Measuring Group Cohesion to Reveal the Power of Social Relationships in Team Production Open Access

A vast array of economic and social activity occurs in groups and teams. People need to coordinate and cooperate as colleagues in the workplace, teams on sports fields, army units on the battlefield, and across a host of less formal interactions with relatives, friends, and neighbors. In this paper, we report an extensive program of conceptual and experimental research building from the arguably plausible idea that the qualities of social relationships within households, firms, or other organizations collectively constitute an important factor of production. While various strands of the literature hypothesize that social relationships may matter for economic outcomes (see section II), our motivation stems from the absence of any systematic approach to measuring the productive value of social relationships. Our primary contribution is to develop and test a measurement tool, based on a new concept of group cohesion, with a view to providing foundations for the study of social relationships as factors of production.

We proceed with two main steps. The first is to introduce a simple but conceptually well-grounded approach to characterizing any real group in terms of a group cohesion index, intended as a summary statistic for aspects of social relationships that matter for team production. The second main step is to test the predictive power of the group cohesion index in a large-scale program of experiments and accompanying analysis investigating (weak-link) team production in real groups that vary in terms of their preexisting social relationships.

Since group cohesion is a novel concept in economics, in section III, we explain the rationale for the concept, our approach to measuring it, and some of its key properties. To preview briefly, our starting point is that members of any real human group inevitably have some relationships to other group members; for example, to begin with a very simple idea that we later operationalize, some people might feel close to other group members, whereas others may feel quite distant. In our approach, we use the term group cohesion (or sometimes just cohesion for brevity) to refer to the state of the aggregate closeness ties within a group. Because closeness is an essentially subjective concept, it is natural to wonder whether it can be reliably measured for either pairs of individuals or aggregated to form a meaningful group-level statistic. Our research supports positive answers to both questions. Our measurement of group cohesion is based on the well-established “oneness scale” (Cialdini et al., 1997) whose psychometric properties we replicated successfully in previous research (Gächter, Starmer, & Tufano, 2015). The oneness scale uses simple and very portable methods to assess how close one person feels to another, based on their own self-reports. From a measurement viewpoint, our innovation is to develop an aggregate statistic, based on oneness, to characterize the set of relationships within a group. Specifically, in our experiments, we ask each group member, privately, to indicate their oneness with every other group member. The group cohesion index is then calculated as an average of individual oneness ratings (full details of our measurement approach and its psychological foundations are in section IIIA).

This seemingly modest measurement innovation generates a tool with considerable predictive power. Across a set of six experiments (see table 1 for a summary of key aspects), we demonstrate that group cohesion is strongly associated with group outcomes. We explain the main experimental setup in section IV. A key feature is that we study the behavior of real groups, not artificially created ones, achieved by recruiting groups of friends to participate. Hence, we observe real closeness ties based on preexisting sociological and psychological characteristics that are absent (by construction) in groups set up on the spot in the lab, including those using minimal group manipulations (Goette, Huffman, & Meier, 2012).¹ As we will show, measured cohesion tracks tangible sociological features of the real groups we study (see section IIIB).

Our workhorse to study group outcomes is a weak-link game, chosen to model coordination problems endemic to real organizations and teams (Camerer & Weber, 2013). In our version of the weak-link game, group members simultaneously choose an “effort level.” Payoffs to each group member then depend on their own effort and the lowest effort chosen by anyone (the weakest link) in the group. The game has multiple strict Pareto-ranked Nash equilibria in material payoffs reflecting two dimensions of group success: coordination (matching the effort level of other group members) and cooperation (achieving Pareto-superior equilibria). Building on the approach of Brandts and Cooper (2006), we designed our game to be harsh in the sense that groups lacking preexisting social relationships would be expected to collapse to the Pareto-worst equilibrium.

Section V presents the key behavioral patterns in our data. We identify a strong, positive association between group cohesion and performance, and although the likelihood of coordinating on some equilibrium is largely independent of the level of cohesion, it is crucial for equilibrium selection: low-cohesion groups usually descend rapidly to the worst Pareto-ranked equilibrium; high-cohesion groups typically achieve higher Pareto-ranked equilibria. We replicate these patterns with an independently conducted, preregistered experiment (study 2—see table 1 above). We also confirm that our results are robust to the timing of oneness measurement (before or after play of the weak-link game), eliminating the interpretation that the experience of game play explains variation in cohesion.

While our results clearly establish that groups with high cohesion systematically outperform low-cohesion groups, one must be cautious about causal interpretation. Ultimately our results are correlational, but we think a plausible interpretation of our findings is that group cohesion is a summary statistic for tangible features of real groups that matter causally for team production (at least in the context of the weak-link settings we study). Interpreted in that way, the group cohesion index as a new tool would be much less valuable if one could predict group performance just as well using a small number of easily measured group characteristics; our results, however, cast doubt on the prospects for doing that.

