Competition for talent: heterogenous abilities in team production

Abstract

Using public goods games in a laboratory setting, we study team-level production, where two teams compete for the resources of a common-member who can benefit from and provide effort in both teams. Intrinsically, the common-member faces divided loyalties. We examine such competition in a setting in which the common-member has productive abilities equal to that of the other team members (dedicated-members), and in two settings where he/she has greater relative potential. When effort (contributions) by the common-member have greater productivity (coupled with higher opportunity costs to contribute) in providing the public good relative to that of dedicated-members, we find team performance is not significantly increased. On the other hand, when the common-member has a greater endowment, sufficient to match the absolute contributions of team members in both teams, there is a significant increase in team performance. The evidence suggests that a norm of reciprocity by dedicated-members based on absolute contributions of the common-member better explains behavior than a norm based on the value added of the common-member's contributions. This behavior, along with fairness norms elicited in a survey, suggests that on average dedicated members do not sufficiently incorporate the common-members' higher opportunity costs in the treatment where his/her productivity is increased. This setting provides an important illustration of where the behavioral response to the type of inequality matters, leading to differences in team efficiency.

1 Introduction

Getting teams to work together to provide greater effort is a long-standing issue for firms/practitioners and scientists alike. A fundamental issue is the incentive to free ride on the efforts of other team members.¹ As a result, examining approaches for increasing effort in teams has received much attention in the experimental literature. Encouraging explicit competition between teams reduces free-riding and increases efficiency (e.g., Nalbantian & Schotter, 1997; Chan et al., 2014). More recently, there has been an investigation of the ability of ‘competition for talent’ to mitigate free riding in teams. In a laboratory setting, Ramalingam et al., (2019, henceforth RSW19) explore whether implicit competition for members with divided loyalties (individuals with joint team membership—the common-member) enhances teamwork and increases efficiency in team-level production (provision of a group-level public good). They find such competition may have limited effectiveness in increasing team effort (contributions). Instead, imposing an additional mechanism—the ability to expel team members—increases the efficacy of competition. Building on this prior study, this paper focuses on team contributions in two group-level public good settings where the common member has enhanced abilities relative to other team members.² In the first setting, the common member has greater productivity (value added) in team production than other team members (herein dedicated-members), but also faces higher opportunity costs of making contributions. In the second setting, the common member is endowed with greater resources than the dedicated-members.

Examining competition for talent of the common-member is motivated by real-life teams such as those found in many research collaborations, bands, departments/divisions within a firm, etc. In such cases, an individual can simultaneously work (e.g., either in the same vicinity or virtually) on multiple research projects, music collaborations, R&D or sales teams, while also benefitting from all of them. In addition, one can think of the competition among groups/institutions for the resources of others (such as donors who might think of themselves as “team” members), where donors make donations, in part, based on the quality of the output relative to other groups/institutions. As discussed in further detail below, our team competition setting is one of incomplete information (similar to many, if not most, team competitions in naturally occurring settings). In our decision setting, the common-member has complete information on the contributions of dedicated-members in both teams. However, dedicated members know only the decisions of members of their team which includes the common-member.

The public good decision setting captures the reality that in many team settings, at least for some time, team members benefit from the value created by other team members and exclusion (ostracism) is not feasible.³ Among the many examples, consider publications from joint research, successfulness of team ventures in jointly owned firms, record sales for groups of musicians, the level of donations of donors who see themselves as team members, etc.

Our setting for competition for the resources of the common-member is not meant to capture the dynamics of competition among teams when all members have common information on the contributions of all participants. We argue that the asymmetry in information is a common characteristic of many naturally occurring team competitions, especially of the type in which we are interested—competition among teams for the resources of a member with greater talent/resources. In addition to the examples above (and below) consider a decision setting such as an individual serving as a Director on the Boards of two companies, while also being a shareholder in both. He/she must decide how much time to devote to each Board. However, ethics and confidentiality requirements prevent him/her from divulging deliberations of one Board to another. The team member common to multiple groups is in the advantaged position of complete information on their contribution to each team and that of the members of each of the other teams. However, the reverse does not hold.

We add to the richness of the common-member setting by allowing heterogeneities in abilities and resource endowments across team members. These two settings capture realities in many settings where the common-member with divided loyalties is also more experienced, better funded, or more skilled than the dedicated-members. Indeed, it may be their higher skill and ability that allows them to be on multiple teams in the first place. For instance, it is often the best musicians who play in multiple bands and more senior researchers who collaborate on more projects simultaneously.

For a variety of reasons, some team members may be in a situation that allows them to provide additional resources, e.g., time or money to the team. For instance, in workplace teams, perhaps the common-member has connections with upper management that lead to additional firm resources being allocated towards his/her projects. In research collaborations, the common-member may have access to more funds available for his/her projects. Access to more RA hours can allow a common-member to spend more time on primary research projects/tasks. Thus, even when they can contribute to both teams, these common-members bring more to the table in each team to which they contribute. Common-members that are more “talented” are worth competing for.⁴

Our baseline treatment (CM) consists of two teams that separately produce their own team output (implemented as public good provision), and share one team member. Team members are homogeneous in their productive capacity. Based on a model of reciprocity (Sugden, 1984), the resources of the common-member are a binding constraint on contributions of dedicated-members. For instance, even if the common-member is contributing all his/her resources equally between the two groups, on average, this implies the common-member's contribution is at most half of the total of dedicated-members' resource capacity. Conditional cooperation, as implied by reciprocity, predicts dedicated-members, on average, will then only contribute up to half of their resources to team production. This theoretical observation and evidence from the CM treatment in RSW19 implies two natural ways to enhance the “talent” of the common-member in our experimental design that removes this binding constraint. The common-member's contributions to the team can be of greater value or the common-member has greater resources at his/her disposal, leading to the two treatments, Productivity and Endowment, studied herein.

In the Productivity treatment, the value of the common-member's contributions to team production are doubled. As discussed in more detail below, for experimental control purposes, the marginal opportunity cost to the common-member contributing to teams is also increased in Productivity. In the Endowment treatment, the common-member has double the endowment of a dedicated-member. From the perspective of reciprocity, the resources of the common-members are no longer a binding constraint on the contributions of dedicated-members. That is, in both Productivity and Endowment, common-members have sufficient resources to match the value of contributions of dedicated-members in both teams. This is the channel through which we expect that common-members with more talent will raise overall team-level production relative to the CM decision setting.

Only a few other experimental studies examine multiple group membership and divided loyalties. Falk et al. (2013) investigate multiple group membership in team production, where all individuals belong to two teams simultaneously, but no two individuals belong in more than one team together. No team member has divided loyalties since each member receives separate resource endowments for each team. In McCarter et al. (2014), every member belongs to two teams simultaneously, and receives only one resource endowment to be shared between the teams.⁵ Hence, every member has divided loyalties and thus there is no clear competition for any one team member. Moreover, all team members are homogenous in both studies. Martinangeli and Martinsson (2020) examine both heterogeneous and homogeneous societies. All individuals belong to two independent teams simultaneously and receive a separate endowment for each group. A “society” includes both homogenous rich and/or poor groups and heterogeneous groups. While their results follow the standard result in heterogenous stand-alone groups (that is, rich contribute a smaller percentage of their endowment than poor members—e.g., Hargreaves-Heap et al., 2016), rich members exhibit an increasing trend in their contributions to their own homogeneous group.

