1 Introduction

In a wide array of charitable donation situations, donors care about a public good that they cannot directly provide. Consider for example programs designed to increase biodiversity in rainforests, or to facilitate education in order to reduce poverty in lower income countries. In such situations, there is a group of individuals (insiders) that can undertake effort (herein contributions) to provide a public good that benefits themselves and a broader group of individuals (outsiders). Outsiders cannot directly provide the public good, for example due to technical, institutional, or geographical restrictions, but can make donations in the form of rewards transferred to the insiders to financially support them in their efforts. Numerous forms of institutions supporting charitable giving, such as local, national, or international charitable organizations, allow outsiders to make donations to insiders who provide an array of goods and services, including environmental conservation, education, or healthier living conditions. Prominent examples are Payments for Ecosystem Services (PES) or conditional cash transfer programs for poverty alleviation. Charitable organizations typically face more requests for support than financial resources available. Thus, a critical institutional design question is how best to allocate limited donations among the different public good providers. For example, previous literature has proposed tournaments as a mechanism to distribute foreign aid to alleviate poverty (see, for example, Epstein & Gang, Reference Epstein and Gang2009; Svensson, Reference Svensson2003). Similarly, conservation auctions are used to distribute pre-defined PES contracts among ecosystem providers (see Ferraro, Reference Ferraro2008). Field trials have shown that discriminative-prize auctions have the potential to increase program outcomes (Khalumba et al., Reference Khalumba, Wünscher, Wunder, Büdenbender and Holm-Müller2014; Ulber et al., Reference Ulber, Klimek, Steinmann, Isselstein and Groth2011). Motivated by this literature and importance of such programs, in this laboratory study we address allocation mechanisms based on competition between recipients of donations in a dynamic setting where donors and public good providers interact over multiple decision rounds.

A novelty of the experimental evidence presented herein is that in the contest settings under consideration public good providers compete for the endogenous funding from outsiders. The primary question being examined is whether the degree and form of exclusion in the contest mechanisms significantly affects the level of public good provision by insiders and the level of donations (herein transfers) from outsiders. This allows us to assess the impact on public good provision of policies that exclude lower performing individuals relative to policies that are fully inclusive. By focusing explicitly on contests, this study differs from the previous experimental studies investigating endogenous transfers by outsiders to insiders of public goods (see Blanco et al., Reference Blanco, Haller and Walker2018, BHW henceforth; Blanco et al., Reference Blanco, Struwe and Walker2021, BSW henceforth). One of the results from this previous literature is that transfers from outsiders do not increase public good provision if transfers are allocated equally (BHW), while it significantly increases public goods provision if transfers are distributed proportional to effort (BSW). Other institutional characteristics such as conditionality of payments or additionality requirements are not found to be critical. By considering endogenous prizes (transfers to insiders through donations from outsiders), this study contributes to the literature on competition among providers of public goods, investigating competition in settings where prizes are not fixed and stable over time, but rather are based on the repeated prosocial or reciprocal decisions by outsiders to the efforts of insiders.

Specifically, we consider a Winner takes All contest (WA) where the insider with the highest contributions in a group receives all transfers made by the group of outsiders and a Loser gets Nothing (LN) contest where the insider with the lowest contribution in a group receives no transfers and transfers are proportionally shared among the remaining three insiders. WA and LN are compared to a contest without exclusion, where transfers are distributed proportionally based on insiders’ relative contributions, Prop, and a setting with no transfers, No-T. All treatments start with an initial phase where insiders provide the public good with benefits to themselves and outsiders, who are inactive. This means groups create a history in providing the public good in the absence of transfers from outsiders and consequently allows us to assess the impact that the contests have relative to each group’s pre-contest cooperativeness. In all contests, after the initial phase, the decision setting then becomes a two-stage game where in stage one outsiders make independent transfer decisions. In stage two insiders observe the sum of transfers offered by the outsiders to the group of insiders and make independent contribution decisions. Transfers are then distributed to insiders based on the specific rules of the contests. Note that WA and LN can be viewed relative to each other as two extreme approaches in applying exclusion based on relative contributions. WA is a contest with extreme exclusion (all insiders excluded except one) while LN is a contest with the mildest exclusion (one insider excluded). Both WA and LN contests have characteristics of all-pay auctions. The experimental economics discipline has a long history of studying auctions as allocation mechanisms (see Kagel & Levin, Reference Kagel and Levin2011, for a general overview, and Dechenaux et al., Reference Dechenaux, Kovenock and Sheremeta2014 for all-pay auctions in particular). To the best of our knowledge, this is the first experimental study to examine behavior in auction-type contests in decision settings in which there is endogenous interaction between donors and public good providers.