In section VI, we present econometric analysis showing that group cohesion is a powerful and dominant predictor of group performance even when controlling for a large range of measured group characteristics; moreover, those characteristics become insignificant as predictors of group outcomes once cohesion is present as a regressor. In the last game period, the model-predicted effects of cohesion on group outcomes are also substantial: minimally cohesive groups are almost certain to collapse to a minimum effort of 1, maximally cohesive groups almost never fall to a minimum effort of 1, and large financial incentives are needed to promote the levels of effort expected for high cohesion groups.

In section VII, we discuss the interpretation of our results considering two main avenues. First, we consider the possibility that because our experiments involve groups of friends, the association between effort and cohesion might be explained by subjects having planned to share their earnings with participating friends. We test and discount this as a plausible account of our main findings. Second, exploiting data on participants’ beliefs and social preferences gathered in our replication study, we explore the extent to which the association between group cohesion and minimum effort is mediated through beliefs or social preferences. In contrast to results found elsewhere (e.g., Chen & Chen, 2011), we find that the effects of cohesion operate mainly via the channel of beliefs with only a limited influence of social preferences.

To preview our conclusion of section VIII, our studies establish proof of concept for group cohesion as a useful new tool of economic analysis to capture and reveal the previously hidden power of social relationships as factors of production.

Before presenting the substance of our paper, we briefly place it in the literature. In the broadest sense, we contribute to the literature on social capital (Putnam, 2000); Glaeser, Laibson, & Sacerdote, 2002) by tackling one of its central problems. In a recent typology of that literature, Jackson (2020) argues that “measuring various forms of social capital is especially difficult as they are dependent upon relationships between people, which are often intangible and only indirectly observed” (333). We demonstrate how (social) relationships can be observed and measured to provide quantitative assessments of the (psychological) quality of social network links (Goyal, 2005), thereby providing a microfoundation of social capital. We do this by introducing the novel psychological concept of group cohesion. As we will explain, group cohesion builds on the concepts of relationship closeness and oneness. These concepts are firmly established in the psychology literature (see section IIIA) but are less considered in economics, with the possible exception of social distance (Akerlof, 1997). In the experimental economics literature, social distance has mainly been juxtaposed to complete anonymity and manipulated experimentally by giving participants cues about the identity of other individuals, for instance, by visual identification (Bohnet & Frey, 1999) or by their names (Charness & Gneezy, 2008). By contrast, we measure the closeness of relationships between group members and construct the concept of group cohesion on such measurements. To our knowledge, this is an entirely new approach in economics.

Another contribution is to the experimental literature on coordination games, which, following seminal papers by van Huyck, Battalio, and Beil (1990, 1991), has largely studied coordination among anonymous individuals without considering the role of social relationships. This research (see Cooper & Weber, 2020, for a recent survey) highlights primarily the importance of structural features that facilitate coordination on efficient equilibria, such as communication (Cooper et al., 1992; Brandts & Cooper, 2007), leadership (Weber et al., 2001), individual incentives (Brandts & Cooper, 2006), group size (Weber, 2006), choice of group members (Riedl, Rohde, & Strobel, 2016), and organizational or societal culture (Weber & Camerer, 2003; Engelmann & Normann, 2010). By studying a fixed weak-link game, we keep structural features constant and show that the sociopsychological property of group cohesion is an independent and powerful predictor of group outcomes.

We also contribute to a growing literature on the economic impact of groups and group identity (Charness & Chen, 2020). This includes studies investigating in-group favoritism (Currarini & Mengel, 2016), interactions among friends (Glaeser et al., 2000; Leider et al., 2009; Babcock et al., 2020; Chierchia, Tufano, & Coricelli, 2020; Gächter et al., 2022), and the role of identity in organizations (Akerlof & Kranton, 2005; Ashraf & Bandiera, 2018), including social-psychological dimensions of employment relationships (Baron & Kreps, 2013). Our work builds most directly on prior experimental work that has established the impact of group identity on behavior in various contexts, including in prisoner's dilemma and battle of the sexes games (Charness, Rigotti, & Rustichini, 2007), in trust games (Hargreaves Heap & Zizzo, 2009), and in weak-link games (Chen & Chen, 2011). While the last of these comes closest to our work in studying weak-link games, relative to all three studies, our work breaks new ground: we study real groups, not artificially constructed ones, and we do this for the novel purpose of developing and providing proof of concept for a tool to measure the quality of behaviorally relevant features of sociopsychological relationships within real groups.

Since group cohesion is a novel concept in economics, we devote section IIIA to explaining the concept, its roots in established psychological literature, and our approach to its measurement. Section IIIB shows that measured group cohesion passes a basic test of construct validity in varying coherently with tangible sociological properties of real groups.

