1 Introduction

Not least since Piketty (Reference Piketty2014), problems arising from inequalities within and between societies are at the heart of many public debates. A main challenge is the impact of inequalities on the provision of public goods. For many global and societal challenges, economic actors differ both in the degree to which they are affected by such issues as well as in the capacity to address them. Compared with the poor, rich individuals within a society, for example, are better able to resolve inequalities and tackle global and societal problems by redistributing wealth or financing public goods (see, e.g., Alesina and Giuliano Reference Alesina and Giuliano2011; Cohn et al. Reference Cohn, Jessen, Klasnja and Smeets2019). Yet, rich individuals contribute proportionately less than poor in experiments with a single public good (see, e.g., Buckley and Croson Reference Buckley and Croson2006; Chan et al. Reference Chan, Mestelman, Moir and Muller1999; Corazzini et al. Reference Corazzini, Faravelli and Stanca2010; Kroll et al. Reference Kroll, Cherry and Shogren2005; Kesternich et al. Reference Kesternich, Lange and Sturm2014; Reuben and Riedl Reference Reuben and Riedl2013) and are generally more likely to oppose redistribution (Cohn et al. Reference Cohn, Jessen, Klasnja and Smeets2019). Inequality may thus negatively impact cooperation and overall public good provision (Anderson et al. Reference Anderson, Mellor and Milyo2008; Cardenas Reference Cardenas2003, Reference Cardenas2007).Footnote ¹

In addition, Blackwell and McKee (Reference Blackwell and McKee2003), Falk et al. (Reference Falk, Fischbacher and Gächter2013) and Fellner and Lünser (Reference Fellner and Lünser2014) show that—without inequalities—individuals tend to give to the public goods that yield a direct benefit to their own (local) sub-group even though cooperation on the broader (global) level may be more efficient. Indeed, cooperation on the global level oftentimes yields higher social returns compared with local cooperation (to combat climate change and reduce CO2 emissions or to tackle inequalities within societies, e.g., global cooperation efforts are needed to obtain large scale social benefits whereas local cooperation such as supporting schools in the own neighborhood only have limited social impact).Footnote ² Thus, while intentions may be good, individuals may not always contribute to the most efficient public good but contribute to public goods closer to themselves (Smith Reference Smith1976), where benefits from cooperation are directly observable (Fellner and Lünser Reference Fellner and Lünser2014) and beneficiaries from cooperation share common characteristics (see, e.g., Balliet et al. Reference Balliet, Wu and De Dreu2014; Fu et al. Reference Fu, Tarnita, Christakis, Wang, Rand and Nowak2012; Goette et al. Reference Goette, Huffman and Meier2006, Reference Goette, Huffman and Meier2012; Lane Reference Lane2016).

The tendency of individuals to cooperate with their peers and on a local level may exacerbate the negative effects of inequality on global cooperation and public goods provision. Since it is impossible and undesired to eliminate inequality per-se, it is important to investigate new and creative measures that foster cooperation between rich and poor and promote efficient public good provision. Raising the awareness about the situation of others and give people the opportunity to (at least partially) experience the situation of the opposite party is an often promoted instrument aiming at improving cooperation between different actors. Study admissions and employers around the world, for example, value volunteering of applicants in poor communities.Footnote ³ Moreover, several governmental programs exist that build on using experience to foster cooperation between individuals from different cultures.Footnote ⁴ Further, some governments offer individuals to volunteer and perform social work as an alternative to mandatory military service (see, e.g., alternative civilian service in countries like Austria, Finland, Greece Israel, Switzerland, South Korea). In addition, experimental research on bargaining games (Brosig et al. Reference Brosig, Weimann and Yang2003; Charness and Rabin Reference Charness and Rabin2002), trust games (Burks et al. Reference Burks, Carpenter and Verhoogen2003) and dictator games (Diekmann Reference Diekmann2004) documents that experiencing the other position, i.e., role reversals may affect outcomes and increase trust and pro-social behavior.