This study adds to the larger literature that examines the issue of finding methods for increasing effort in teams and possible paths to increasing efficiency.⁶ A large sub-area of the literature focuses on organizing contests between teams, where effort/bids in the contests double as contributions to an intra-team public good. More efficient teams receive an additional reward (e.g., Bornstein et al., 1990; Gunnthorsdottir & Rapoport, 2006; Hargreaves-Heap et al., 2015) or, upon winning the contest, receive a higher marginal per-capita return for their contributions (Tan & Bolle, 2007). The general consensus is that such explicit competition over outputs increases effort in teams (Chan et al., 2014; Chen & Lim, 2013; Guillen et al., 2014).

In contrast, we study implicit competition for resources across teams, a naturally occurring feature of teams where individuals are members of multiple teams. In many workplace settings, some members of teams perform multiple tasks, and thus have a choice of which task(s) to focus their efforts on. As discussed above, the novel aspect of our study is the examination of settings where heterogeneities among members lead to competition between teams for the contributions of more talented (productive) members.

Our results show that the source of greater ability of the common-member is a crucial determinant of the efficiency-enhancing effects of such competition. When a common member's contributions are more valuable as in Productivity, but his/her opportunity costs of contributing to a team are higher, gains in efficiency are muted. On the other hand, when a common-member has greater resources at their disposal as in Endowment, members of both teams are spurred to compete for those resources, thus leading to significant increases in efficiency through greater team public good contributions.

The difference in behavior we observe appears to be related to the prevalence of conflicting contribution norms in heterogeneous teams that arise as a result of differences in the nature of enhanced abilities of the common-member in Productivity and Endowment. As noted by Reuben and Riedl (2013), “In heterogeneous groups, however, it is not clear what contribution norm may emerge, if one emerges at all. If people differ, fairness principles of equality, equity, and efficiency will often stipulate different normatively appealing rules of behavior.” (p. 123) Two related studies examine normative conflict in games with heterogeneous returns from a public good. Nikiforakis et al. (2012) examine punishment in such games with the opportunity for counter punishment (i.e., feuds). Gangadharan et al. (2017) examine communication and rewards. In both papers, contributions and earnings are lower in heterogeneous groups than in homogeneous groups, providing evidence of the negative effects of normative conflict on cooperation. Importantly, results from our main experiments, and from supplementary experiments and a survey with teams without a common-member, show that, on average, the contributions of the enhanced common-members add approximately the same value to team production in both Productivity and Endowment. The contributions of non-enhanced dedicated-members are best explained by a norm of matching absolute token contributions of enhanced members. In the case of Productivity, this norm implies that dedicated-members, on average, largely ignore the greater value added of contributions by the common-member, as well as the greater opportunity costs of common-members in choosing the level of their contributions to the team public good, leading to lower efficiency in public good provision.⁷ We find that this norm creates behavioral spillovers (interdependence) across competing groups when common-members favor one group over the other. Reciprocity then implies that dedicated-members in the favored (other) group increase (decrease) their contributions in response.

Section 2 presents the game settings for CM and Productivity, as well as hypotheses that rely on a model of reciprocity. Section 3 contrasts behavior in Productivity with that of CM. Section 4 then presents the game setting for Endowment, hypotheses, and contrasts of behavior between CM and Productivity. Section 5 presents results from an additional experiment and a survey motivated by the initial findings exploring the prevalence of contribution norms in groups without a common-member. Section 6 concludes. Appendix A in the Electronic Supplementary Material includes additional data analyses supporting results presented in the main text, as well as results from additional experiments with no common-member in the Endowment treatment. Appendix B contains experiment instructions and screen shots. Appendix C contains the survey.

2 Competition in the CM and Productivity settings

2.1 The CM decision setting

In each decision round in CM, each group of n team members participates in providing a group good that yields homogenous returns to each group member, regardless of their contribution. In this sense, the group good is a team level public good. Each individual receives an endowment e > 0 that he/she can allocate between a group account (0 ≤ $g_i$ ≤ e) and a private account (e – $g_i$ ). The return from the private account is 1 while the return to the individual from the group account (the group good) is a fraction m (0 < m < 1 < mn) of the total allocation to the group account by all members of the group, $G={\sum }_j{g}_j$ . As is standard in the literature, herein we refer to allocations to the group account as contributions.

Team members participate in groups that are paired—Group X and Group Y. Each group consists of (n − 1) dedicated-members who belong only to that group, and one common-member who belongs to both groups. Figure 1 describes the interaction structure in the game (RSW19).

Fig. 1 Structure of interaction with divided loyalties

Each of the 2(n − 1) + 1 members receives an endowment of e > 0. Note that the common-member does not receive an additional endowment for belonging to multiple groups. Within the stage game, contributions to the group good by members of Groups X and Y impact only their group. Each dedicated-member can contribute to, and receive returns from, the group good in his/her group alone. The common-member can contribute to, and receives returns from, the group good in Groups X and Y.

The payoff of a dedicated-member i who belongs to Group $k\in \{X,Y\}$ is given by.

$\left(e,-,g_{\mathrm{ik}}\right)+m\sum _{j\in k}{g}_{jk.}$

In both groups, j includes the common-member. The payoff of the common-member, c, is given by

$\left(e,-,g_{\mathrm{cX}},-,g_{\mathrm{cY}}\right)+m\sum _{j\in X}{g}_{\mathrm{jX}}+m\sum _{l\in Y}{g}_{\mathrm{lY}}.$

As in standard in linear (VCM) public goods settings, assuming self-regarding preferences and common information, the single period Nash Equilibrium (as well as for finitely repeated decision settings) is zero contributions to the group account. Maximum group earning requires all group members to contribute their full endowment to the group account, where the common-member splits (not necessarily equally) his full endowment to contributions between the two groups.

2.2 Experimental procedures and treatment CM

In treatment CM, Group X and Group Y consist of two dedicated-members each and one common-member who is a member of both groups, i.e., n = 3. Each of the five subjects receives a per-round endowment of 20 tokens. Subjects simultaneously choose how many tokens to contribute to their respective group accounts, retaining the rest of the endowment in their private accounts. Each token retained in the private account yields a return of 1 token to the individual. Each token contributed to the group account yields a return of 0.6 tokens to each group member. This parameterization was chosen to allow for the potential for efficiency gains in groups consisting of only two dedicated members; that is, in situations which a common member does not contribute (or contributes little) to a particular group X or Y. Subjects interact repeatedly for 20 decision rounds, and this is public information provided before the first decision round.

Feedback at the end of a round included individual and total contributions to the group account, and a history of only total contributions in past rounds. Group members were identified by ID letters—A, B and C in Group X, and C, D and E in Group Y (C is the common-member). Dedicated members receive feedback on their own group and the common-member received feedback on both groups. Group members also see their own payoffs in the round, along with detailed steps showing how their payoffs from team output were calculated. They were not shown the payoffs of other group members. Screenshots of feedback screens are available in Appendix B.III.

All sessions were conducted at Appalachian State University using student subjects. Following the procedure used in RSW19, we implemented a between-subject design with randomly formed groups that stayed fixed throughout a session.⁸ Roles within groups (A–E) were also assigned randomly at the beginning and stayed fixed. Subjects were given printed instructions and, after 10 min, were presented a summary of important features of the game. Subjects answered control questions (available in Appendix B.II) to ensure understanding before the experiment began, and a short demographic survey at the end.