Our study involves the development and application of a new tool: a simple and portable measure of group cohesion designed to summarize the social and psychological relationships that exist among members of any group. To this end, we build on an established literature that has developed tools to measure the nature and strength of bilateral relationships between pairs of individuals. This literature demonstrates that important features of possibly complex bilateral relationships can be summarized by simple measurement tools, which ask subjects to report how “close” they feel toward another focus person (Aron, Aron, & Smollan, 1992). Our strategy builds on and extends this literature by assuming that important aspects of relationships that exist within groups can be summarized in terms of the set of pairwise closeness relationships within them. On our measure, a group will be more cohesive to the extent that its members collectively feel closer to one another. Since individual judgments of relationship closeness will be its foundation, we now describe the key properties of tools for measuring bilateral relationship closeness.

Aron et al. provide statistical evidence that the IOS scale successfully tracks key dimensions of relationship closeness: people tend to pick more overlapping pairs of circles for a given other, the more frequent or diverse their interactions, and the stronger their perceptions of mutual influence. Subsequent research, most notably by Starzyk et al. (2006), developed the 18-item Personal Acquaintance Measure intended for application to a wider range of relationships including acquaintances. Their measure also correlates strongly with the IOS scale. Together these results make the IOS scale a promising tool for our purposes. It also has the decisive advantage of being intuitive for respondents and very simple to implement.

Since our research relies critically on the IOS scale, in a background paper (Gächter et al., 2015), via a study with 772 subjects, we assessed the psychometric validity of the IOS scale for a wide range of relationships (from strangers to close friends) by testing whether we could replicate key findings in the foundational psychological research that validated the IOS scale as a reliable predictor of relationship closeness. Our results replicate, remarkably closely, the correlations of the IOS scale with the Relationship Closeness Index reported by Aron et al. The IOS scale also varies coherently with the form of the relationship (lowest for acquaintances, medium for friends, and highest for close friends), with the Personal Acquaintance Measure of Starzyk et al. and with Rubin's Loving and Liking Scale. In Gächter et al. (2015), we also find that the principal components of the questionnaire-based measures correlate strongly (0.85) with the IOS scale. Hence, we conclude that the IOS scale is a psychologically meaningful and reliable tool for measuring bilateral relationship closeness.

In our measurement of relationship closeness, we follow Cialdini et al. (1997), who combine the IOS scale with the “We Scale,” depicted in figure 1b. The Cialdini et al. measure is calculated as the average of responses on these two scales. They call this the “oneness scale,” which they interpret as reflecting a “sense of shared, merged, or interconnected personal identities” (483). In Gächter et al. (2015), we confirmed Cialdini et al.’s claim that oneness correlates slightly better with the questionnaire-based measures than the IOS scale alone; hence, we use the oneness scale for our analysis.

We deployed the oneness scale as follows (wider procedural details are in section IV). Subjects participated as groups of four, and each person rated three other visually identified group members, separately and privately, on the IOS and We Scales as depicted in figure 1; group members knew they would not receive feedback about each other's ratings. Both IOS and We Scale responses are scored on a scale from 1 to 7. Oneness is the average of the two measures and ranges from 1, “lowest oneness,” to 7, “highest oneness.”

Since groups contain four people, who each rate the three other members in their group, any group generates 12 bilateral oneness ratings. We construct our group cohesion index by selecting for each group member the oneness score for the person they rated lowest. We then compute group cohesion as the average of these four scores. Hence, our index can be thought of as summarizing the minimum envelope of oneness in a group. Our results are not sensitive, however, to different ways of averaging the individual oneness reports (see section VIB).

In much of this paper, we focus on whether or how well group cohesion predicts performance in stylized “production tasks.” Before pursuing this, however, we briefly probe the validity of our measurement tool using some simple tests examining whether measured cohesion varies as expected with tangible, sociodemographic features of the groups in our experiments.

For a more sophisticated test of construct validity, we use individual-level data on 15 characteristics of our participant, collected with postexperimental questionnaires. The characteristics range from self-reports of relatively concrete variables (e.g., age or gender) through to more subjective self-assessments of dispositional traits (e.g., political attitudes or happiness). An established literature related to homophily and the sociology of friendship (Baccara & Yariv, 2013; Dunbar, 2018; McPherson, Smith-Lovin, & Cook, 2001) shows that like-befriends-like; hence, members of self-assorted groups are expected to be more similar in terms of sociodemographic characteristics than members of other groups.