The idea that experiencing “the other side” and “walking in someone else’s shoes” may change the perspective and lead to different actions, seems to be a deeply rooted belief within societies.Footnote ⁵ Numerous fairy tales and fictional stories build on the potential power of temporal role reversal on cooperation and generosity. “King Thrushbeard”, “The Mouse, the Bird and the Sausage” (both by the Brother’s Grimm), “The Life of Henry the Fifth” (by William Shakespeare), “The Prince and the Pauper” (by Mark Twain), as well as the movie “Trading Places”Footnote ⁶ and the TV show “Rich House, Poor House”Footnote ⁷ are just some examples of many that show the deep rooted belief that experience and role reversal shapes understanding and cooperation.Footnote ⁸ However, such new experiences and role reversals are not confined to fiction or individual choice.

Because of exogenous events like job loss, health shocks or economic downturns, individuals may be forced to temporarily experience relative changes in their (income) position. Assuming that the great emphasis and value government programs and admissions put on this experience and that findings from other experimental games on role reversal transfer to public good games, it seems plausible that role reversal may affect cooperation between rich and poor positively.

In this paper, we provide (to our knowledge) first experimental evidence on the effect of income heterogeneity between groups on contributions to multiple (local and global) public goods. In addition, we provide empirical evidence on the causal effect of role reversal on cooperation and public good contributions.

To study how income inequality affects cooperation and public good provision in a multiple public goods setting and to identify the causal effect of role reversal on contributions we implement a linear public goods game consisting of three parts. Participants can allocate their endowment to a private account that only benefits themselves, a global public good that benefits all subjects (high and low endowment types), a local public good that benefits only subjects of their own endowment type (high or low endowment) and another local public good that benefits subjects of the other endowment type (low or high endowment). In the Equal Endowment treatment (EE), subjects receive the same endowment in all three parts of the experiment. Two Inequality conditions (IE) explore role reversal: in our Constant Role treatment (CR) subjects receive a high endowment or a low endowment in the first part of the experiment and remain in their endowment positions throughout the three parts of the experiment. In our Temporary Role Reversal treatment (TRR), subjects receive a high or a low endowment in the first part of the experiment. In the second part of the experiment, roles are temporally reversed, i.e., endowment positions change. The role reversal is revoked and subjects change back to their initial endowments in the third part of the experiment. Thus, subjects who have a high (low) endowment in the first part of the experiment, experience a low (high) endowment in the second part of the experiment and have again a high (low) endowment in the third part of the experiment.

Comparing decisions under equal endowment (EE) and inequality (IE) in the first part of our experiment allows to identify the effects of inequality on voluntary contributions when cooperation is possible at different levels. We find that, compared to subjects who have low endowments, subjects with a high endowment contribute lower shares of their endowment to both the local and the global public good. Moreover, subjects with a high endowment in the IE treatment contribute substantially less to the more efficient global public good compared with subjects in the EE treatment. In addition, inequality leads to higher contributions to the own local public good by subjects with a low endowment. These decisions result in a decline of average income in the presence of inequality.

Comparing behavior in the treatments with inequality (CR vs. TRR) allows to assess the impact of role reversal on contribution rates and cooperation. Consistent with the evidence presented in the extant public goods literature, contributions to public goods decrease over time (see Chaudhuri Reference Chaudhuri2011; Ledyard Reference Ledyard, Kagel and Roth1995, for reviews on the literature). The negative time trend, however, is less pronounced in the treatment in which subjects temporarily change endowment positions. Having experienced a role reversal in part two, has a positive effect on the contributions of subjects with a high endowment to the global public good in part three. Consequently, role reversal also decreases the income gap between high and low endowment players.

