chellew et al.,2016) 37.5 22.5 15.0 - 40 France (Préget et al.,2016) 81.7 6.7 6.7 - 36 Germany (Björk et al.,2016) 73.6 16.9 6 - 201 USA 3(Cherry et al.,2017) 49 9.5 4.5 4 299 China (Vollan et al.,2017) 59.7 25.6 -1592 UK (Cubitt et al.,2017) 64 17 - - 444 UK (Gächter et al.,2017) 48.9 26.6 - - 184 UK (Weber et al.,2018) 56.4 21.6 - - 227 Denmark (Nagatsu et al.,2018) 66 12 - 2 134 Italy (Bigoni et al.,2019) 67 21.6 7.5 - 134 Italy (Andreozzi et al.,2020) 42 33 9 - 88 Czech Republic (Katušˇcák & Nikolaychuk,2023) 57.4 3.1 - - 3653 UK (Isler et al.,2021) 50 0 11.1 - 36 Italy (Bergantino et al.,2023) 80 8 - - 703 USA (Gächter et al.,2022) 76 10 - - 845 Switzerland (Burton-Chellew et al.,2022) 64.4 2 5.2 - 250 USA/UK (Bilancini et al.,2022) 50 30 5.2 - 192 France (Grandjean et al.,2022) 57.6 12.0 12.6 - 192 Czech Republic (Katušˇcák & Miklánek,2023) 63.4 15.1 6.5 - 93 Germany (Granulo et al.,2023) 55 11 22.6 - 106 USA (Weber et al.,2023) 52 22 18.2 - 88 UK (Weber et al.,2023) 48 8 28.7 - 80 Morocco (Weber et al.,2023) 47 20 7 - 86 Turkey (Weber et al.,2023) 47.7 20.1 15.6 1.5 66 USA (Li & Noussair,2024) 80.4 6.8 0.7 1.5 265 Hungary This study The percentages of conditional cooperators, free riders, hump-shaped cooperators (or triangular cooperators), and unconditional full cooperators are given. The remaining percentage falls under the “others” category, which is not displayed here—this category was not reported in the studies. 1 There were triangular cooperators in the sample, but too few, and so these respondents were categorized as “others”. 2 All non-cooperators were pooled into the “others” category. We cannot distinguish between the categories. 3 The experiment was conducted via Mechanical Turk, and so subjects could come from any country. 4 The method only states that the experiment was conducted in a European university. 2. Results The results are based on 265 responses collected online in Hungary. The questionnaire was open to everyone, but most respondents were university students. The respondents were asked about their unconditional contributions and conditional contributions (according to the strategy method) to a common pool. Furthermore, data on demographics, risk-taking attitudes, attitudes toward competition, and perceived past and present economic status were recorded. The study was voluntary and unincentivized. There were two questions assessing if the respondent understood the game. Responses from those correctly answering both assessment questions and those failing at least one of them did not differ significantly, and thus all responses were retained (see Materials and Methods for details). 2.1. Unconditional Contribution The average unconditional contribution to the common pool was 54%. The respondents, most commonly (34%), invested half of their initial endowment to the common pool. The second most commonly invested amount was the maximum (20%), followed by no investment (9%) (Figure 2).