There is consensus in the theoretical and experimental literature that contests increase effort, both in individual task settings (see Dechenaux et al., Reference Dechenaux, Kovenock and Sheremeta2014; and Sheremeta, Reference Sheremeta2018 for overviews), and in public good provision settings (Corazzini et al., Reference Corazzini, Faravelli and Stanca2010; Lange et al., Reference Lange, List and Price2007; Morgan, Reference Morgan2000; Morgan & Sefton, Reference Morgan and Sefton2000; Orzen, Reference Orzen2008). Considering first the literature on contests involving individual tasks, the results addressing the performance of single versus multiple-prizes are mixed, suggesting that the relative performance of winner or loser contests are context dependent. For example, Moldovanu and Sela (Reference Moldovanu and Sela2001) provide theoretical evidence for contests with multiple prizes in which agents have private information about their effort ability affecting costs. The authors show that for linear or concave effort cost functions, single prizes maximize expected efforts, however when costs are convex multiple prizes might be optimal. Cason et al. (Reference Cason, Masters and Sheremeta2018) compare both theoretically and experimentally a single winner-take-all prize lottery and a deterministic contest in which prizes are shared proportional to effort. The single prize contest leads to higher effort (desirable to contest designers), while the proportional share rule generates more equitable payoffs to the contest participants. Similarly, Sheremeta (Reference Sheremeta2011) show that a single prize lottery outperforms a multiple-prize lottery in terms of aggregate effort. In contrast to these studies, Dutcher et al. (Reference Dutcher, Balafoutas, Lindner, Ryvkin and Sutter2015) use rank-order tournaments with deterministic prizes and find that a proportional mechanism including a top, middle and bottom prize induces the highest effort, followed by a single loser contest, and a single winner contest being the worst performing contest.Footnote ¹

Closest to our decision setting is the literature on competition for exogenous prices in single group public good settings, where contributions of one group member provide positive externalities to other group members.Footnote ² In these studies, the size of contest prizes is exogenously pre-defined and financed either by the experimenter or by being deducted from the group’s contributions to the public good. The distribution of prizes is subsequently based on individual contributions relative to the group’s aggregate contributions to the public good, either probabilistically through lotteries or deterministically through all-pay auction settings. In these settings, the experimental evidence suggests that a single prize (winner takes all) yields higher public good provision compared to multiple prizes (including the case of loser gets nothing). For example, by extending the single-prize lottery in Morgan (Reference Morgan2000) and Morgan and Sefton (Reference Morgan and Sefton2000) to a lottery with multiple-prizes, Lange et al. (Reference Lange, List and Price2007) find that the winner takes all outperforms the loser gets nothing in terms of total provision of a public good. Similarly, using a field experiment on donations, Landry et al. (Reference Landry, Lange, List, Price and Rupp2006) find that average donations are larger in a single prize lottery compared to a multiple prize lottery. Finally, using all-pay auction type contests, Faravelli and Stanca (Reference Faravelli and Stanca2012) study public good provision within groups, comparing single winner prizes to a case with multiple winners receiving equal prizes and excluding the lowest contributor. They find that public good contributions are the highest with a single winner prize. As compared to these settings, we are the first to study single versus multiple prize contests in a setting where donors make endogenous donations that determine contest prizes and benefit from public good investments.