Our paper contributes to the literature in three ways: first, we complement the existing literature on public goods games and inequality which thus far studied cooperation and contributions under inequality in single public good games (see, e.g., Buckley and Croson Reference Buckley and Croson2006; Chan et al. Reference Chan, Mestelman, Moir and Muller1999; Corazzini et al. Reference Corazzini, Faravelli and Stanca2010; Kroll et al. Reference Kroll, Cherry and Shogren2005; Kesternich et al. Reference Kesternich, Lange and Sturm2014; Reuben and Riedl Reference Reuben and Riedl2013). Second, we add to the literature on cooperation and multiple group membership (Blackwell and McKee Reference Blackwell and McKee2003; Falk et al. Reference Falk, Fischbacher and Gächter2013; Fellner and Lünser Reference Fellner and Lünser2014). We contribute to these literatures by studying endowment inequality in multiple group membership settings. We show that rich subjects contribute less than subjects with a low endowment and subjects who experience the situation without inequality in the EE treatments. Our setting allows us to quantify the effect of inequality on contributions to public goods. Heterogeneity in endowment between groups exacerbates income disparities and leads to lower average incomes compared with a situation of endowment equality. Third, we add to the experimental literature by providing first evidence on the effects of (temporal) role reversal in a public good setting. Studies on such role reversals in bargaining experiments (Brosig et al. Reference Brosig, Weimann and Yang2003; Charness and Rabin Reference Charness and Rabin2002) and trust games (Burks et al. Reference Burks, Carpenter and Verhoogen2003) show that behavior may be influenced when roles are exchanged. Diekmann (Reference Diekmann2004) investigate pro-social behavior in dictators games when dictators also experience the role of a receiver. Cassar and Klein (Reference Cassar and Klein2019) shows that redistribution behavior of subjects is affected by experiencing good and bad luck. We show that role reversal increases cooperation between heterogeneous groups of subjects. Mechanisms that increase trust or pro-social behavior may therefore also be used to foster cooperation in public goods games. Consequently, interventions studied in other experimental games may thus be transferable to public good settings.

Our findings also have implications for policy makers and practitioners. Many cooperation problems exist in which some parties may temporarily be better able to cooperate than others. Within a given supply chain, for example, volatile business cycles may make some firms better able to cooperate and show leniency to business partners than others. Our positive effect of (temporary) role reversal suggests that cooperation may be more stable in volatile environments in which the relative ability of actors to cooperate changes. In case of economic shocks, this may inform whether or not (governmental) interventions may be needed (or should prioritize on other less volatile industries). Additionally, our findings may inform policymakers interested in reducing inequality on the societal level. Although such strong forms of role reversal may be impossible to impose in practice, fostering the interaction between rich and poor within a society might be an adequate tool to increase support for the provision of public goods benefiting society as a whole.Footnote ⁹

The remainder of this paper is organized as follows. Section 2 presents our experimental design. Results are presented in Sect. 3. Section 4 provides a concluding discussion.

2 Experimental design and procedure

We set up a local and global public goods game (see, e.g., Blackwell and McKee Reference Blackwell and McKee2003; Fellner and Lünser Reference Fellner and Lünser2014, for experiments using a similar set-up) to study how income inequality between actors and temporal role reversal, i.e. a temporal change in endowment positions affect cooperation on different group levels.

This design choice was inspired by frequent real life situations where individuals belong to several groups at the same time. Literature from in-group favoritism indeed shows that individuals have a tendency to cooperate with peers who share similar characteristics (see, e.g., Balliet et al. Reference Balliet, Wu and De Dreu2014; Fu et al. Reference Fu, Tarnita, Christakis, Wang, Rand and Nowak2012; Goette et al. Reference Goette, Huffman and Meier2006, Reference Goette, Huffman and Meier2012; Lane Reference Lane2016). Balliet et al. (Reference Balliet, Wu and De Dreu2014) and Lane (Reference Lane2016) perform meta analysis on in-group favoritism and show that imposed differences between groups may increase in-group favoritism.Footnote ¹⁰ Relying on a local and global public good game with endowment differences between the local groups, our design choice not only enables us to study cooperation in multiple group membership settings but also helps from a methodological point of view as the differentiation between low and high endowment groups becomes salient for subjects. The temporary role reversal thus specifically forces subjects to experience cooperation on the local and the global level when their endowment is low and vice versa.