Games 2025,16, 22 7 of 21 Games2025,16,xFORPEERREVIEW7of23 fromthosecorrectlyansweringbothassessmentquestionsandthosefailingatleastone ofthemdidnotdiffersignificantly,andthusallresponseswereretained(seeMaterials andMethodsfordetails). 2.1.UnconditionalContribution Theaverageunconditionalcontributiontothecommonpoolwas54%.The respondents,mostcommonly(34%),investedhalfoftheirinitialendowmenttothe commonpool.Thesecondmostcommonlyinvestedamountwasthemaximum(20%), followedbynoinvestment(9%)(Figure2). Figure2.Frequencyofthegiveninvestmenttothecommonpoolamongtherespondents. 2.2.ConditionalContribution AccordingtotheoriginalcategorizationofFischbacheretal.(2001)(see Introduction),18(6.8%)respondentswerefreeriders;4(1.5%)wereunconditional cooperators;2werehump‐shapedcontributors(0.7%);213wereconditionalcooperators(80.4%); and26wereconsideredtobe“others”(9.8%)(seethegraphicalrepresentationofthe strategyofrespondentsinAppendixA). Thehump‐shapedcooperatorsfoundinoursurvey(Figure3)weremostlyfarfromthe idealcase.WealsofoundoneexampleofaV‐shapedcontributionpattern,whichisthe oppositeofthepatternexhibitedbyahump‐shapedcooperator.Thisunderscoresthatthe detectionofrarevariantsrequiresalargersamplesize,andtheoriginalcategorization missedsomesuchpatterns. Figure 2. Frequency of the given investment to the common pool among the respondents. 2.2. Conditional Contribution According to the original categorization of Fischbacher et al. (2001) (see Introduction), 18 (6.8%) respondents were free riders; 4 (1.5%) were unconditional cooperators; 2 were humpshaped contributors (0.7%); 213 were conditional cooperators (80.4%); and 26 were considered to be “others” (9.8%) (see the graphical representation of the strategy of respondents in Appendix A). The hump-shaped cooperators found in our survey (Figure 3) were mostly far from the ideal case. We also found one example of a V-shaped contribution pattern, which is the opposite of the pattern exhibited by a hump-shaped cooperator. This underscores that the detection of rare variants requires a larger sample size, and the original categorization missed some such patterns. Games2025,16,xFORPEERREVIEW7of23 fromthosecorrectlyansweringbothassessmentquestionsandthosefailingatleastone ofthemdidnotdiffersignificantly,andthusallresponseswereretained(seeMaterials andMethodsfordetails). 2.1.UnconditionalContribution Theaverageunconditionalcontributiontothecommonpoolwas54%.The respondents,mostcommonly(34%),investedhalfoftheirinitialendowmenttothe commonpool.Thesecondmostcommonlyinvestedamountwasthemaximum(20%), followedbynoinvestment(9%)(Figure2). Figure2.Frequencyofthegiveninvestmenttothecommonpoolamongtherespondents. 2.2.ConditionalContribution AccordingtotheoriginalcategorizationofFischbacheretal.(2001)(see Introduction),18(6.8%)respondentswerefreeriders;4(1.5%)wereunconditional cooperators;2werehump‐shapedcontributors(0.7%);213wereconditionalcooperators(80.4%); and26wereconsideredtobe“others”(9.8%)(seethegraphicalrepresentationofthe strategyofrespondentsinAppendixA). Thehump‐shapedcooperatorsfoundinoursurvey(Figure3)weremostlyfarfromthe idealcase.WealsofoundoneexampleofaV‐shapedcontributionpattern,whichisthe oppositeofthepatternexhibitedbyahump‐shapedcooperator.Thisunderscoresthatthe detectionofrarevariantsrequiresalargersamplesize,andtheoriginalcategorization missedsomesuchpatterns. Figure 3. Minor contribution types: hump-shaped contributors and V-shaped contributors. The examples are as found in our dataset. The gray lines depict the quintessential form of such contribution patterns and are given as reference. In this study, we observed no instances of negative cooperators (Bergantino et al.,2023; Burton-Chellew et al.,2016) who contributed much when others did not, and then reduced their contributions. We only found four full cooperators contributing all their initial endowment and found no one unconditionally investing 80% or 90% of it. We proceeded with the definition of free riders (selfish players) which specifies the contribution as never exceeding 25%, as proposed by (de Oliveira et al.,2015;Nagatsu et al., 2018). There are 113 (42.6%) perfect conditional cooperators in our sample. This can be considered a category of its own.
