Abstract
Group outcomes are difficult to model and predict using individual-level metrics. We use shared cognition concepts and the social relations model to predict cooperative group outcomes in two social dilemmas to test whether social projection or consensus among group members would best predict cooperation. Group-level variance components derived from the social relations model were used as indices of social projection and consensus. Groups played five rounds of two social dilemmas and predicted their partners’ behavior on the following round. Results demonstrate that participants expect other group members to respond to the situation like the participant will and that shared expectations predict less competitive group behavior, but only when group members’ expectations have little to no variance. This article demonstrates the utility of the social relations model in predicting group-level outcomes from individual inputs, as well as providing novel findings regarding the complex effects of shared expectations on collective outcomes.
The city in which we live has a self-stated problem with drivers running red lights. Considering the amazing frequency in which drivers run red lights—shown by one local newscast (Kurtz, 2011) to be nearly two cars per light at one busy intersection—one might predict frequent negative consequences associated with this behavior. Anticipating these negative consequences, money has been spent for billboards and television advertisements with the slogan “Red Means Stop.” Signs have been placed at problem intersections reminding drivers of the consequences of running red lights, including damage to their vehicles, fines, and lost driver’s license points. Yet, in spite of the public relations campaign, the behavior persists.
Drivers running red lights are essentially creating a hazardous situation for the community by being individually selfish. Individually, drivers are attempting to gain the benefits of continuing on their preferred course unimpeded. Collectively, this behavior creates the potential for increased traffic accidents. One might fear that everyone would start trying to gain these individual rewards at the expense of the safety of the entire group. If the situation were taken to an extreme, all drivers would start running red lights at all times, traffic laws would become meaningless, and the roads would be a much more dangerous place for everyone. However, this does not happen. When drivers are waiting at a red light and the light turns green, they do not immediately accelerate into the intersection. Instead, they wait, possibly because they are expecting that other drivers will run the red light and will still be in their way when their light turns green. Because they have expectations about how people in this city generally respond to red lights—that is, treat them as if they were yellow lights—they adjust their behavior to get the best possible outcome for themselves.
This running red lights example follows the general pattern of the classic “tragedy of the commons” (Hardin, 1968). In the tragedy of the commons, a selfish or individualistic gain for an individual is rationalized due to the relatively small cost to the collective of exploiting the resource. The benefits to running the light for one person are meaningful, while the cost to the group—inconveniencing the driver whose light has turned green but now must wait for the intersection to clear—is relatively small. The small cost to the collective is exactly what leads to the collapse of the entire resource (Hardin, 1968; Komorita & Parks, 1996). One would expect running red lights to become more and more common until the situation collapses. However, the traffic situation in this city did not collapse. Traffic lights are still obeyed in a general sense. As the traffic lights example follows the general pattern of the tragedy of the commons, we must explain why the resource is not being exploited to the point of mutual destruction. To this end, we will demonstrate that the idea of shared cognition—typically used in interacting teams—can explain how the distribution of expectations within a group can provide valuable insights into cooperation and competition in collectives (Hinsz & Ladbury, 2013; Ladbury & Hinsz, 2013).
Shared Cognition
Shared cognition is involved in a large and diverse literature concerned with information sharing among individuals (Hinsz, Tindale, & Vollrath, 1997; Nye & Bower, 1996; Salas, Fiore, & Letsky, 2013; Tindale, Meisenhelder, Dykema-Engblade, & Hogg, 2001). The general ideas take many forms in research, but shared mental models is one common notion by which researchers have come to understand shared cognition. Shared mental models have been identified as a means by which team performance and interaction is enhanced (DeChurch & Mesmer-Magnus, 2010; Mathieu, Heffner, Goodwin, Salas, & Cannon-Bowers, 2000; Mohammed, Ferzandi, & Hamilton, 2010). Shared mental models have been defined in many ways, all centering around the sharing of information within a team concerning how the team itself will function (Hinsz, 1995, 2004). Decades of empirical work on interacting teams has shown the utility of shared mental models for understanding team performance when a task is interdependent (DeChurch & Mesmer-Magnus, 2010; Mohammed et al., 2010). It is commonly proposed that shared mental models influence task performance because they encourage sharing of information on coordinated tasks (Larson, 2010; Mesmer-Magnus & DeChurch, 2009).