Our experiment thus has three key features and allows us to estimate the causal effects of experiencing another endowment perspective on cooperation: (i) By comparing homogenous and heterogeneous endowment settings, we elicit the effect of income inequality on cooperation of rich and poor subjects separately. (ii) By exogenously forcing subjects to change roles, we rule out selection and subjects experience the benefits or disadvantages of the respective other income category. (iii) By letting subjects switch back into their initial role, we study whether experiencing a new role has an effect on behavior over time, i.e., when subjects are back to their initial role.

2.1 Experimental design

In all treatments, subjects are randomly divided into global groups of six (group AB). Within a global group of six, two local groups of three subjects are randomly formed: group A and group B. Figure 1 graphically demonstrates the group composition.

Fig. 1 Constitution of the local and the global groups. A global group AB consists of six subjects. The numbers 1, 2, 3 represent three of the six subjects that belong to group A, and the numbers 4, 5, 6 represent three of the six subjects that belong to group B. The circles represent the two groups A and B and also highlight which subjects benefit from the respective accounts A and B, i.e., the local public goods. All subjects benefit from contributions to the account AB, i.e., the global public good

All six players of a global group face the same decision. They can either keep their endowment or contribute to three accounts: a local public good “A” that only benefits subjects in the local group A, a local public good “B” that only benefits subjects in the local group B, and a global public good “AB” that benefits all subjects in the global group of six. The contributions by individual i are denoted by $g_i^A$ , $g_i^B$ , and $g_i^{\mathrm{AB}}$ , respectively. The payoff of subject i that is a member of group $G\in \{A,B\}$ is given by:

$\begin{array}{c}{\Pi }_i^G=m^G-g_i^A-g_i^B-g_i^{\mathrm{AB}}+\alpha \sum _{j=1}^6{g}_j^G+\beta \sum _{j=1}^6{g}_j^{\mathrm{AB}}.\end{array}$

Here, $m^G$ denotes the endowment of subjects in group G which may differ between group A and group B. $\alpha$ is the marginal per capita return (MPCR-Local) of contributions to the local public good of group G, and $\beta$ is the marginal per capita return for contributions to the global public good AB, with $\alpha =0.5$ and $\beta =0.35$ . These parameters have been chosen because they have typical public good properties, $\alpha <1<3\alpha$ and $\beta <1<6\alpha$ , such that contributions are beneficial to the respective group of 3 (local) or 6 (global) players, while individually freeriding is a dominant strategy. Additionally, our parameter choice was inspired by Fellner and Lünser (Reference Fellner and Lünser2014) who choose $\alpha$ and $\beta$ such that contributions to the global public good are more efficient in generating total payoff than contributions to the respective local public goods. Our parameter choice of $3\alpha <6\beta$ fulfills this criterion. Our payoff structure also implies that subjects do not benefit if they contribute to the local public good of the other group, i.e. if a subject in group A contributes to account B or a subject in group B contributes to account A. Since subjects do not materially (directly or indirectly) benefit from this contribution it resembles an (altruistic) selfless donation to the other group.

In all our treatments, subjects play the local and global public goods game in three parts of five periods each. Thus, the experiment consists of 15 periods. At the beginning of the first part subjects learn whether they are in group A or group B. In part 2, we randomly rematch groups A and B in a new global group. Specifically, all subjects in group A(B) are matched with subjects from a different group B(A) than in part 1 and play the game for additional five periods. Figure 2 demonstrates this procedure graphically.Footnote ¹¹ After part 2, groups are rematched with the same group B(A) as in part 1 and play the game for five more periods in part 3 in the initial constellation from part 1. This matching procedure is the same in all treatments.