This is clearly true of our self-selected groups (i.e., the F-matching groups): Based on both parametric and nonparametric tests, the null of equal variance between and within F-matching groups is rejected in the expected direction at p < 0.05 for 11 of the 15 characteristics (see table SM2.1 in the supplemental material, henceforth SM). In contrast, no significant differences are found for N-matching groups. This analysis demonstrates that homophily is an indicator of preexisting relationships among group members. Hence, if group cohesion measures what we intend, we should expect that group cohesion and group homophily will be correlated. To test this prediction, we construct a simple homophily index that increases with the similarity of group members on each of the 15 variables we measured to capture tangible sociological features of group members. We explain the construction of the homophily index in detail in section VI, where it is featured as a control variable. For now, however, we note that an OLS regression of group cohesion on the homophily index produces a highly significant coefficient (p < 0.001) with an R² of 0.37. We take this as reassuring evidence that as well as being a simple, intuitive, and portable group-level statistic capturing bilateral assessments or relationship closeness, the group cohesion index also reflects homophily within groups, consistent with the literature on the sociology of friendship.

Our workhorse for studying team performance is the so-called weak-link game. Since the seminal papers by van Huyck et al. (1990, 1991), it has been widely studied in the lab, partly because it represents a form of coordination problem endemic to organizations (Camerer & Weber, 2013). A classic example is workers preparing an aircraft for takeoff: the plane can leave only once the slowest worker has fulfilled their task (Knez & Simester, 2001).

We use a version of the weak-link game due to Brandts and Cooper (2006). In a group of four, players simultaneously choose one of five “effort levels” 1 to 5. The payoff to each player i is given by π_i = 190 – 50e_i + 10b$·$ [min(e₁, . . . , e₄)], where e_i is player i’s own effort, min(⁠$·$⁠) is the lowest effort in the group, and b is a bonus rate controlling the marginal return to changes in minimum effort. In our main experiment, we set b = 6 mimicking Brandts and Cooper's baseline treatment. Table 2 illustrates the payoff matrix as generated by the payoff function π_i.

Each player chooses an effort level (i.e., a row of table 2), and their payoff then depends on their own choice and the minimum effort among all members of their group (given by the column). The key tension embodied in the weak-link game is easy to see: everyone prefers that everyone chooses maximum effort (of 5) because this is the unique social optimum, which simultaneously maximizes everyone's payoff (at 240 points); but the optimum may not be achieved because it is costly for any individual to exceed the minimum of efforts. On standard analysis, rational players will match their expectation of the minimum of others’ efforts. The game has five strict Pareto-ranked equilibria on the diagonal of table. Notice that the achievement of high payoffs requires elements of coordination (choosing the same effort level as other group members) and cooperation (groups achieving Pareto-superior Nash equilibria).

We chose this specification of a weak-link game as our baseline setup in the expectation that in the absence of aids to cooperation (e.g., communication), low-cohesion groups, typical of those used in prior experimental implementations of this game (Brandts & Cooper, 2006, 2007), would rapidly descend to the worst equilibrium.²

Since our goal was to study the performance of real groups, invitations to prospective participants asked each invitee to bring three additional people who all knew each other and the invitee. Hence, participants (n = 260 student in study 1) arrived at the lab in sets of four acquaintances. Upon arrival, we assigned them to one of two matching protocols, the F-matching (47 groups) or the N-matching (18 groups). In the F-matching, each quartet of acquaintances was allocated to the same group (``Friends''). By contrast, in the N-matching, each set of four acquaintances was split up so that each was randomly assigned to become a member of a different experimental group (“Nonfriends”). Thus, the only difference between the two matching protocols is that under F-matching, group members are selected to have some prior history of social interactions with each other, whereas the N-matching aims to minimize the likelihood of prior social interaction but keeping the recruitment procedures constant. Using these two matching protocols, we achieved the desired variation in pre-existing cohesion across groups (figure 2).

Since our setup required participants to both provide oneness ratings of other group members and play a (repeated) weak-link game, an important issue is whether the experience of one type of task might affect behavior in the other. We addressed this issue in two ways. First, pilot experiments revealed that measuring oneness before the weak-link game does have some influence on minimum effort. A key question is then whether prior play of the game affects subsequently measured oneness. To test this, we ran a within-subject experiment (172 new subjects; 27 F-matching groups and 16 N-matching ones) conducted in two stages. We refer to this as our “two-week experiment” (see table 2). In week 1, we measured oneness and elicited various individual characteristics. In week 2, the same subjects in the same groups played the weak-link game followed by elicitation of oneness. Since in our context relationship closeness should not change systematically over the course of one week, any systematic changes in oneness ratings would be likely due to effects of the experience of game play.

Our results show that the oneness scores are not significantly different between week 1 and week 2 (individual average ratings as observations, Wilcoxon signed ranks test, z = $-$1.033, p = 0.302). At the group level, the Spearman rank order correlation between weeks 1 and 2 group cohesion is 0.928 (n = 43; p < 0.001). This demonstrates an encouraging degree of test-retest reliability at the level of the individual. To further test the impact of game play on oneness ratings, we regressed changes in group cohesion on average minimum effort. The coefficient on minimum effort is insignificant (ordered probit, β = $-$0.032, z = $-$0.28, p = 0.783).³ We conclude that prior play of the weak-link game has no detectable impact on subsequent measurement of oneness. This provides strong support for the sequence where we elicit the oneness ratings for the construction of group cohesion after the weak-link game.