The experiment was programmed in z-Tree (Fischbacher, 2007). A total of 60 subjects (12 independent paired-groups of five subjects) participated in CM. In all treatments, accumulated token earnings from all 20 rounds were converted to cash at the rate of 30 tokens to US$1. Each session lasted approximately 60 min. Subjects earned an average of $18.90 (min = $13.37, max = $31.05, st. dev. = $4.20) in CM. Subjects were not paid a separate show-up fee.

2.3 Treatment productivity

The procedures for conducting Productivity are identical to those of CM, except in Productivity, the value of the contributions made by the common-member to the group account in each group was doubled. More specifically, each token contributed by a common-member generated a return of 1.2 tokens for each group member, as opposed to 0.6 tokens by a dedicated-member. Further, for experimental control, the return from the private account received by the common-member was also doubled from one token to two tokens. That is, the common-member's marginal rate of substitution between the group account and the private account was held constant to that of the dedicated-members (MPCR = 0.6). Note that without changing the private return, the common-member's marginal rate of substitution would be 1.2, greater than the return from allocations to his/her private account, making contributing a dominant strategy for the common-member. In summary, doubling the value of contributions made by the common-member enhanced the “talent” of the common-member, enhancing the rationale for competition between the dedicated-members of the two groups. Yet, the common-member's cost of contributing to either group account was twice that of dedicated members.

Feedback at the end of the round was the same as in CM. As mentioned above, the feedback explicitly showed the calculation of payoffs. This meant group members were reminded every round that the common-member's token contributions were doubled in value, relative to those of dedicated members, to calculate earnings from team production. The experimental instructions and control questions also informed all group members that the common-member received twice the return (relative to dedicated-members) for tokens maintained in his/her private account.

Importantly, common-members in Productivity and Endowment (discussed in more detail in Sect. 4) are equally talented in the sense of their ability to increase the value of group-level public goods. On the other hand, the two competing groups now face a different challenge in Productivity – the outside option for the common-member. That is, relative to dedicated-members, the opportunity cost to the common-member of contributing a token, i.e., the marginal opportunity cost doubled from 0.4 (= 1 – 0.6) tokens to 0.8 (= 2 – 1.2) tokens.

A total of 55 subjects (11 independent paired-groups of five subjects) participated in Productivity. Subjects earned an average of $21.33 (min = $11.38, max = $40.79, st. dev. = $6.31).

2.4 Reciprocity in teams that share a member in CM and productivity

In the stage game in both settings, the self-interested Nash equilibrium is zero contribution by all group members, while the social optimum is 100% contribution by all. Any split of the common-member's endowment to the group goods between the two teams is optimal. Models of reciprocity explain and predict positive contributions in voluntary contribution games (Falk & Fischbacher, 2006; Sugden, 1984). RSW19 present a model of contributions in teams with reciprocal members, extending the ‘principle of reciprocity’ introduced by Sugden (1984). More specifically, the model explains contribution behavior in a VCM setting where teams share a member with divided loyalties. Here, we briefly summarize the model for the CM decision setting, as presented in RSW19. We then build on that model to generate hypotheses for our new settings with enhanced members.⁹

The principle of reciprocity as developed in Sugden (1984) requires that in every possible sub-group (with at least one other member) in which a team member can be in, he/she must at least match the minimum contribution of the others in that sub-group. Here, we modify the model by changing the reference point for team members' contributions to match the average contribution of others in each team they belong to. This change reflects the finding of higher prevalence of matching the mean or median contribution (see Croson, 2007; RSW19).¹⁰

In our CM setting where all team members are equally productive, a dedicated member's decision problem in Group X is

$\underset{g_{\mathrm{iX}}}{\text{max}}\left(e,-,g_{\mathrm{iX}}\right)+m\sum _{j\in X}{g}_{\mathrm{jX}}$

subject to.

$g_{\mathrm{iX}}\ge {\overline{g}}_{-iX}$ and $g_{\mathrm{iX}}\le e$ , where ${\overline{g}}_{-iX}=(g_{\mathrm{jX}}+g_{\mathrm{CX}})/2$ (with $i,j\in \left(A,,,B\right),i\ne j$ ) is the average contribution of all other members of Group X. The decision problem for a dedicated-member in Group Y is equivalent.

The common-member's decision problem is

$\underset{g_{\mathrm{CX}},g_{\mathrm{CY}}}{\text{max}}\left(e,-,g_{\mathrm{CX}},-,g_{\mathrm{CY}}\right)+m\sum _{j\in X}{g}_{\mathrm{jX}}+m\sum _{k\in Y}{g}_{\mathrm{kY}}$

subject to

$g_{\mathrm{CX}}\ge {\overline{g}}_{-CX},g_{\mathrm{CY}}\ge {\overline{g}}_{-CY}$

and $g_{\mathrm{CX}}+g_{\mathrm{CY}}\le e$ , where ${\overline{g}}_{-CX}=(g_{\mathrm{AX}}+g_{\mathrm{BX}})/2$ and ${\overline{g}}_{-CY}=(g_{\mathrm{DY}}+g_{\mathrm{EY}})/2$ are the average contributions of the other team members in Groups X and Y respectively, and the final constraint is the resource constraint that follows from the observation that a common-member can split his/her resources between the two teams.

In the above model of reciprocity for CM, and assuming common-members contribute at least some resources to both teams (Result 2 in RSW19), even though dedicated-members are allowed to contribute 100% of their endowments, reciprocity will never oblige them to do so. This is the sense in which the budget constraint of the common-member creates interdependencies between Group X and Group Y. A common-member's decision to contribute (or not) to one group impacts the resources that he/she has to allocate to the other group. In particular, dedicated-members can infer that the more the common-member contributes to their group, the less they have to contribute to the other group. Thus, a common-member's decision has potential implications for the decisions of dedicated-members in both groups. This interdependence between the two groups and the incomplete information about the common-member's contribution to the other group are the reasons we envision competition will work to raise contributions of dedicated-members.

Further, in the case where dedicated-members make some contributions, reciprocity and the fact that the common-member in CM is allowed to split his/her resources between the two teams implies that his/her contribution will be below 100% of endowment in both teams. Thus, the average contribution that a dedicated-member is obliged to match in his/her team can never reach 100%, even if the other dedicated-member contributes 100% of his/her endowment. Moreover, the common-member's resource constraint also implies that even if both dedicated-members contribute 100% of their endowments, the common-member can never reciprocate this level of contribution in both teams. This further reduces the obligations of dedicated-members (in at least one team) and, hence, their contributions. The resource constraint faced by the common-member, through the interdependence it creates between the two groups, effectively acts as a binding constraint on pairs of teams achieving efficient outcomes in CM. Thus, the model of reciprocity specified above is consistent with a central finding in RSW19 of inefficient outcomes.

We now turn to the decision setting, Productivity. In this setting, the contributions of the common-member are twice as effective (twice the value added) as those of dedicated-members.¹¹ The resulting changes in the objective functions for the common-member and dedicated-members are one of scale alone, i.e., they merely reflect the increased productivity of the common-member's contributions. In particular, the objective function of the common-member is now given by

$\underset{g_{\mathrm{CX}},g_{\mathrm{CY}}}{\text{max}}2\left(e,-,g_{\mathrm{CX}},-,g_{\mathrm{CY}}\right)+m\left(\sum _{\begin{array}{c}j\in X\\ j\ne C\end{array}},g_{\mathrm{jX}},+,2,g_{\mathrm{CX}}\right)+m\left(\sum _{\begin{array}{c}k\in Y\\ k\ne C\end{array}},g_{\mathrm{kY}},+,2,g_{\mathrm{CY}}\right)$

while a dedicated-member's objective function is given by

$\underset{g_{\mathrm{iX}}}{\text{max}}\left(e,-,g_{\mathrm{iX}}\right)+m(\sum _{\begin{array}{c}j\in X\\ j\ne C\end{array}}{g}_{\mathrm{jX}}+2g_{\mathrm{CX}})$

Since the actual endowments of group members (including the common-member) do not change, the resource constraints of all members remain unchanged.