Further, by considering the decisions of donors to subsidize the provision of public goods, this study contributes to the large body of literature on the behavioral drivers of charitable donations (e.g. Andreoni, Reference Andreoni1990; Vesterlund, Reference Vesterlund2003; Frey & Meier, Reference Frey and Meier2004; Bénabou & Tirole, Reference Bénabou and Tirole2006; Ariely et al., Reference Ariely, Bracha and Meier2009; Gneezy, et al., Reference Gneezy, Keenan and Gneezy2014; Garcia et al., Reference Garcia, Massoni and Villeval2020). By allowing interactions between donors and public good providers over multiple decision periods, we address the relevance of competition in the dynamic interaction between donations and the public good efforts that donations support. Thereby, this study intersects with a broad program of economic research that deals with social preferences (e.g. Cooper & Kagel, Reference Cooper, Kagel, Kagel and Roth2015), as well as cooperation and strategic interactions between groups (e.g. Cooper & Kagel, Reference Cooper and Kagel2005; Kagel & McGee, Reference Kagel and McGee2016).

In the insider–outsider setting we study, we find that all three contest settings increase contributions to the public good relative to the setting with no transfers. We find that the WA and the LN contests yield similar increases in public good provision. Moreover, the WA outperforms the proportional sharing contests initially, but this difference vanishes over time. Lastly, we find that donors offer contest prizes at similar levels across contests. In this sense, our results point to the value of competition in allocating transfers from donors that can be used for multiple projects. On the other hand, the results suggest that contests that fully exclude subsets of public good providers from receiving transfers may not achieve better outcomes than inclusive mechanisms distributing transfers proportional to effort, which might be politically more attractive.

The remainder of this manuscript is structured as follows. In Sect. 2 we present the decision setting and hypotheses. In Sect. 3 we describe the experimental design and procedures. Sect. 4 presents an overview of the data, average treatment results and determinants of individual behavior across treatments. We conclude by discussing the results and respective policy implications in Sect. 5.

2 Competition in insider–outsider settings

The insider–outsider decision settings consist of a group of $n_I$ insiders and $n_o$ outsiders. Insiders can make contributions $g_i$ out of endowment $w$ , with $g_i\in \left(0,w\right)$ to a Group Account $G={\sum }_{i=1}^{n_I}{g}_i$ that constitutes a public good with an equal marginal return of $a$ for insiders and outsiders, where $\frac{1}{(n_I+n_O)}<a<1$ , so that the cumulative value of a contribution across all recipients (insiders and outsiders) exceeds the marginal cost of a contribution. Outsiders cannot make contributions but benefit from public good provision. However, outsiders can send transfers $t_j\in \left(0,,,w\right)$ from an endowment $w$ to compensate insiders for their contributions. Transfers from outsiders are added together in a Transfer Account of size $T={\sum }_{j=1}^{n_o}{t}_j$ . The Transfer Account is distributed to insiders through the different contest mechanisms based on the treatment condition. Importantly, because transfers are distributed after insiders have made their contribution decisions, transfers do not increase the resources insiders have for making contributions but enhance their payoffs in the form of rewards. Maximum efficiency in public good provision is achieved when insiders contribute their full endowments to the public good.

A broad range of research has analysed the complex and diverse motivations in social dilemma settings beyond simple self-income maximization (see Sugden, Reference Sugden1984; Ostrom & Walker, Reference Ostrom and Walker2003; Camerer & Fehr, Reference Camerer and Fehr2006; Chaudhuri, Reference Chaudhuri2011; Cooper & Kagel, Reference Cooper, Kagel, Kagel and Roth2015). One of them is the basic human motivation of cooperation (Andreoni, Reference Andreoni1995;Henrich et al., Reference Henrich, Boyd, Bowles, Camerer, Fehr, Gintis and McElreath2001; Goeree et al., Reference Goeree, Holt and Laury2002; Brandts et al., Reference Brandts, Saijo and Schram2004; Kagel & Schley, Reference Kagel and Schley2013).Footnote ³ Previous evidence in the donors – public good providers environment studied here (BHW and BSW) shows significant positive levels of public good provision and transfers under varied allocation mechanisms for transfers. Thus, we allow that outsiders derive some non-monetary utility from offering transfers to insiders, given by $y_j\left(t_j\right)$ , with $y_j\left(0\right)=0,$ $y_j^{{}^{\prime }}\left(t_j\right)>0$ , and $y_j^{{}^{″}}\left(t_j\right)<0$ .Footnote ⁴ Eq. (1) gives outsiders’ utility function in a given period:

(1) $U_{\mathrm{Oj}}=w+aG-t_j+y_j\left(t_j\right)$

For the competition settings, an insider’s utility function in a given period is given by Eq. (2).