Fig. 2 Constitution of the global and local groups in the three parts. In part 1, six subjects [denoted 1, 2, 3, 4, 5, 6 (for simplicity)] are in the same global group A1B1. Subject 1, 2, 3 form the local group A1 and subjects 4, 5, 6 constitute the local group B1. Six other subjects (denoted 7, 8, 9, 10, 11, 12) equivalently constitute the global group A2B2. In part 2, subjects in group A1 are matched with subjects from group B2. Subjects from group A2 are matched with subjects from group B1. Hence, subjects 1, 2, 3, 10, 11, and 12 form the global group A1B2 and subjects 4, 5, 6, 7, 8, and 9 form the global group B1A2. In part 3, subjects switch back in their roles and the initial group constellation from part 1 is reinstalled

We implement three different treatments in order to study the effects of heterogeneous endowments and role reversal. In our Equal Endowment Treatment (EE) condition, subjects in group A and group B receive the same endowment ( $m^A=m^B=30$ ) and play the local and global public goods game in three parts of five periods each. To have a clean comparison to the other treatments, we match the three subjects of each local group with three other subjects in part 2 as described in Fig. 2. In part 3, they are rematched with the same subjects as in part 1. Total wealth is equal within each global group in all treatments. Hence, we have equality of income in our EE treatment, while we establish income heterogeneity between groups in the other two treatments.

In the Constant Role (CR) treatment, we keep the total endowment as in EE, but implement endowment heterogeneity: Subjects in group A receive an endowment of $m^A=40$ , while subjects in group B receive an endowment of $m^B=20$ . We apply the same matching mechanism as described above and endowments remain the same throughout the three parts. Subjects in group A who receive a high endowment in part 1 also receive a high endowment in part 2 and part 3 and subjects in group B who receive a low endowment in part 1 also receive a low endowment in parts 2 and part 3. In other words, subjects stay in their role as being rich or poor throughout the experiment. The procedure, however, is similar to that in the EE (and TRR) treatment as the global groups consist of new subjects in part 2. In other words, subjects from each local group are matched with three other subjects from another local group in part 2 and rematched again with the same subjects as in part 1 in part 3.

Finally, we implement the Temporal Role Reversal (TRR) treatment. Subjects receive the same endowment as in the CR treatment in part 1 of the experiment. That is, subjects in group A are rich and subjects in group B are poor ( $m_{\mathrm{part}1}^A=40$ and $m_{\mathrm{part}1}^B=20$ ). In part 2, subjects change roles and endowments. Specifically, we apply the same matching mechanism as in the other treatments but we also change the endowment assignment among subjects. Hence, we exogenously change the income and thus the roles of both rich and poor subjects.Footnote ¹² Subjects who have a high endowment of 40 points in part 1 have the low endowment of 20 points in part 2 and subjects who have a low endowment of 20 points in part 1 have a high endowment of 40 points in part 2. In part 3, subjects switch back into their initial role from part 1 ( $m_{\mathrm{part}3}^A=40$ and $m_{\mathrm{part}3}^B=20$ ). The endowment of all subjects in all parts is common knowledge. Hence subjects in the different treatments know the endowment of others in their own local group, the other local group and the total endowment in the global group.

Part 1 of our experiment allows us to study the effect of income heterogeneity in the CR and TRR treatments compared to our baseline condition in which subjects have the same endowment (EE treatment). Table 1 summarizes the main treatment variation as well as the number of sessions conducted. The table also highlights the number of subjects who participated in each session and the number of independent observations on the part 1 global group (before two global groups interact) and the matching group level per treatment (two global groups constitute one matching group).

Table 1 Treatments and endowment parameters in the three parts of the experiment

Part	Treatment
	Equal endowment (EE)		Constant roles (CR)		Temporary role reversal (TRR)
	All Subjects		Group A	Group B	Group A	Group B
1	30		40	20	40	20
2	30		40	20	20	40
3	30		40	20	40	20
Sessions	5		7		7
Subjects	120		168		168
Global groups	20		28		28
Matching groups	10		14		14

The table presents the different treatments and corresponding endowments of subjects in the different parts of the experiment. Furthermore, the table presents the number of sessions conducted in each treatment, the number of subjects in a treatment and the resulting number of observations at the matching group level. In the EE treatment, subjects have an endowment of 30 in all three parts of the experiment. In the CR treatment, rich subjects have an endowment of 40 and poor subjects have an endowment of 20 in all parts. In the TRR treatment, rich subjects and poor subjects change endowment positions in part 2

4 Discussion and conclusion

In this paper, we provide first evidence on cooperation decisions in a public good game with multiple group memberships in the presence of income heterogeneities. Additionally, we explore the impact of temporal change in endowment positions on voluntary contributions. Subjects are simultaneously members of a local group as well as a global group. They may contribute to a local public good that benefits only subjects of their own endowment category (cooperation with peers), a local public good that benefits subjects of the other endowment category (altruistic contribution), or to a global public good that benefits all subjects (global cooperation).