The effect on the reciprocity constraints of the common-member and dedicated-members in Productivity is potentially more involved. The productivity differential essentially introduces heterogeneity among team members. Several works explore the impact of heterogeneity in such settings. For example, Cherry et al. (2005), Buckley and Croson (2006), Reuben and Riedl (2013), Kölle (2015) and Hargreaves Heap et al. (2016) examine heterogeneity in productivity, in resource endowments and in marginal benefits from team production.¹²

As noted in the Introduction, the study most relevant for us is Reuben and Riedl (2013), who compare two sources of heterogeneity—in endowments and in marginal benefits from the public good. They find evidence of the presence of two important “relative contribution norms”—equal contributions and contributions in proportion to benefits received. While they do not explore heterogeneity in productivity as we do, we extrapolate the findings in their heterogeneous benefit setting to our heterogeneous productivity setting. In particular, we postulate the effects of two corresponding contribution norms in our setting: (i) equal absolute contributions, and (ii) contributions in proportion to effectiveness (value added). In each case, we assume the same norm applies to all team members, dedicated and common. As shown in detail below, these two norms (and their expected effect on behavior) are based on the natural consequences of Sugden's model of reciprocity and the design of the two “enhanced” treatment conditions Productivity and Endowment, respectively.¹³

Such norms are relevant in our setting due to the crucial role played by the average contribution reference point in the reciprocity constraints. If the equal absolute contribution norm prevails, one is obliged to match the average absolute contributions (tokens) of other team members. If the proportional contribution norm prevails, one is obliged to match the average effective (value-added) contributions (i.e., productivity-adjusted tokens) of other team members. We deal with each in turn.

In the case of equal absolute contributions serving as the norm, the reciprocity constraints remain unchanged from CM, for both dedicated-members and the common-member. Importantly, the resources (token endowment) of the common-member still pose the same binding constraint on the output that teams can produce. As a result, the solutions also remain unchanged. Thus, if the equal absolute contribution norm is the relevant one, Productivity is not expected to lead to different outcomes relative to CM. This is our first hypothesis.

Hypothesis 1

(Equal absolute contribution norm): Efficiency in team public good provision in Productivity and CM are not different.

Now consider Productivity from the perspective of the proportional norm. This norm requires that dedicated-members recognize that each token contributed by a common-member is twice as effective as a token contributed by them. Because the common-member's contributions are doubled in value, this increases the average contribution that dedicated-members are obliged to match. More precisely, the constraints of a dedicated-member are now given by

$g_{\mathrm{iX}}\ge \frac{1}{2}(g_{\mathrm{jX}}+2g_{\mathrm{CX}})$

and $g_{\mathrm{iX}}\le e$ ,

while the constraints of the common-member are given by

$g_{\mathrm{CX}}\ge \frac{1}{2}{\overline{g}}_{-CX},g_{\mathrm{CY}}\ge \frac{1}{2}{\overline{g}}_{-CY}$

and $g_{\mathrm{CX}}+g_{\mathrm{CY}}\le e$ .

In Productivity, the resources of the common-member no longer present a binding constraint on the contributions of dedicated-members. Consider the case of achieving maximum efficiency within a group. Assuming the common-member splits his/her entire endowment equally between the two groups, each dedicated-member would need to contribute his/her entire endowment, if he/she chose to match the value of the common-member's contribution. All parties can meet their obligations. Unlike in CM or under the equal contribution norm, higher absolute contributions by dedicated-members (relative to the common-member's contributions) can now be sustained. This leads to the feasibility of maximum efficiency for the Group (X or Y). Thus, by eliminating the resource constraint faced by the common-member, and if the proportional contribution norm is the relevant norm, Productivity leads to higher public good provision than in CM. This leads to our second, mutually exclusive, hypothesis.

Hypothesis 2

(Proportional contribution norm): Efficiency in team public good provision is higher in Productivity than in CM.

3 Behavior in CM and productivity

When making comparisons across treatments, unless otherwise stated, p-values are reported from two-sided Wilcoxon ranksum tests (RS). When making comparisons within treatments, p-values are reported from two-sided Wilcoxon signrank tests (SR). In both cases, an independent observation is the average value of the relevant variable of interest. The number of observations in each ranksum test is the combined number of groups/pairs in the treatment comparisons, while signrank tests depend on the number of groups/pairs within a treatment. All results are supported by regression analysis. For the sake of brevity, we report the regression results in Appendix A.II.¹⁴

Table 1 reports the mean (over all 20 rounds) percentage efficiency in provision achieved by pairs (Group X and Group Y), measured as the value of total contributions (measured in tokens) earned in each round relative to the maximum possible value (i.e., the value of the group account in tokens when the full endowment is contributed). Figure 2 provides a measurement of efficiency achieved in pairs of teams across decision rounds. The maximum value of the group accounts in Productivity is 1.8*(20 + 20 + 20 + 20) + 3.6*(20) = 216 tokens. For comparison, the maximum value of the group accounts in CM is 1.8*(20 + 20 + 20 + 20 + 20) = 180 tokens. Actual earnings are calculated in a similar manner, except tokens remaining in the Private Account were valued at 1 token for dedicated-members and 2 tokens for common-members.

Table 1 Efficiency in contributions across treatments

Treatment	Independent pairs (subjects)	Mean efficiency (St Dev)
CM	12 (60)	52.19% (16.07)
		[93.94 tokens out of a maximum of 180]
Productivity	11 (55)	41.62% (14.94)
		[89.90 tokens out of a maximum of 216]

Fig. 2 Efficiency across decision rounds

Relative to CM, efficiency is weakly lower in Productivity (RS p = 0.0648). Thus, we find mixed support for Hypothesis 1, which predicts that efficiency is similar in the two treatments. However, we find clear evidence against Hypothesis 2, which predicts that efficiency is higher in Productivity than in CM. We conclude that our evidence is more indicative of the presence of the equal absolute contribution norm rather than the proportional contribution norm.¹⁵

Result 1: Efficiency is weakly lower in Productivity than in CM, indicative of the presence of a norm of reciprocity based on equal absolute contributions between team members.

To understand the behavior driving Result 1, we next consider decisions across groups using group contributions in the first round as an indicator of a group's initial attitude toward cooperation. More specifically, we define a LowC (HighC) group as the group within a pair with the lower (higher) combined contributions by dedicated-members in the first round.¹⁶ Averaging across all 20 decision rounds, LowC groups in CM had lower group contributions than HighC groups in 11 out of 12 paired comparisons of the five-member groups and LowC groups in Productivity had lower contributions than HighC groups in 7 out of 11 of the five-member groups.¹⁷

Table 2 Mean contributions of HighC and LowC groups: CM and Productivity

	CM				Productivity
	Common		Dedicated		Common		Dedicated
Round	HighC	LowC	HighC	LowC	HighC	LowC	HighC	LowC
First	6.00 (2.00)	5.83 (2.48)	13.54 (3.59)	5.92 (2.79)	13.27 (4.92)	13.27 (4.92)	9.05 (4.04)	5.05 (3.07)
Second	8.33 (2.23)	7.58 (3.03)	15.38 (4.03)	7.13 (2.95)	14.91 (8.69)	12.55 (6.33)	9.91 (5.79)	5.45 (3.84)
All 20	8.65 (4.15)	4.83 (1.87)	13.13 (4.97)	6.22 (2.24)	14.28 (10.12)	9.06 (4.74)	9.33 (4.15)	3.97 (5.82)

To provide more detail, Table 2 reports average contributions by common-members and dedicated-members in HighC and LowC groups in CM and Productivity. For comparison purposes, and to give more context to the formation of HighC and LowC groups, mean contributions are reported for rounds 1 and 2, as well as across all rounds. Figure 3 provides further evidence on average contributions, providing time trends across all rounds.¹⁸ Importantly, for purposes of comparability, contributions by common-members in Productivity are doubled to accurately compute their value added (henceforth, effective contributions of the common-members) to the group.