Games 2025,16, 22 8 of 21 2.3. Recategorization of Conditional Contribution Strategies Here, we offer, based on the literature, a new categorization scheme. Patterns should be categorized in this order; if a pattern matches more than one rule, then it falls into the first category whose criterion it fulfills. •Unconditional cooperators: contribution is always higher than 75%. •Unconditional free riders: contribution is always below 25%. •Perfect conditional cooperators: contributions match the others’ contributions exactly. • Hump-shaped contributors: the contribution schedule has a maximum contribution that is not at 0 or the maximum contributions of others. The increasing part (from the beginning to the maximum of the contribution) has a positive Spearman correlation, which is significant at the p≤ 0.05 level. The decreasing part has a negative Spearman correlation, which is significant at the p≤0.05 level. • V-shaped contributors: the contribution schedule starts and ends high, but decreases in the middle. The decreasing part (from the beginning to the minimum of the contributions) has a negative Spearman correlation, which is significant at the p≤ 0.05 level. The increasing part has a positive Spearman correlation, which is significant at the p≤0.05 level. • Conditional cooperators: the contribution is always at least as high as the others’ average contributions. The bottom right panel in Figure 1shows a conditional cooperator. • Conditional free riders: the contribution is at most as high as the others’ average contributions. The bottom left and bottom center panels in Figure 1show conditional free riders. • Conditional contributors: the Spearman correlation between the others’ investments and the contribution of the focal player is positive and significant at p≤0.001. Some investments are above and some are below the others’ average contributions. • Negative conditional contributors: the Spearman correlation between the others’ investments and the contribution of the focal player is negative and significant at p≤ 0.001. • Others: if the contribution pattern does not fit into any of the above categories, it is labeled as “others”. The ordering of categories makes the rule a bit simpler. For example, we categorized any contribution pattern an “unconditional free rider” if it was consistently below 25%. However, the pattern in the left panel of Figure 4also fulfills the condition for “conditional free riders”. Similarly, the patterns in the middle and rightmost panels of Figure 4 correspond to unconditional cooperators, albeit they fulfill the conditions for conditional cooperators and negative conditional contributors, respectively. The most frequent strategy type is Perfect conditional cooperator (Table 2), followed by Conditional free riders and Unconditional free riders. The categorical changes we suggest have two motivations. One is to showcase some minor variants that emerge in a larger dataset. They have low frequencies, but if we want to map the true strategic diversity of contribution types, then we need to identify these. There might be other meaningfully distinct strategy types that are currently still being relegated to the “others” category. The second motivation is the necessary change in language. Former studies mostly went with the notion that anyone willing to contribute any non-zero amount is a cooperator. Some authors (de Oliveira et al.,2015;Grandjean et al.,2022;Nagatsu et al., 2018) have already extended the definition of free riders to include low contributors. Other authors have distinguished low reciprocators (Teyssier,2012) or own-maximizers (Fallucchi et al.,2019) among those contributing some but not as much as the others. We suggest labeling anyone a free rider who consistently contributes less than others. Furthermore, we only consider someone a cooperator if they consistently contribute at least as much as others (but potentially more in some cases). In our new categorization scheme, there is an
Games 2025,16, 22 15 of 21 Appendix A Games2025,16,xFORPEERREVIEW15of23 competitionavoidance(ADCA);self-developmentalcompetitiveorientation(SDCO);and fearoflosingcompetitionorientation(FOL). Individualdifferencesinperceivedresourceavailabilitywereassessedthroughthree questionsabouttheperceivedsocioeconomicstatusinchildhoodandthreequestions aboutthepresent/nearfutureperceivedresourceavailability(Griskeviciusetal.,2011a, 2011b). Bothquestionnaireshadfurtheritemsassessingotherpersonalitytraitsaswellas attitudestowardclimatechangethatarenotanalyzedhereanddidnotoverlapbetween thequestionnaires.Allthenon-demographicquestionscameafterthemainquestionsto avoidpriming. SupplementaryMaterials:Thefollowingsupportinginformationcanbedownloadedat: https://www.mdpi.com/article/doi/s1,TableS1:Recordedresponses;TextS1:Thequestionnaire. AuthorContributions:initiationandconceptualization,Á.K.;questionnairedevelopment,A.K.and Á.K.;datacollection,K.S.;datacuration,K.S.andÁ.K.;statisticalanalysis,A.K.andÁ.K.;writing— originaldraftpreparation,Á.K.Allauthorscontributedtotheeditingandfinalizationofthemanuscript.Allauthorshavereadandagreedtothepublishedversionofthemanuscript. Funding:ThisworkwassupportedbyHUN-REN(grantnumberELKHSA-50/2021). DataAvailabilityStatement:TheresponsesareavailableinSupplementaryTableS1. ConflictsofInterest:Theauthorsdeclarenoconflictsofinterest.Thefundershadnoroleinthe designofthestudy;inthecollection,analyses,orinterpretationofdata;inthewritingofthemanuscript;orinthedecisiontopublishtheresults. AppendixA Games2025,16,xFORPEERREVIEW16of23 Figure A1. Cont.