(2) $U_{\mathrm{Ii}}=w-g_i+aG+z\left(g_i,g_{-i}\right)T+f_i\left(g_i\right)$

As in Orzen (Reference Orzen2008), $z(.)$ represents the allocation rule of the prize in a given contest and $g_{-i}$ is the vector of contributions of the other members of the group. The function $z(.)$ links relative contributions of insiders to the amount of rewards to be received, designating a competitive rewarding scheme defined for each specific contest, as described in Sects. 2.1 and 2.3 We also assume that insiders may derive utility from the act of giving, given by $f_i\left(g_i\right)$ , with $f_i\left(0\right)=0$ , $f_i^{{}^{\prime }}\left(g_i\right)>0$ and $f_i^{{}^{″}}\left(g_i\right)<0$ .Footnote ⁵

Note that if we presume self-interested profit-maximizing preferences for outsiders, that is if $y_j\left(t_j\right)=0$ for all $j$ , outsiders’ marginal utility from sending transfers would be $\frac{\partial U_{\mathrm{Oj}}}{\partial t_j}=-1$ . Being negative, outsiders would send no transfers and consequently there would be no contests, as the transfer account remains empty and no prize is offered. Thus with $y_j\left(t_j\right)=0$ there would be no treatment variations in outsiders’ behavior ( $t_j=0$ for all $j)$ .

Further, if in addition to $y_j\left(t_j\right)=0$ , we also assume $f_i\left(g_i\right)=0$ for all $i$ , that is, self-interested profit-maximizing preferences for insiders, their marginal utility from contributing to the public good would be $\frac{\partial U_{\mathrm{Ii}}}{\partial g_i}=-1+a$ . Since we have assumed that $a<1$ , $\frac{\partial U_{\mathrm{Ii}}}{\partial g_i}<0$ and consequently $g_i=0$ for all $i$ . In sum, with self-interested profit-maximizing preferences $t_j=0$ , $g_i=0$ , and earnings for all participants would be that of their initial endowment.

It is sufficient that $y_j\left(t_j\right)>0$ to change the result above based on purely self-interested behavior by insiders and outsiders. If outsiders derive sufficient utility from sending transfers, specifically if $y_j^{{}^{\prime }}\left(t_j\right)>1$ , $\frac{\partial U_{\mathrm{Oj}}}{\partial t_j}=\left(-1+y_j^{{}^{\prime }}\left(t_j\right)\right)>0,$ they would send positive transfers ( $T>0)$ . Insiders would now find themselves in contests for an expected prize equal to their expected share of the transfer account, where the share received varies across treatment conditions based on relative contributions. If the size of the expected prize $z\left(g_i,g_{-i}\right)T$ is sufficiently large, insiders would have an incentive to contribute to the public good. In such cases, the marginal utility for insiders from contributing is larger in all contests than in the decision setting with no transfers, as insiders receive a higher (expected) marginal utility from contributing due to transfers from outsiders $.$ Notice that the expected prize can motivate $g_i>0$ even for fully self-interested profit-maximizing public good providers, with the optimal value of $g_i$ varying for the different treatment conditions, as discussed further in Sects. 2.1 and 2.3. This outcome provides a critical difference between this study and the decision settings previously considered in BHW and BSW.

Below, we will assume that $y_j\left(t_j\right)>0$ and $f_i\left(g_i\right)>0.$ Previous evidence shows that: (i) insiders make positive contributions to the public good even when the outsiders are inactive (BHW), supporting an interpretation that insiders derive utility from providing the public good (even if outsiders cannot offer transfers), and (ii) outsiders make positive transfers when allowed, a result that can be supported by reciprocity or other social motivations such as fairness (see, for example, Kagel et al., Reference Kagel, Kim and Moser1996 who suggest fairness as one reasonable motivation for reciprocal actions, and Fehr & Schmidt, Reference Fehr, Schmidt, Kolm and Ythier2006 for an overview of the impact that fairness considerations have on cooperation).