The impact of inequality is established by comparing the Equal Endowment condition (EE) with a setting where subjects had either a high or low endowment (IE). Our experimental data suggest that inequality in multiple group membership settings leads to a lower level of contributions of subjects with a high endowment. When benchmarked against the behavior of subjects with a low endowment and against the behavior of subjects with equal endowments, these subjects particularly contribute less to the global public good which benefits all subjects. This, in turn, aggravates income disparities between subjects with a high endowment and subjects with a low endowment. Additionally, this behavior reduces aggregate payoffs between treatments with endowment heterogeneity and the equal endowment group. Existing literature documents that efficient public good provision on a global level may already be problematic without inequality between groups (see, e.g., Fellner and Lünser Reference Fellner and Lünser2014). Inequality between groups seems to further reduce cooperation on a global level limiting the provision of efficient public goods which benefits all.

We investigated the impact of role reversal on cooperation and public good provision by comparing a Constant Roles condition (CR) with a Temporary Role Reversal condition (TRR). In TRR, high and low endowment subjects switched income positions in part 2 of the experiment, but the role reversal was revoked in the part 3 such that subjects switched back to their initial endowment position from part 1. We identify spillover effects from role reversal on behavior. Experiencing the other income position and being relatively worse/better off than the other group for a period of time affects behavior. The temporal role reversal increased contributions by subjects with a high endowment to their local but also to the global public good after initial roles are reinstalled. These additional contributions benefit subjects with a low endowment and thereby directionally moderate income inequality between groups. Subjects with a low endowment who experienced the high income position in part 2, however, were adversely affected as these subjects decreased their contributions. Yet, the average effect on subjects with a low endowment is substantially weaker. Our findings suggest that cooperation within and between heterogeneous groups is more stable if the groups also experience the situation from the viewpoint of the other group.

Our findings complement the literature on cooperation in public goods games by studying inequality in a multiple public goods setting. In addition, we contribute to the literature by showing that role reversal which affects behavior in other experimental economic games, e.g., trust, dictator and bargaining games also affects cooperation in public goods games. Our findings thus add a new mechanism which helps increasing cooperation in public goods settings with inequality to the experimental tool box.

While our results on the behavior of students in the laboratory are confined to relatively low stakes (and thus inequality levels),Footnote ²⁵ we may cautiously interpret our finding in light of real world cooperation problems. Many economic cooperation problems exist in which some parties may temporarily be better able to contribute than others. Our findings suggest that cooperation in volatile environments in which the relative ability of actors to cooperate changes and actors can associate with the disadvantageous position of others may be more stable. Although difficult to implement in practice, our findings may inform policymakers interested in reducing inequality at the societal level. We provide evidence that experience may (to some extent) foster cooperation. Thus, increasing the interaction between rich and poor within a society and raising awareness for the situation of the other side might be a tool to increase support for the provision of public goods benefiting society as a whole. Although forced participation in social programs that raise awareness of living conditions of others, however, may be difficult to implement some variations of such policy tools may be possible. Some countries, for instance, offer alternative social work (e.g., in poor communities) as an alternative to military service.Footnote ²⁶ Implementing programs with a mandatory period of social service for everyone graduating from school/in school may thus be realistic (e.g., a temporarily limited mandatory internship at a not for profit organization helping the poor). However, we identified only moderate effects from an exogenously imposed role reversal. As such the gains from encouraging people to “put themselves into the shoes of others” might be limited.

To fully assess the potential of role reversal, further research in the lab and in the field is needed. It appears important to identify determinants of changing attitudes towards cooperating at the local vs. global level, i.e. caring for people alike or people who differ.