In all matching conditions, each group sat at a block of four computer workstations with partitions to prevent them from seeing each other's screens and responses. Each session started with an introduction read aloud by the experimenter. After that, each group of four participants was asked to stand up, one group at a time, so that each of its members could see the other members of their group.⁴ Subjects then followed computerized instructions on their own screens. These first introduced the weak-link game followed by questions to test subjects’ understanding of it. After the test, subjects played eight periods of the weak-link game. In each period, after each group member had (privately) entered their own effort level, their computer screen reported their own choice, their group's minimum, their own points for the current period, and their own accumulated points for all completed periods. Subjects knew that total accumulated points across the eight periods would be converted to cash at an exchange rate of 500 points = £1.00. For oneness measurements (elicited after game play for reasons explained above) after computerized instructions, each participant was asked to focus on each other group member in turn and to respond, in sequence, to both the IOS scale and the We Scale (see figure 1) tasks. The full experimental instructions are in the supplemental material (see section SM14).

We recruited participants via Online Recruitment Software for Economic Experiments (ORSEE; Greiner (2015) and ran the experiments with z-Tree (Fischbacher, 2007) in the CeDEx lab at the University of Nottingham. Sessions lasted about one hour. Participants received task-related payoffs plus a £2.00 show-up fee (the mean payment was £7.88). Payments were made privately.

Before presenting our primary results, we note that our experimental environment is “harsh,” as intended, in that groups whose participants have no significant history of prior social interaction tend to quickly gravitate toward the lowest-ranked equilibrium of the weak-link game. Using data from the N-matching, we find that by period 8, 90% of groups collapse to minimum effort = 1; only two groups do better, achieving effort levels 2 and 3, respectively.⁵ These results confirm existing evidence (Brandts & Cooper, 2006, 2007) and establish that there is ample scope for improvement in cooperation in our environment if the factors captured in the group cohesion index measure matter for team production.

To further examine the dynamics suggested by figure 3a, we separate the full set of 65 groups into three subsets of low-, medium-, and high-cohesion groups (for details of partitions see the figure 3 caption). Figure 3b reveals marked differences in the dynamics by showing the time path of (average) minimum effort, separately by partition. This reveals differences in both the initial levels of and trends in minimum effort across partitions: in contrast to low- and medium-cohesion groups, high-cohesion groups cooperate more effectively in the initial period and do not experience a decay of minimum effort over time.

Interestingly, the dynamics of “wasted effort” (the total of effort in a group above the group minimum in a particular period) seem largely independent of cohesion levels, and the uniformly low rates of wasted effort by period 8 imply strong convergence on equilibrium play for all levels of cohesion.⁶ As Figure 3c shows, average wasted effort in period 1 is around 5 and collapses to about 1 by period 8. The analyses of figures 3b and 3c suggest that group cohesion is primarily associated with cooperation (decisions consistent with higher- ranked equilibria), with relatively little connection to coordination success (group members coordinating on the same equilibrium, regardless of its ranking).

A natural question to ask is whether our results are robust to the timing of the oneness elicitation. We use the data generated by our two-week experiment (where oneness is also elicited one week before the weak-link experiment; see section IVB) to conduct a simple but informative check comparing average minimum effort across experiments (original versus two-week experiment) using the partitions for group cohesion (low, medium, and high) introduced in figure 3b. These tests show that for both low- and high-cohesion groups, the achieved levels of minimum effort are statistically indistinguishable across the two experiments. For groups with midrange cohesion, minimum effort is somewhat higher for the two-week experiment. For both experiments, however, we identify a strong, positive association between cohesion and minimum effort regardless of the timing of the oneness elicitation. This holds regardless of whether we include observations from groups with midrange cohesion (for more details of analysis see supplemental material, section SM4).

While the results just presented are encouraging, they are also novel. Therefore, replicability is of first-order importance to establish confidence in the behavioral patterns just reported (Camerer et al., 2019). We therefore replicated the experiment and report the results in this section. In the following, we sometimes use “study 2” as a convenient label for the replication study and refer back to the original study as “study 1.” To provide a credible replication, we preregistered the experiments⁷ for study 2, and we hired an independent contractor (the University of Birmingham Experimental Economics Laboratory (BEEL)) to implement them. We provided the experimental protocol, software, and instructions, but we were not involved in data collection. BEEL followed our original recruitment procedures but with a new subject pool from Birmingham University. The protocols and instructions were as for study 1 except that to probe the relationship identified in study 1, we introduced two further sets of measurements. First, subjects’ beliefs about the minimum effort in their group were elicited in each round of the weak-link game. Second, the postexperimental questionnaire included incentivized elicitation of Social Value Orientation (Murphy & Ackermann, 2014) as a measure of group social preferences. We discuss the details of these measures and the associated results in section VII.