2.1 Proportional contest

With the proportional contest mechanism, the distribution of transfers from outsiders is proportional to insiders’ individual public good contributions, thus $z\left(g_i,g_{-i}\right)=\left(\frac{g_i}{\text{G}}\right)$

Adding $z(.)$ into Eq. (2) gives an insider’s utility function for the proportional contest.

(3) $U_{\mathrm{Ii}}=w-g_i+aG+\left(\frac{g_i}{\text{G}}\right)T+f_i\left(g_i\right)$

An insiders’ marginal utility from contributing to the public good is given by

(4) $\frac{\partial U_{\mathrm{Ii}}}{\partial g_i}=\left(\frac{G_{-i}}{{\text{G}}^2}\right)T-1+a+f_i^{\prime }\left(g_i\right)$

where $G_{-i}$ is the sum of contributions of other insiders (excluding i). As shown by Eq. (3), due to the additional marginal utility from contributing associated with transfers, insiders in the proportional contest have a higher incentive to contribute to the public good as compared to insiders in the no-transfers condition (where $T=0$ ).

2.2 Winner-takes-all contest

In the winner-takes-all contest, the insider with the highest contribution in a group receives the entire Transfer Account ( $T$ ). Thus, this contest formally resembles an all-pay auction, in which all agents have the same endowment, which is public information, and the distribution of the prize to the highest contributor is deterministic.Footnote ⁶ This type of game has been formally analyzed in Orzen (Reference Orzen2008). As in that model, $z(.)$ defines here a deterministic allocation of the contest prize, where the insider with the highest contribution wins, subject to a tie-breaking rule. Thus,

(4) $z\left(g_i,g_{-i}\right)=\left(\begin{array}{cc}1& if{g}_i>max\left(g_{-i}\right)\\ \frac{1}{m}& incaseitieswithm-1otherplayers\\ 0& if{g}_i<max\left(g_{-i}\right)\end{array}\right)$

Considering only potential earnings from winning, an insider’s optimal behavior in the WA contest depends both on the expectation of the behavior of other insiders, and on the size of the prize. Specifically, following the proof presented in Orzen (Reference Orzen2008), one can show, if $0<T<\left(1,-,a\right)\ast n\ast w$ , insiders will randomize their contributions following the cumulative distribution function $F\left(g\right){=\left(\frac{\left(1,-,a\right)g}{T}\right)}^{\frac{1}{n-1}}$ on the interval $\left(0,,,\frac{T}{(1-a)}\right)$ . This implies, based on payoff maximization, that the maximum amount an insider is willing to contribute is ${\widehat{g_i}}_{\mathrm{WA}}=\frac{T}{(1-a)}$ , independent of expectations regarding the behavior of others. Notice that there can be situations where it is profitable for the insider to contribute more than the Transfer Account, and contribute up to their endowment $w$ , even if $T<w$ . How much to contribute below this threshold ${\widehat{g_i}}_{\mathrm{WA}}$ , will depend on the expectations of others’ behavior. Disregarding motives other than maximizing earnings, insiders would want to win with the lowest possible contribution. In the limit, if an insider i expects $g_{-i}=0$ , for any positive $T$ , the best response of i would be to contribute one unit and thereby receiving the full Transfer Account, as opposed to tying with the other insiders and receiving only 25% of T. It follows that the best response of a different insider would be to increase their contribution by one unit above that of insider i. Thus, strategically, one can assume that insiders in this contest form an expectation at the margin of “beating” the second highest contributing insider. This iterative argument holds true until ${\widehat{g_i}}_{\mathrm{WA}}.$ Contributions above this level are strictly payoff dominated by contributing zero.

Alternatively, if $T\ge \left(1,-,a\right)\ast n\ast w$ , insiders have an incentive to contribute their full endowment (i.e. $g_i=w)$ . The intuition is the following: an insider expecting others in their group to contribute $w-1$ can increase their payoff by investing $g_i=w$ , making them strictly better off as compared to $g_i=0$ . At $T=\left(1,-,a\right)\ast n\ast w$ , insiders are exactly indifferent between tying with all others with contributions of w or deviating individually to zero contributions.