Fig. 3 Mean individual contributions of HighC and LowC groups

Contributions by common-members in Productivity are effective contributions (double the absolute token contribution). Recall, each individual's token endowment per round equaled 20. Figures in parentheses are standard deviations. For both treatments, “Dedicated” is the average contributions of the two dedicated-members.

First, consider contributions in CM. As shown in Table 2 and Fig. 3, in HighC groups, dedicated-members contribute more than common-members on average, and this ranking is robust across decision rounds (SR p = 0.0047). This is evidence that dedicated-members in HighC groups contribute more in an effort to compete for the resources of the common-member. This ranking only holds weakly for LowC groups, where average contributions by dedicated-members and common-members are more equal (SR p = 0.0774). Thus, the evidence suggests LowC groups compete less for the resources of the common-member.

Average contributions of dedicated-members in CM are lower in LowC groups than in HighC groups (SR p = 0.0037). Further, contributions of common-members are lower in LowC groups than in HighC groups (SR p = 0.0029). This is consistent with common-members reacting reciprocally to competition between the dedicated-members of the two Groups; he/she favors the more cooperative dedicated-members. Thus, as found in RSW19, competition in CM creates winners and losers. Note that these inferences are about reciprocity at the level of average behavior. There is heterogeneity in behavior across pairs or groups.

In Productivity, average contributions of dedicated-members are significantly lower than the effective contributions of common-members (HighC 9.33 vs. 14.28; LowC 3.97 vs. 9.06; SR p < 0.05 in both cases). That is, on average, dedicated-members do not match the effective contributions of common-members in both groups. However, their average contributions are closer to the absolute token contributions of common-members—they are slightly higher in HighC groups (9.33 vs. 7.14), but not in LowC groups (3.97 vs. 4.53).¹⁹ This provides further evidence in support of the equal absolute contribution norm, one that is explored further in an additional heterogeneous No-CM Productivity experiment and survey presented in Sect. 5.

Further, comparing results from Productivity to CM, we observe the following. In both HighC and LowC groups in Productivity, common-members on average contribute (weakly) higher effective amounts than common-members in CM (HighC groups, Productivity 14.28 vs. CM 8.65, RS p > 0.1028, LowC groups, Productivity 9.06 vs. CM 4.83, RS p = 0.0524.) In addition, there is some evidence that dedicated-members in Productivity contribute lower average amounts than dedicated-members in CM, significantly lower in LowC groups (HighC groups—Productivity 9.33 vs. CM 13.13, RS p > 0.1757; LowC groups—Productivity 3.97 vs. CM 6.22, RS p = 0.0193). This behavior of dedicated-members reduces efficiency in Productivity relative to CM.

Result 2: For both LowC and HighC groups, average contributions of dedicated-members in Productivity are significantly lower than effective average contributions of common-members, and somewhat lower compared to dedicated-members in CM. Both results provide support for reciprocity based on equal absolute contributions.

4 Enhancing competition through differences in resources

The above results on Productivity are not encouraging from the point of view of enhancing competition and increasing efficiency relative to CM. The treatment, Endowment, where the common-member is endowed with more resources (tokens) explores the effects of an alternative source of heterogeneity among team members.

4.1 The decision setting in Endowment

The procedures for conducting Endowment are identical to those of CM, except in Endowment the common-member's endowment is increased to 40 tokens, matching the sum of the endowments for the dedicated-members in each group. Unlike Productivity, the opportunity cost of each token contribution by the common-member is the same as the per-token opportunity cost faced by dedicated-members.

If the common-member in CM is allocating tokens to both groups, this implies their maximum potential contribution in each group is less than that of the dedicated-members’. As discussed above, in this sense, a norm of reciprocal obligations among dedicated-members and the common-member in each group would limit contributions by dedicated-members based on the limited endowment of the common-member. Importantly, the endowment of the common-member in Endowment was increased to a level where, if halved, would equal the endowment of dedicated-members in each group.²⁰ Feedback at the end of the round was identical to that in CM.

The 55 subjects (11 independent paired-groups of five subjects) who participated in Endowment earned an average of $24.42 (min = $13.85, max = $42.87, st. dev. = $8.36).

4.2 Reciprocity in endowment

As above, we model reciprocal team members as being required to match the average contribution of others in each team they belong to. If the norm is equal absolute contributions, there is a change in the resource constraint for the common member, his/her resource constraint is now $g_{\mathrm{CX}}+g_{\mathrm{CY}}\le 2e$ . That is, the common-member can now contribute as much as a dedicated-member's endowment in each Group, thus making it feasible in all cases to meet his/her reciprocal obligations in each Group. Likewise, this allows dedicated-members to match token contributions of both members in their group up to their full endowment. The common-member's resource constraint is no longer binding, and pairs of teams can attain full efficiency. Based on the equal contribution norm, Endowment is expected to lead to higher efficiency than in CM.

Hypothesis 3

(Equal absolute contribution norm): Efficiency in team public good provision is higher in Endowment than in CM and Productivity.

If the norm is to contribute proportional to endowments, because the common-member has an endowment twice as large as that of dedicated-members, then common-members are expected to contribute twice as much as the average token contribution of the dedicated-members in both Groups. The reciprocity constraints for the common-member are now $g_{\mathrm{CX}}\ge {2\overline{g}}_{-CX}$ and $g_{\mathrm{CY}}\ge 2{\overline{g}}_{-CY}$ in Group X and Group Y respectively. Relative to CM, the common-member's reciprocal token obligations are higher in both Groups. Based on the reciprocity constraint for the common-member, the reciprocity constraint for a dedicated-member is now $g_{\mathrm{iX}}\ge \frac{1}{2}(g_{\mathrm{jX}}+\frac{g_{\mathrm{CX}}}{2})$ , where token contributions of common-members are only given half the weight of contributions by dedicated-members. Thus, for a given value of $g_{\mathrm{CX}},$ the reference point to match for dedicated-members' contributions is lowered relative to CM, leading to lower token contributions.

Importantly, with a proportional norm, if dedicated-members contribute all 20 tokens (100% of their endowment) in their group, they would expect the common-member to contribute all 40 tokens (100% of his/her endowment) to their Group. This would never be possible in both Groups. Thus, if the norm is one of proportional contributions, the common-member faces the same binding resource constraint as in CM, despite the increased endowment. As a result, pairs of teams cannot achieve full efficiency, and the situation resembles CM. Based on the proportional norm, this leads to Hypothesis 4.

Hypothesis 4

(Proportional contribution norm): Efficiency in team public good provision in Endowment is no different than in CM, and lower than in Productivity.