Notice that the time profile of average individual effort is clearly different comparing low- and high-cohesion groups: for low-cohesion groups, it starts just above 3 and descends close to the minimum of 1 by period 8, whereas for high-cohesion groups, it starts higher (close to 4) and descends less steeply, converging by period 8 to an average effort level of around 3. Persistent differences in the distributions of effort are also apparent comparing low- and high-cohesion panels (e.g., there is markedly more incidence of efforts above 3 in the high-cohesion panels). An econometric analysis also finds a highly significant positive influence of individual average oneness on individual effort choices.¹⁰

We further examine these dynamics by focusing on each individual's change in effort following rounds in which they delivered above-minimum effort. A subject who did not choose the minimum effort in period t is modeled as having a choice among three (mutually exclusive and exhaustive) options in period t + 1, which we label nice, moderate, or harsh: nice agents deliver at least as much effort as before, moderate agents reduce effort but no lower than the previous period minimum, and harsh agents reduce their effort below the previous minimum. We conjectured that subjects with high average oneness ratings of their fellow group members would be more likely to be nice, with the reverse true for individuals with low average oneness ratings of their fellow group members. An ordered probit analysis (using cases where a subject did not choose the minimum effort in period t) shows that their reaction in t + 1 (respectively coded 1, 0 or $-$1 for nice, moderate, or harsh) varies positively with their average oneness ratings of the other three group members (β = 0.067, p = 0.002, pooled for studies 1 and 2).

The combined results of the two studies presented in section V establish a strong and replicable positive association between group cohesion and minimum effort. In this section, we probe the robustness and scale of that relationship through two sets of additional analyses.

This section presents regression analysis assessing the power of group cohesion as a predictor of minimum effort with a particular focus on the impact of controls for homophily. For this analysis, we address an issue raised in section I: since we interpret group cohesion as capturing the effects of real relationships that exist among group members, could we achieve comparable or better predictive power through use of information about observable individual characteristics? The main analysis we report makes use of the homophily index, first introduced in section III, but here we provide more details of its construction.

Table 3 reports results for three models of group-level minimum effort that feature either group cohesion or the homophily index or both as independent variables. The homophily index combines data on 15 individual characteristics that we measured for this purpose (see SM1 for details).¹¹ For each of these 15 variables, we construct a homophily subindex by first coding observations for each variable into a small number of mutually exclusive categories (e.g., two genders; three nationality groups). For each variable, we then assign a homophily subindex to each group calculated as the proportion of group members associated with the highest-proportion category (e.g., suppose that in a group, three members are female and one is male; then by definition, the gender homophily subindex for that group is 3/4 = 0.75). The homophily index used in the regressions of table 3 is then the average of the 15 subindices for each group. The models are estimated using standard ordered probit with clustering at group level since groups make multiple decisions.¹² The regressions pool data for all eight periods with separate panels for study 1 (panel A), study 2 (panel B), and the combined data set (panel C).

The estimated models that include group cohesion without homophily (models 1, 4, and 7 in table 3) show that cohesion is a stable and strongly significant predictor across the two subject pools and the pooled data set. Similarly, when the homophily index enters without cohesion, consistent with our prior expectation, we find a strongly significant association for homophily in each case (models 2, 5, and 8). Critically, however, when both variables enter together, the homophily index is never significant while group cohesion remains strongly significant and with a coefficient very similar to that in the regression without the homophily index. As robustness checks, we conducted similar analysis along two further routes, either entering all 15 homophily subindices as separate variables in regressions alongside group cohesion or by using the 6 main principal components of the 15 homophily subindices as regressors alongside group cohesion (see SM8 for details).¹³ The consistent outcome of this analysis is that various homophily-inspired measures do not match the performance of the group cohesion index in predicting group minimum effort.

We now consider the magnitude of the effects of group cohesion on minimum effort, observed in our data. As one approach to this, we explore the predictive power of group cohesion by regressing it on minimum effort in the last period (period 8) to generate the predicted probabilities for each possible level of minimum effort, conditional on different levels of group cohesion. The results (presented in detail in SM9) demonstrate a sizable predicted impact of group cohesion on minimum effort as we move between the extreme points of the group cohesion scale. For example, imagine a group characterized by minimum cohesion (equal to 1): such a group is almost certain to be at minimum effort of 1 (the actual probability of minimum effort in this case is approximately 93%, based on pooled data from studies 1 and 2). By contrast, a group with maximum possible group cohesion (equal to 7) is unlikely to end up at minimum effort of 1 (probability of less than 12%) and is predicted to achieve minimum effort of at least 3 with a probability of about 83%.