2.3 Loser-gets-nothing contest

In the loser-gets-nothing contest, the single insider with the lowest contribution in a group in a given period is excluded from receiving transfers. The Transfer Account is then shared among the remaining three insiders based on an insider’s contribution relative to the sum of contributions of the three remaining insiders.Footnote ⁷ In case there is no unique loser (i.e. if there is a tie for the lowest contribution between at least two insiders), the Transfer Account is shared proportionally among all insiders. Thus,

(6) $z\left(g_i,g_{-i}\right)=\left(\begin{array}{cc}\left(\frac{g_i}{{\text{G}}_w}\right)& if{g}_i>min\left(g_{-i}\right)\\ \left(\frac{g_i}{\text{G}}\right)& incaseofanyties\\ 0& if{g}_i<min\left(g_{-i}\right)\end{array}\right)$

where $G_w$ equals the sum of contributions of the top three insiders.

Observe that this contest has similarities with symmetric multiple-prize all-pay auctions with complete information (without a public good provision environment). Barut and Kovenock (Reference Barut and Kovenock1998) show that in such a contest only mixed strategy equilibria exist and that expected expenditures are highest by defining the lowest prize equal to zero, as we do.Footnote ⁸ Note, however, in the decision setting we investigate, once the loser is determined, the size of the individual prizes to each of the winners in the LN contest are not fixed but are based on each winner’s contribution relative to the total contributions by all outsiders in that particular decision period. This feature makes our loser-gets-nothing contest similar to the proportional contest. Specifically, note that there are two cases when the payoff structure is identical to that of the proportional contest, namely (i) in case of ties at the lowest contribution, and (ii) in case that at least one insider in the proportional contest contributes zero to the public good. Increasing the number of insiders in a group, the loser-gets-nothing contest converges to the proportional contest.

As in the winner-takes-all contest, if an insider expects the other group members to contribute zero, she has an incentive to contribute one unit and thereby receiving the full Transfer Account (the same holds true for the proportional contest). However, contrary to the winner-takes-all scenario, increasing contributions further in order to be the highest contributing individual only results in an increase in the proportional share of transfers received, not $T$ . Thus, for a given level of contributions $g_{-i}$ and payoff maximization, the maximum amount an insider is willing to contribute depends directly on the expected behavior of others, and is given by ${\widehat{g_i}}_{\mathrm{LN}}=\frac{T}{(1-a)}-g_{-k}$ , where $g_{-k}$ are the expected contributions of the other two members in a group receiving transfers (i.e. excluding the expected contribution of the lowest contributor). In addition to the return from the public good, contributions above $\widehat{g_i}$ imply that the proportional share from transfers received (for an insider that is not the lowest contributor) is strictly lower than the individual contribution, and so the insider is better off contributing zero. Notice, for a given level of $T$ , unless $g_{-k}$ is expected to be zero, ${\widehat{g_i}}_{\mathrm{LN}}$ is per definition strictly lower than ${\widehat{g_i}}_{\mathrm{WA}}$ .

3 Experimental design and procedures

Table 1 provides an overview of the four treatment conditions (WA, LN, Prop and No-T) implemented and the respective attributes of the decision settings. The data from Prop were initially reported in BSW. All remaining data presented herein is previously unpublished. We conducted a total of 20 experimental sessions during March 2018 and January 2020 at the EconLab of the University of Innsbruck, Austria, consisting of 24 participants per session. The experiments were programmed using zTree (Fischbacher, Reference Fischbacher2007) and subjects were recruited using the HROOT system (Bock et al., Reference Bock, Baetge and Nicklisch2014). Our sample consists of 53.7% females and participants are on average 22.4 years old (sd = 0.14).