Games 2025,16, 22 16 of 21 Games2025,16,xFORPEERREVIEW16of23 Games2025,16,xFORPEERREVIEW17of23 FigureA1.All265conditionalcontributionpatternfromtherespondents.Eachofthesubplotshas x-andy-axesgoingfrom0to10,000,withxbeingtheaveragecontributionoftheotherplayers’and ybeingtherespondent’scontribution.Subplotsareshadedaccordingtothecategorizationby (Fischbacheretal.,2001,2012):conditionalcooperators—yellow;freeriders—gray;unconditional cooperators—green;andothers—white. References (Abeler&Nosenzo,2015)Abeler,J.,&Nosenzo,D.(2015).Self-selectionintolaboratoryexperiments:Pro-socialmotivesversus monetaryincentives.ExperimentalEconomics,18(2),195–214.https://doi.org/10.1007/s10683-014-9397-9. (Adresetal.,2016)Adres,E.,Vashdi,D.R.,&Zalmanovitch,Y.(2016).Globalizationandtheretreatofcitizenparticipation in collectiveaction:Achallengeforpublicadministration.PublicAdministrationReview,76(1),142–152. https://doi.org/10.1111/puar.12424. (Ahmed&Salas,2009)Ahmed,A.M.,&Salas,O.(2009).IsthehandofGodinvolvedinhumancooperation?InternationalJournalof SocialEconomics,36,70–80. (Aimoneetal.,2013)Aimone,J.A.,Iannaccone,L.R.,Makowsky,M.D.,&Rubin,J.(2013).Endogenousgroupformationvia unproductivecosts.TheReviewofEconomicStudies,80(4),1215–1236.https://doi.org/10.1093/restud/rdt017. (Alencaretal.,2008)Alencar,A.I.,deOliveiraSiqueira,J.,&Yamamoto,M.E.(2008).Doesgroupsizematter?Cheatingand cooperationinBrazilianschoolchildren.EvolutionandHumanBehavior,29(1),42–48. https://doi.org/10.1016/j.evolhumbehav.2007.09.001. (Andreozzietal.,2020)Andreozzi,L.,Ploner,M.,&Saral,A.S.(2020).Thestabilityofconditionalcooperation:Beliefsalonecannot explainthedeclineofcooperationinsocialdilemmas.ScientificReports,10(1),13610.https://doi.org/10.1038/s41598-020-70681z. (Arecharetal.,2018)Arechar,A.A.,Gächter,S.,&Molleman,L.(2018).Conductinginteractiveexperimentsonline.Experimental Economics,21(1),99–131.https://doi.org/10.1007/s10683-017-9527-2. (Attanasioetal.,2009)Attanasio,O.,Pellerano,L.,&Reyes,S.P.(2009).Buildingtrust?Conditionalcashtransferprogrammesand socialcapital.FiscalStudies,30(2),139–177.https://doi.org/10.1111/j.1475-5890.2009.00092.x. (Ballietetal.,2014)Balliet,D.,Wu,J.,&DeDreu,C.K.W.(2014).Ingroupfavoritismincooperation:Ameta-analysis.Psychological bulletin,140(6),1556–1581.https://doi.org/10.1037/a0037737. (Barretal.,2014)Barr,A.,Packard,T.,&Serra,D.(2014).Participatoryaccountabilityandcollectiveaction:Experimentalevidence fromAlbania.EuropeanEconomicReview,68,250–269.https://doi.org/10.1016/j.euroecorev.2014.01.010. Figure A1. All 265 conditional contribution pattern from the respondents. Each of the subplots has xand y-axes going from 0 to 10,000, with x being the average contribution of the other players’ and y being the respondent’s contribution. Subplots are shaded according to the categorization by (Fischbacher et al.,2001,2012): conditional cooperators—yellow; free riders—gray; unconditional cooperators—green; and others—white. References Abeler, J., & Nosenzo, D. (2015). Self-selection into laboratory experiments: Pro-social motives versus monetary incentives. Experimental Economics,18(2), 195–214. [CrossRef] Adres, E., Vashdi, D. R., & Zalmanovitch, Y. (2016). Globalization and the retreat of citizen participation incollective action: A challenge for public administration. Public Administration Review,76(1), 142–152. [CrossRef] Ahmed, A. M., & Salas, O. (2009). Is the hand of God involved in human cooperation? International Journal of Social Economics,36, 70–80. [CrossRef] Aimone, J. A., Iannaccone, L. R., Makowsky, M. D., & Rubin, J. (2013). Endogenous group formation via unproductive costs. The Review of Economic Studies,80(4), 1215–1236. [CrossRef] Alencar, A. I., de Oliveira Siqueira, J., & Yamamoto, M. E. (2008). Does group size matter? Cheating and cooperation in Brazilian school children. Evolution and Human Behavior,29(1), 42–48. [CrossRef]
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