One might wonder how far these results depend on the specification of the group cohesion variable. Recall that we calculate group cohesion as the average of the minimum oneness ratings in a group. While this minimum envelope seems a natural statistic, particularly in the context of the weak-link game, there is no “special sauce” involved here: indeed, using the group average of individual oneness ratings as an alternative cohesion metric delivers very similar results (see supplemental material, table SM10.1).

As a second approach to assessing the scale of cohesion effects, we ran a series of new experimental treatments that varied the bonus (b in the payoff function π_i of the weak-link game; see section IVA). In these treatments, in line with the earlier research by Brandts and Cooper (2006) and others, we recruited unrelated individuals (not groups of friends), and they completed eight rounds of the weak-link game. The bonus rates in four between-subjects’ treatments (60 subjects each) were set at 6, 14, 22, and 30, respectively (see the supplemental material, table SM3.1, for the respective payoff tables). The first two bonus levels correspond to the lowest and highest bonus payments implemented by Brandts and Cooper (2006), while the other two go substantially higher in steps of 8 (the highest more than doubles their maximum). Increasing the bonus monotonically increased the average minimum effort. At bonus level 6, it was close to the minimum possible value of 1 and corresponds with the expected minimum effort associated with low-cohesion groups (a cohesion level of approximately 3; see figure SM12.1). Our results show that substantial increases in the bonus, beyond those used by Brandts and Cooper, are needed to induce average minimum effort levels comparable to those associated with high cohesion (see SM12 and figure SM12.1 for details). For example, a bonus level of 22 in the bonus study produces an average minimum effort comparable to that expected from groups with a cohesion level of approximately 6. These results show that the economic value of group cohesion, or, more precisely, the value of the factors it proxies, is substantial when gauged by the financial incentives needed to induce effort levels comparable to those of high-cohesion groups.

Bringing real groups to the lab, as we have done, is a departure from classic lab experiments that might initially trouble those who presume that (at least approximate) anonymity is a sine qua non principle for experimental games, required to avoid the shadow of the future “infecting” strategic behavior in the lab. We aim to convince readers otherwise. A key rationale for our approach comes from the fact that real groups, and the real relationships that have developed within them, are our object of study. Yet working with real groups does create some methodological challenges and issues of interpretation, one of which we address next.

A possible interpretation of the relation between cohesion and effort is that the members of high-cohesion groups, by virtue of tending to know one another, might have agreed to share their payoffs, thus changing the payoff structure of the weak-link game making cooperation easier.¹⁴ In the postexperimental questionnaire, we asked participants whether they planned to share their earnings with other group members and whether their expectation of sharing had affected their game decisions. Our robustness tests extend the analysis of table 3 by adding controls for self-reports of sharing. While this reached significance in some specifications, it had only a modest impact on the coefficient for group cohesion, which remained strongly significant in all cases (see SM11 for details). While this is reassuring, self-reports of sharing may not be entirely reliable and may also be partly endogenous to game play.

With these limitations in mind, we ran a further set of treatments that we call the sharing study (table 1). For this study, we recruited fresh participants individually (hence, subjects typically did not know any other participant). Subjects played the weak-link game of table 2 (where b = 6) following other standard procedures used across our studies but with the distinguishing feature that before making their game decisions, subjects were told that there was some probability that we would pool all individual earnings within each group and share them equally among group members. We implemented three versions of this protocol (n = 60 each) with the known probability of sharing being 0.5, 0.8, or 1. This allows us to assess an upper bound for the impact of sharing (when sharing is certain) and its sensitivity to different levels of uncertainty associated with any potential sharing arrangement.

The treatment where sharing is certain generated an average minimum effort of 2.73, which is comparable to the expected minimum effort associated with a group cohesion of close to 5 (see SM12). While introducing a little uncertainty about sharing (by setting the sharing probability at 80%) depressed average minimum effort a little (to a value just below 2.5), when the likelihood of sharing was only 50%, average minimum effort fell dramatically to a level only slightly above 1 (see figure SM12.1). While this evidence does not eliminate the possibility that expectations of sharing played some role, it counts against it being a convincing explanation of the broad patterns in our data; this is so because the ceiling of the sharing effect is well below the predicted effect of maximal cohesion (= 7) and because uncertainty about sharing, quite likely in any actual sharing arrangements, rapidly diminishes its impact.