Table 1 Overview of implemented treatment conditions

Treatment	Contest	Nr. of observations
WA	winner-takes-all contest	13 groups 104 subjects
LN	loser-gets-nothing contest	12 groups 96 subjects
Prop	proportional contest	21 groups* 168 subjects
No-T	no contest	14 groups 112 subjects
Total		60 groups 480 subjects

^*The data collection took place in two waves, one in 2018, with 12–14 groups per treatment, and one in 2020 that started with the proportional treatment, reaching the full set of planned observations (about 20 groups in each treatment). Due to the outbreak of Covid-19 in the spring of 2020 and ongoing restrictions with running laboratory experiments, we could not complete the observations for the other treatments. Section 1 in the Supplementary Matierals presents a robustness analysis on treatment effects considering only the 2018 observations for Prop. The main text includes all observations, for transparencyFootnote ¹¹

An experimental group is composed of two randomly assigned types of subjects, $n_I=4$ insiders and $n_O=4$ outsiders, for a total group size of 8. An experimental session consists of multiple decision-making periods and includes two parts, 5 periods of Part 1 and 10 periods of Part 2. Part 1 is equivalent in all treatments. Subjects learned the decision-making details of Part 2 only after the completion of Part 1. Subjects participated in only one of the treatment conditions in a between-subjects design. Groups and participants’ roles remained fixed for the duration of the experiment. Instructions were read aloud by the experimentalist (see the Supplementary Materials for instructions, which were common knowledge among insiders and outsiders) and subjects were required to answer a series of control questions on the screen before making decisions.

In Part 1, in all treatment conditions, outsiders are inactive and insiders make contributions $g_i$ from an endowment of $w=100$ ECUs (Experimental Currency Units), with $g_i\in \left(0,100\right)$ to the Group Account $G$ that constitutes a public good with an equal marginal per capita return of $a=0.4$ for insiders and outsiders. Outsiders have an equivalent endowment of $w=100$ ECUs, but cannot make allocation decisions, they simply receive the benefits of the public good provision by insiders, which is common information. Outsiders were, however, asked to provide an estimate of the average individual contribution of insiders to the Group Account in the given period. It can be argued that in most (or many) field settings with insider–outsider interactions there is a history where insiders provide a public good with benefits extending to a broader population. Including Part 1 in the experimental design is important as we are interested in providing such a history, where insiders have not been compensated for their contribution efforts. Further, Part 1 provides evidence of variation across groups within a treatment and serves as a statistical control when examining variation in behavior due to treatment effects.

The decision-making setting in Part 2 depends on the specific treatment condition. The role of outsiders, and the specific allocation of transfers varies depending on the specific treatment condition. In the No-T decision setting, Part 2 is equivalent to Part 1. In the treatments with transfers, Part 2 becomes a two-stage game. In stage 1, each outsider makes a transfer decision $t_j\in \left(0,100\right)$ to be sent to the insiders in the form of the Transfer Account. In stage 2, insiders are informed of the size of the Transfer Account and make their Group Account contribution decisions, as in Part 1. Similar to the estimate that outsiders provided on insiders’ expected behavior, insiders were asked to provide an estimate on their expectations about outsiders’ average transfer offers.Footnote ¹² At the end of each period in Part 2, the sum of contributions is communicated to all subjects in a group. Both insiders and outsiders are also informed of the collective contributions of insiders and the collective transfers of outsiders, as well as their individual earnings. Importantly, in none of the contest treatments is the group informed about individual insiders’ contributions and which insider in a group won or lost the respective contest, such that there is no reputation building across decision rounds.

In the Prop treatment, at the end of each period, each insider is privately informed of the amount of transfers they receive, as well as the share of transfers it represents. In the WA treatment, at the end of each period, insiders receive feedback on whether or not they are the highest contributor in the group and thus whether or not they receive the Transfer Account. Importantly, if there is a tie for the highest contributor, the group is informed of the tie and the Transfers Account is shared equally among the winners who are informed of their share of transfers in that case. In the LN treatment, in the case of a unique lowest contributor, at the end of a period, the lowest contributor learns (s)he was the insider with the lowest contribution in the group and thus receives no transfers. The remaining group members are privately informed of their share of the Transfer Account. If there is a tie for the lowest contribution (i.e. no unique lowest contributor), the group is informed of this and the Transfer Account is shared proportionally among all four insiders in a group.

5 Discussion and conclusion

This study examines the behavioral response to three contest mechanisms used for distributing donated transfers from outsiders to insiders who contribute to a public good benefiting both groups. The mechanisms differ in the degree of competition among insiders within a group for transfers. In addition to a contest where transfers are allocated to individual insiders in proportion to their contributions relative to other insiders in their group (Prop), we study two contests which allow for exclusion from receiving transfers, namely a winner-takes-all (WA) and a loser-gets-nothing (LN). We compare behavior in these three decision settings to the default setting of no-transfers (No-T).