4.3 Behavior in endowment

As in the case of Productivity, efficiency is measured as value of contributions measured in tokens made to the group account relative to the maximum value obtainable from contributions to the group account. The maximum value of the group account in Group X plus Group Y in Endowment is 1.8*(40 + 20 + 20 + 20 + 20) = 216 tokens, the same as in Productivity.

The average efficiency for pairs in Endowment is 65.75% (st dev = 19.24). Figure 4 provides average efficiency across decision rounds. For purposes of comparison, the figure also presents the averages over time in CM and Productivity. As shown in Fig. 4 and Table 1, efficiency in Endowment is weakly higher than in CM (65.75% vs. 52.19% RS p = 0.0848), and significantly higher than in Productivity (65.75% vs. 41.62% RS p = 0.0053). Thus, we find general support for Hypothesis 3, against Hypothesis 4. This result is consistent with an equal absolute contribution and not a proportional contribution norm.²¹

Fig. 4 Efficiency across decision rounds

Result 3: Consistent with an equal absolute contribution norm, efficiency in Endowment is weakly higher than in CM, and significantly higher than in Productivity.

We now consider behavior from the perspective of individuals' contributions to the group account. Parallel to earlier discussion, we focus on decisions in LowC and HighC groups. Recall, we define a LowC (HighC) group as the group within a pair with the lower (higher) combined contributions by dedicated-members in the first round.²² Table 3 reports average contributions by HighC and LowC groups, for both common-member's and dedicated-members' contributions. As before, mean contributions are reported for rounds 1 and 2, as well as across all rounds. Figure 5 provides time trends across all rounds.

Table 3 Mean contributions of HighC and LowC groups: Endowment

	Endowment
	Common		Dedicated
Round	HighC	LowC	HighC	LowC
First	13.27 (4.98)	13.18 (5.13)	12.59 (3.25)	7.95 (4.90)
Second	15.18 (8.91)	10.91 (6.25)	15.45 (2.70)	11.32 (6.08)
All 20	16.01 (6.43)	11.90 (7.02)	15.31 (4.15)	10.19 (5.82)

Fig. 5 Mean individual contributions of HighC and LowC groups: Endowment

Figure 5 and Table 3 show that contributions of common- and dedicated-members are similar in both HighC and LowC groups in Endowment (HighC 16.01 vs. 15.31; LowC 11.90 vs. 10.19; SR p > 0.14 in both cases). We thus find additional support for the equal absolute contribution norm.²³

As in Productivity, dedicated-members' contributions in Endowment are weakly higher in HighC groups than in LowC groups (15.31 vs. 10.19, SR p = 0.0505). Further, contributions of common-members, while higher in HighC groups than in LowC groups, are not significantly different (16.01 vs. 11.90, SR p > 0.10). Relative to CM (Table 3 vs. Table 2), dedicated-members in Endowment contributed somewhat greater amounts than in CM in HighC groups (Endowment 15.31 vs. CM 13.13, RS p = 0.1569) and (weakly) significantly higher amounts in LowC groups (Endowment 10.19 vs. CM 6.22, RS p = 0.0848).²⁴ In total, increases by common- and dedicated-members lead to higher efficiency in Endowment, over efficiencies in CM and Productivity.

Result 4: Consistent with a norm of reciprocity based on absolute contributions, but not a proportional contribution norm, contributions of dedicated-members in both HighC and LowC groups in Endowment are weakly higher compared to CM.

4.4 Further evidence on equal vs. proportional contributions in Productivity

Comparing absolute contributions by common-members in Endowment to effective contributions by common-members in Productivity, common-members in HighC and LowC groups are similar in each treatment (HighC 16.01 vs. 14.28; LowC 11.90 vs. 9.06; RS p > 0.30 in both cases). Thus, the lower efficiency in Productivity compared to Endowment is not due to common-members behaving significantly differently between the two treatments.²⁵

Dedicated-members, however, respond very differently to increases in the endowment of common-members versus increases in productivity of common-members. Compared to dedicated-members in Endowment, contributions of dedicated-members in HighC and LowC groups in Productivity are significantly lower (HighC 15.31 vs. 9.33; LowC 10.19 vs. 3.97; RS p < 0.02 in both cases). Instead of matching value added of the common-members' contributions (effective contributions), average contributions by dedicated-members in Productivity more closely match the absolute token contributions of common-members (HighC 9.33 vs. 7.14; LowC 3.97 vs. 4.53; SR p > 0.10 in both cases).

Based on the result above, it appears that the response by dedicated-members in Productivity is driving the lower efficiency in Productivity compared to Endowment. Below, we explore the relative prevalence of both reciprocal norms in Productivity. Figure 6 presents distributions of the ratio of contributions of dedicated-members to the lagged (since current contributions are unknown when making decisions) absolute contribution of common-members in their groups for HighC and LowC in Productivity. In every round in every group, there are two such ratios—one for each dedicated-member in the group, i.e., the figure does not use the average of the contributions of dedicated-members in a group in a round.

Fig. 6 Distributions of token contributions of each dedicated-member relative to lagged absolute token contributions of common-members in Productivity

Note: zero contributions by dedicated-members are included in these histograms. However, undefined ratios are excluded, i.e., where lag contributions by common-members are zero. Appendix A.IV of the ESM presents an analysis of the contributions of dedicated-members in these instances.

A ratio of 1 (2) indicates that the dedicated-member matches the absolute (effective) lagged contribution of the common-member. A ratio lower than 1 implies a contribution less than the absolute contribution of the common-member, while a ratio greater than 2 implies a contribution greater than the effective contribution of the common-member. A ratio between 1 and 2 indicates intermediate behavior. Table 4 shows the percentage of dedicated members displaying these forms of behavior.

Table 4 Distribution of matching behavior by dedicated-members in Productivity

	HighC		LowC
Ratio	Number	%	Number	%
0	49	14%	85	27%
> 0 & < 1	89	24%	91	29%
1	70	19%	34	11%
> 1 & < 2	65	18%	55	17%
2	26	7%	14	4%
> 2	67	18%	39	12%
Total	366	100%	318	100%

Ratio = contribution of dedicated-member / lagged absolute contribution of common-member

In both HighC and LowC groups in Productivity, the majority of dedicated-members' decisions display a contribution ratio that is less than or equal to 1; i.e., at best, they match the absolute contribution of the common-member, but not the effective contribution. While there are instances where dedicated-members match (or more than match) the effective contributions of the common-member, they are a significant minority of all dedicated-members' contributions. This tendency of dedicated-members renders Productivity ineffective in raising contributions relative to levels observed in CM. This finding lends support to our earlier conclusion that it is the dedicated-members who drive the lower efficiency in Productivity because they ignore the common-member's opportunity costs and the effective value of his/her contribution.

The above-noted tendencies in Productivity are more prevalent in LowC groups than in HighC groups. The percentage of dedicated-members' ratio of contributions that are less than 1 is higher in LowC groups than in HighC groups. Accordingly, the percentage of dedicated-members' ratio of contributions that are greater than or equal to 1 is higher in HighC groups than in LowC groups.

We now examine evidence of whether dedicated-members pay greater attention to the contributions of common-members or the other dedicated-members in their group. Table 5 presents panel random effects regressions of dedicated-members' contributions in a round based on the one-round lagged contribution of the other dedicated-member in the group, the one-round lagged contribution of the common-member in the group, a dummy for the HighC group, interactions of the dummy with the lagged contribution variables, and a time trend. Standard errors are reported clustering on independent 5-person pairs. For Productivity, regressions are reported for two cases: 1) the common-member's lagged contribution is measured in absolute value (number of tokens contributed) and 2) effective contribution (double the absolute contribution). In Endowment, absolute contributions and effective contributions of the common-member are identical. In all cases, dedicated-members' contributions are absolute token contributions.