The results of the sharing study are interesting for the further reason that the treatment where sharing is certain can be interpreted as implementing an extreme form of social preferences in which each agent places the same weight on the earnings of all group members, including themselves. Viewed in this way, the results are consistent with some explanatory role for social preferences, albeit a limited one. A natural question is then, what is the relative importance of social preferences versus beliefs in mediating the impact of cohesion on effort?¹⁵

The first equation posits beliefs, (social) preferences, and group cohesion as determinants of minimum effort. Group cohesion is treated as the unique (a priori) exogenous variable that can influence minimum effort directly (equation (1)) and, indirectly, via beliefs (equation (2)), or social preferences (equation (3)).¹⁸ In the spirit of models linking social preferences and beliefs (Dufwenberg, Gächter, & Hennig-Schmidt, 2011), the model also allows social preferences to influence beliefs (equation (2)). Although very simple from a psychological point of view, the model is presented in the spirit of a tool for assessing the relative importance of beliefs and social preferences as channels mediating the impact of group cohesion on effort, in our data.¹⁹

The estimated model produces significant coefficients (at 5% or 1% levels) for every β coefficient except one: we find no direct effect from social preferences to minimum effort (i.e., β₂ is not significantly different from 0). Hence, group cohesion has an impact on minimum effort through three active channels: it operates directly (via β₃) and through its impacts on both beliefs and social preferences, though the last of these channels works entirely through the secondary effect of social preferences on beliefs. (Detailed estimation results are in the supplemental material, table SM13.1.)

For a variety of reasons, we suggest that the results of this decomposition be treated as tentative, absent further replication or other support. For example, we note a difference between the status of our measurements of beliefs and social preferences: specifically, while elicited beliefs measure something intrinsic to the weak-link games played by our participants, the measured social preferences capture something external to the game context. This might have led to underestimation of the role of social preferences.²⁰ We could also measure social preferences in multiple different ways and an approach combining alternative ways of measuring them (Gillen, Snowberg, & Yariv, 2019) could be an interesting avenue for checking the robustness of our conclusions from the mediation analysis. In addition, we cannot rule out the possibility that measured social preferences were to some extent influenced by experiences in the play of the weak-link games, although conditional on there being such an effect, it seems most plausible to assume that success in the weak-link game would have encouraged more generous allocations in social value orientation SVO tasks. In that case, our decomposition analysis should be interpreted as identifying an upper bound on the contribution of social preferences. Notwithstanding these potential reservations, however, the fact that the lion's share of the work is done by beliefs in our data stands in distinct contrast to results based on experiments using artificially induced groups (see Chen & Chen, 2011). At a minimum, we therefore suggest that our results should unsettle any presumption that social preferences are the primary channel through which within-group relationships affect success in team production.

It is hard to deny that social relationships may affect many variables that naturally interest economists. An open question is how much they matter and whether economic analysis could take account of them in a sufficiently parsimonious way to render the undertaking tractable and worthwhile. The research presented in this paper sheds new, and positive, light on these issues.

In this paper, we have explored the power of group cohesion, a hitherto unobservable characteristic and potential “production factor” of any real group, as a tool for predicting strategic behavior, adopting the weak-link setting as a workhorse for proof of concept. Our previous related research has established that the oneness scale, on which our measurement of group cohesion is based, is simple to implement, highly portable, and correlates extremely well with more detailed measures of personal relationships (Gächter et al., 2015). We used our measure of group cohesion, a group-level statistic of the oneness scale, to study the cohesion of real groups. We showed that group cohesion varies across groups as predicted by relevant sociological and psychological literature and is stable based on test-retest measurement.

Using an extensive set of experiments involving 1,160 participants and including a variety of robustness tests, benchmarking exercises, and an independent preregistered replication, we examined the predictive power of group cohesion in the context of experimental weak-link coordination games played by real groups that vary in the extent of preexisting social relationships among their members. Despite no possibilities for communication, high-cohesion groups do much better in terms of the equilibria they achieve in weak-link games, and low-cohesion groups rarely, if ever, do well. We used an econometric approach to explore possible mechanisms underpinning the association between group cohesion and group minimum effort and found that in our model, group cohesion shapes both beliefs and social preferences but with beliefs emerging as the primary channel. We have also presented evidence that the changes in effort associated with variation in cohesion can be considered large in the context we have studied.

While we cannot directly extrapolate to predict the scale of comparable effects in other lab or in field contexts beyond those we have studied, our results do provide motivation for exploring such issues using our group cohesion index. On the assumption that our results do translate to the field, they have particular potential significance in the context of organizational performance (Akerlof & Kranton, 2005); Ashraf & Bandiera, 2018). If group cohesion is associated with desirable team or group outcomes across a variety of organizational settings, then our tool may facilitate a wide range of productive applied research. And for those with interests in engineering better organizational or team performance, oneness measurement techniques may be valuable for assessing the impact of interventions, including the variety of team-building activities in which so many organizations already invest.

More generally, beyond the new evidence we have presented, we believe we have provided proof of concept for a new simple and portable tool designed to facilitate the quantitative study of social relationships as factors of team production.

Data and analysis code are available at https://osf.io/g9u3e.