We report three main results. First, we find that all contest mechanisms generate an increase in public good provision relative to No-T. Second, as compared to Prop and LN, the WA contest generates greater increases in public good provision in the first period in which transfers are allowed. Third, across repeated periods of the decision settings, the observed differences vanish and the two contests with exclusion result in similar levels of public good provision relative to that of the proportional contest.

Thus, competition is found to be a useful mechanism to increase program outcomes in terms of public good provision, while contests with exclusion are not found to bring additional significant and stable increases in public good provision as compared to inclusive proportional prizes. From a policy perspective, our results can be considered as evidence in support of charitable giving programs that rely on inclusive programs such as proportional payments. This policy implication is reinforced by previous experimental results showing that inclusive proportional payments have a similar impact than individually targeted payments and do better than equal payments (BSW). Inclusive proportional payments have additional advantages in that they are simpler to implement in field settings, simpler to communicate, simpler to enforce, and may be perceived as outcome-based fairer (Wells et al., Reference Wells, Ryan, Fisher and Corbera2020). Importantly, based on the results in this study and in BSW, the evidence points to the conclusion that inclusive proportional payments are able to sufficiently motivate donors, which is also critical to overall program success (Wunder et al., Reference Wunder, Brouwer, Engel, Ezzine-De-Blas, Muradian, Pascual and Pinto2018, Reference Wunder, Brouwer, Engel, Ezzine-de-Blas, Muradian, Pascual and Pinto2020).

The results related to the effects of implementing the different contests in our insider–outsider decision setting were not expected. In particular, evidence from prior experimental studies suggests that exclusion in single winner prizes generates greater public good contributions, both for Tullock-style lottery contests and all-pay auctions (e.g. Faravelli & Stanca, Reference Faravelli and Stanca2012; Lange et al., Reference Lange, List and Price2007). We conclude that the differences in our insider–outsider decision environment, as compared to other studies, is the source of these differences in behavior. In particular, previous studies entail exogenous prizes to a single-group of individuals providing the public good. Our decision settings, however, include group-to-group interactions between outsiders and insiders, where outsiders provide endogenously determined transfers (prizes) to insiders who compete for transfers through their contributions.

Considering the determinants of individual behavior in the contests, we interpret our results as evidence for positive across-group reciprocity from insiders to the behavior of outsiders and vice versa.Footnote ²² From the perspective of outsiders, this evidence is found to be more robust in Prop than in WA and LN. This latter result raises the question of why outsiders' response to insiders’ behavior might differ between the three contest treatments. In a related study that focused on self-reported motivations of outsiders there is evidence of three primary motivations: cooperation, egoism and insider–outsider-reciprocity (Struwe et al.,, forthcoming). While the insider–outsider reciprocity motivation negatively affects transfers in WA, it has no effect in Prop or LN. Further, outsiders report to be overall less satisfied with the behavior of insiders in WA and LN as compared to Prop, leading to a significant negative effect on transfers in the case of the WA contest. These results suggest the need for further research on fairness considerations in the insider–outsider group-to-group interaction, in particular, as related to the mechanisms used to allocate transfers to insiders.Footnote ²³

Broadly, our results contribute to the study of effective institutional design and implementation in a broad range of programs where donors provide transfer payments or donations. The research contributes to understanding the effectiveness of alternative funding mechanisms, in particular contests. For example, in conservation programs based on payments for ecosystem services, there is a recurring discussion on how to efficiently allocate scarce funds via compensation payments among landowners qualifying to participate. Our results support the conclusion that excluding low-performers from donor payments may not be more effective than inclusive proportional payments, where low-performers receive a positive but smaller amount than others who put in more effort. This conclusion supports the need for further research on testing the effectiveness of competition in increasing public good provision (or more broadly on pro-social behavior) under varied decision environments, specifically situations that rely on the distribution of endogenously funded contest prizes. This view is in line with the approach to research discussed in Cooper and Kagel (Reference Cooper and Kagel2009), where the authors provide an insightful discussion of context and learning across game types (decision settings), linking experimental research in economics and psychology.