Table 5 Determinants of contributions of dedicated-members

	Productivity		Endowment
	Absolute	Effective	Absolute
Lagged other DM's	0.172***	0.172***	0.260***
contribution	(0.064)	(0.064)	(0.075)
Lagged common-member's	0.132**	0.066**	0.114***
contribution	(0.060)	(0.030)	(0.037)
HighC dummy	1.788	1.788	2.870
	(1.760)	(1.760)	(2.510)
HighC × Lagged other	0.036	0.036	0.049
DM's contribution	(0.101)	(0.101)	(0.134)
HighC × Lagged common-member's	0.282***	0.141***	-0.018
contribution	(0.078)	(0.039)	(0.068)
Round	− 0.106**	− 0.106**	− 0.158***
	(0.049)	(0.049)	(0.031)
Constant	3.763***	3.763***	7.961***
	(0.956)	(0.956)	(1.822)
Observations	836	836	836
Chi-sq Test p-value	0.5987	0.0947	0.0299

Notes: Panel RE regressions with standard clustered on independent pairs in parentheses. DM = dedicated-member in group. Absolute refers to the number of tokens contributed. In Endowment, absolute contributions equal effective contributions. Chi-sq test refers to the null hypothesis: Lagged other DM's contribution = Lagged common-member's contribution. p-values are for two-tail tests

In Productivity, the evidence suggests dedicated-members condition their current contributions on the past contributions of both the other dedicated-member and the common-member, whether examining absolute or effective contributions of the common-member. Post-regression tests provide evidence that, in LowC groups, dedicated-members' responses do not or weakly distinguish between the lagged contributions of the common-member and the other dedicated-member in the group, whether we look at absolute (p = 0.5987) or effective (p = 0.0947) value of the contributions of the common-member.

Further, in Productivity, the interaction between HighC and lagged contributions of the common-member is positive and significant in both regressions. The evidence suggests that dedicated-members in HighC groups are more likely to track the contributions of the common-member than dedicated-members in LowC groups, thus making higher contributions and attracting the common-member to their group (HighC × Lagged common-member's contribution coefficient, p < 0.001 for absolute & effective contributions of the common-member). Further, post-regression tests provide evidence that, in HighC groups, dedicated-members are more responsive to absolute contributions of the common-member (p = 0.0169) than to the contributions of the other dedicated-member in the group, but not in effective contributions (p = 0.9895). As discussed above, HighC groups “win” the competition for the resources of the common-member. The evidence here for HighC groups corroborates the earlier finding on the prevalence of the absolute contribution norm in Productivity – dedicated-members respond to the absolute contributions of the common-member, and not their effective contributions.

In Endowment, the evidence also suggests that dedicated-members react both to the contributions of the common-member and the other dedicated-member in the group. However, post-regression tests provide evidence that dedicated-members are more responsive to the other dedicated-member's contributions than the common-member's contribution (p = 0.0299 in LowC groups; p = 0.006 in HighC groups). Finally, no difference is found between HighC and LowC groups in the extent to which they react to past contributions of the common-member (HighC × Lagged common-member's contribution coefficient, p = 0.792). Thus, both groups respond to competition, and benefit from it.²⁶

Note that the Productivity instructions and control questions informed all group members that common-members earned twice as much from tokens left in their private account and that their contributions were double in value relative to those of dedicated-members. Thus, lack of pertinent information is not the reason why the majority of dedicated-members (when reacting to the contribution decisions by common-members) did not fully incorporate the differences in opportunity costs of contributions or the value added (effectiveness) of contributions by the common-member.

In summary, changing the parameters for earnings from the private and group accounts in Productivity, even while keeping the MPCR constant compared to Endowment, appears to affect other group members' ‘perceptions' of the enhanced player's behavior, rather than behavior of the enhanced player. The findings suggest that a majority of dedicated-members in both Endowment and Productivity follow the equal absolute contribution norm. However, the same norm leads to different outcomes in the two treatments; it leads to higher efficiency in Endowment (Hypothesis 3) and lower efficiency in Productivity (Hypothesis 1). In Sect. 5, we report the results from an additional experiment and survey designed to test the robustness of this norm, investigating the prevalence of this norm when there is no common-member.

5 Robustness: no-CM-productivity and survey

The resulting differences between Endowment and Productivity (relative to CM) suggest that a majority of dedicated-members in Productivity follow a norm of absolute contributions instead of a proportional norm based on effective contributions. We infer that this behavior is a result of a majority of dedicated members not fully accounting for differences in the value added and marginal opportunity costs of contributions by common-members. In particular, despite the enhanced impact of the common-member's token contributions, dedicated-members are equally likely to follow the equal absolute contribution norm as in Endowment. It is possible, however, that this result is related to other features of the decision environment, such as the mere presence of a common-member.²⁷ To investigate this issue, we conducted an additional treatment with three-player groups with no common-member, but where one member has enhanced productivity (No-CM-Productivity).²⁸ In addition, in Sect. 5.2 we discuss the results from a survey designed to supplement these results where those completing the survey were asked their opinions from the perspective of neutral uninvolved arbitrator.

5.1 No-CM-productivity

Game parameters in No-CM-Productivity are identical to Productivity except there is no common-member. That is, all three group members received an endowment of 20 tokens. However, the enhanced member's contributions are doubled in value to 1.2 vs 0.6 for the two other groups members. Further, tokens in the enhanced-member's private account are also doubled to hold his/her MPCR constant (from 1 to 2). Prior to all decision rounds, one-member is chosen randomly to have enhanced capabilities and maintains this capability across all decision rounds.²⁹

Table 6 reports average efficiency in No-CM-Productivity, as well as contributions for group members, separated by those with and without higher productivity in providing the group good. As before, effective contributions for enhanced-members in No-CM-Productivity are computed by doubling their token contributions.

Table 6 Efficiency and contributions across treatments

	Efficiency Mean (St Dev)	Members' token contributions Mean (St Dev)
Treatment	Efficiency at group level	Enhanced	Non-Enhanced
No-CM-Productivity	48.21% (24.27) [69.43 out of 144]	18.62 (11.01)	9.98 (4.50)

Contributions by Enhanced members in No-CM-Productivity are effective contributions based on their higher return to the group account. For both treatments, “Non-Enhanced” is the average contributions of the two members

As shown, in the absence of a common-member, average enhanced members' (effective) contributions are higher than those of average of the non-enhanced members (SR p = 0.002).

Non-enhanced and enhanced members contribute similar shares of their endowments (49.89% vs. 46.54%, SR p = 0.27). This suggests, as was observed in treatment Productivity, non-enhanced members in No-CM-Productivity focus more on matching absolute token contributions of their fellow group members than effective contributions.

5.2 Survey

To supplement the results reported above, we conducted a survey on Qualtrics using student subjects from the same pool of subjects that was used in the experiments reported herein (i.e., Appalachian State University students). A total of 139 respondents completed the survey (via a link sent through the subject database) knowing that 10 would be randomly chosen to receive $50 cash prizes. Respondents first read the No-CM-Productivity instructions and answered review questions. For any review question answered incorrectly, subjects were shown the correct answer with an explanation. Respondents then answered the four questions shown below, where they were informed to use a perspective of a neutral uninvolved arbitrator, similar to those asked in Reuben and Riedl (2013).

5.2.1 Suppose a participant in the experiment was GROUP MEMBER A or B:

1. (1) From the viewpoint of a neutral uninvolved arbitrator, what do you think is the fair amount that group member A or group member B should each allocate to the Group Account?

2. (2) Suppose group member C allocates 10 tokens to the Group Account. From the viewpoint of a neutral uninvolved arbitrator, what do you think is the fair amount that group member A or group member B should each allocate to the Group Account?

5.2.2 Suppose a participant in the experiment was GROUP MEMBER C:

1. (3) From the viewpoint of a neutral uninvolved arbitrator, what do you think is the fair amount that group member C should allocate to the Group Account?

2. (4) Suppose group members A and B each allocate 10 tokens to the Group Account. From the viewpoint of a neutral uninvolved arbitrator, what do you think is the fair amount that group member C should allocate to the Group Account?

The questions of particular interest are #2 and #4. Potential answers supporting equal contribution norm would be 10 tokens for #2 and 10 tokens for #4 (matching absolute token contributions). Potential answers supporting proportional contribution norm would be 20 tokens for #2 and 5 tokens for #4 (matching effective contributions).

The survey findings reveal the average response to #2 is 9.25 tokens and to #4 is 11.19 tokens. Comparing the absolute differences between the equal contribution and proportional contribution norms, the responses are clearly closer to the equal contribution norm than the proportional contribution norm (p < 0.001 in both cases).³⁰ Figure 7 displays histograms of responses to the conditional-fair-contribution questions (#2 on the left and #4 on the right). The modal response for a fair contribution when others contribute 10 tokens is clearly to match based on absolute contributions, for both non-enhanced and enhanced members. Interestingly, for each type, the second most-common response is in the opposite direction of the prediction of a proportional contribution norm (A & B: 5 tokens vs. 20-token prediction; C: 15 tokens vs. 5-token prediction). The findings from the No-CM-Productivity survey clearly indicate that subjects consider an absolute contribution norm fairer than a proportional contribution norm.

Fig. 7 Histograms of Survey Responses for Fair Contributions Based on Contributions of 10 tokens by Others

In summary, referring back to the treatments with a common-member, the additional treatment and survey lead us to conclude that the differences observed between Endowment and Productivity are most likely due to the lack of behavioral differences in how dedicated-members respond to the differences in the source of enhanced capabilities of the common-member. Specifically, there is evidence that a majority of dedicated-members focused on the absolute contributions of common-members, suggesting they did not pay sufficient attention to the higher value added and higher opportunity costs faced by the common-member in contributing to the group account in treatment Productivity. This behavior by dedicated-members in Productivity led to lower contributions on their part, that did not “match” the value added of the common-member's contributions. On the other hand, dedicated-members' average contributions are equal to average absolute contributions by the enhanced common-member in Endowment (refer to Table 3 and Fig. 5), which is equivalent to matching the value added by them. Dedicated members following the equal absolute contribution norm in Endowment and Productivity has a significant impact on overall levels of efficiency achieved, leading to lower efficiency in Productivity.

6 Conclusion

This experimental study provides evidence on team productivity in a decision setting where two groups compete for the resources of a common-member. Team production takes place through contributions to a group-level public good. In the baseline CM setting, where the common-member is in both groups and has resources and productivity equal to that of dedicated-members who are only in one group, we find evidence of competition for the resources of the common-member. The average contribution of dedicated-members is higher than that of the common-member. However, the dynamic across decision rounds leads to winners and losers. Initially and across decision rounds, the common-member contributes more to the group with initially higher contributions by the dedicated-members. In addition, the common-member's limited resources prevent him/her from matching the higher contributions of dedicated-members in both groups which, in accordance with norms of reciprocity, prevents contributions of dedicated members from rising higher. This leads to wasted potential.

Based on these initial results, this study examines behavior in two additional treatments where the common-member has greater productive potential than dedicated-members, designed to increase competition for the resources of the common-member. Productivity holds the resource endowment of the common-member constant, but doubles the value of resources contributed to a group by the common-member. To hold the marginal incentives from contribution constant for the common-member, the marginal opportunity cost of the common-member is also doubled. Endowment doubles the resource endowment of the common-member to enable him/her to have the potential to contribute the maximum contribution of dedicated-members in both groups.

The striking result in these treatments is that, while efficiency increases in Endowment relative to CM, efficiency decreases in Productivity. Examining individual group-member decisions in Productivity reveals that this result can be attributed to a majority of dedicated-members making contributions that are more in line with absolute contributions of the common-member (equal absolute contribution norm), instead of the value added of the contributions (proportional contribution norm). We interpret this behavior in Productivity as a result of dedicated members not fully incorporating the higher value added and opportunity costs that common-members face in making contributions.

Our results offer insights into the design of teams in organizations. Providing opportunities for some members to participate in multiple teams can increase efficiency, but not always. That is, within an organization, our results suggest that multiple team membership can be valuable under certain conditions. The results from Endowment suggest that organizations could screen for potential common-members to allow only those with greater resources at their disposal to work on multiple teams. Our results from Productivity point to the possibility that having common-members with higher productivity can be counter-productive in some settings.

More specifically, high-skilled team members with greater marginal opportunity costs of contributing may undermine overall team productivity through decreased effort by other team members. In an organizational setting, individuals can contribute to other endeavors within or outside the firm. These opportunities can lead naturally to different opportunity costs. Such opportunities are likely to be better for common-members with greater capabilities. Results from Productivity suggest dedicated-members, even if informed of these higher opportunity costs, might not fully incorporate these costs into how they interpret the common-member's contribution to their team. Without such appreciation, the competition for contributions of common-members would diminish, leading to lower levels of team productivity. This result points to the importance of both providing common-information among team members regarding heterogeneities and how to interpret and process such differences when making choices.

Although dedicated-members in Productivity were provided information regarding the higher marginal opportunity costs of the common-member, one could imagine that in small group settings, interactions such as face-to-face communication could make the importance of this point more transparent. In that sense, small experimental groups with anonymity and without communication opportunities may have characteristics more similar to larger groups where members are unable to accurately signal important differences among team members in regard to attributes such as opportunity costs.

Clearly our results are specific to a setting designed around the linear public good game (VCM). An interesting avenue for future research is to examine the robustness of these results to alternative public good settings. A similar point can be made by our decision to examine settings in which the common-member can contribute to both teams in a given decision round, as well as including multiple rounds with fixed groups. Our initial motivation for this study came from a relative of one of the authors who is a member of multiple bands simultaneously. Of course, in continuous time he/she is not playing simultaneously. However, the context is quite similar to ours—joint membership and a competition for the talents of the most skilled musicians. To be sure, our controlled experimental environment is somewhat “stark” in relation to the information or history that might lie behind the relationships in teams where there is heterogeneity in talent. Our goal, like most experimental studies, was to first investigate decision making in such environments devoid of these underlying factors that could affect dynamics and performance in team settings in the field.

Finally, our results can be more broadly interpreted concerning the effect of heterogeneity impeding cooperation in groups/teams. Heterogeneities (observed or not), regarding motives for taking (or not taking) actions, as well as the costs of taking actions, hinder our ability to understand what is perceived as non-cooperation. Future experimental work provides a rich setting for gaining a better understanding of how heterogeneities, coupled with asymmetries in information and interpretation of productivity, combine to influence how group/team members interpret and act on heterogeneities as they make choices regarding cooperation.