However, we should more closely examine the concept of information sharing in shared cognition. The tradition of shared mental models and, more generally, shared cognition typically assumes accuracy of shared information by the members (Hinsz & Ladbury, 2013). This assumption is reasonable because shared mental models are usually used to model interacting groups that experience either the same circumstances or receive some form of cross-role training that gives the members some expertise. For shared information to facilitate coordination, the shared information must be accurate (Hinsz & Ladbury, 2013; Lim & Klein, 2006; Mathieu et al., 2000). If two people share an incorrect idea about how a process is supposed to occur, outcomes are unlikely to improve. If two people are in a mathematics study group and both believe that 2 + 2 = 5, that shared, but incorrect, information will be accepted as valid. There will be no disagreement that would facilitate accuracy.
As we examine the idea of sharing, we should also recognize that it is possible to share information in more than one way. It is possible that sharing can imply that all members of a group have the same piece of information. Alternatively, the group could share information about what everyone’s role is and have consensus that if a particular situation arises that should be under the auspices of Person A’s role, then Person A will handle it, as in transactive memory (Littlepage, Hollingshead, Drake, & Littlepage, 2008; Moreland, Argote, & Krishnan, 1996). Or, sharing could also imply that all group members share the expectation that each group member has the same information, but reality does not meet that expectation and everyone actually has different information. In this way, our conceptualization is more akin to shared representations (Tindale, Smith, Thomas, Filkins, & Sheffey, 1996) or team member schema similarity (Rentsch & Hall, 1994). Yet, it is important to recognize that these mental models encapsulate the expectations members have about the knowledge and anticipated behaviors of fellow group members. Moreover, these expectations are relevant for groups performing a variety of tasks (DeChurch & Mesmer-Magnus, 2010).
Social Dilemmas
We chose to apply the ideas of shared cognition to interdependent situations known as social dilemmas. 1 More specifically, the social dilemmas we refer to reflect two types of situations: (a) individuals within a group are endowed with resources and must donate some of those resources to a collective pool to achieve some collective reward (i.e., a public goods game) or (b) individuals within a group are given access to a shared pool of resources and will receive some bonus if the resource is managed and conserved effectively (i.e., resource allocation game).
In addition, the dilemmas we focus on had a particular payoff structure known as a threshold system. In a threshold system, the benefit of providing for the public good or managing the resource is granted if a particular threshold of giving is crossed, as in the case of the public goods game, or if a particular threshold of taking is not crossed, as in the case of the resource allocation game. Focusing on this payoff structure allowed for intriguing behavior, because in each situation, there are two methods of group action that could be considered rational (Abele, Stasser, & Chartier, 2010). In game-theory terms, such situations are known as dual-equilibrium situations (Kollock, 1998). The first set of rational actions would be to exploit the others. In the public goods game, this would mean a player would hold all of their own points while hoping the other players are donating a greater proportion of their own. In this way, the player does not spend any of their own resources but still benefits from the collective reward that the others generated. Similarly, in resource allocation games, one player could attempt to take as much as possible from the resource while hoping that the other players are committed to conservation. The second possible rational course to follow is to opt for collective action. In the public goods game, each individual could put forward just enough resources so that, when combined with all other group members, the threshold to create the public good is just crossed. Similarly, in the resource allocation game, groups could choose to harvest from the collective pool so that the remaining pool will be just large enough to restock itself. In this way, these dilemmas create opportunities for either exploitation or cooperation, both of which could be considered rational. Thus, we can investigate exploitation as well as trust (i.e., willful exposure to potential exploitation), competition and cooperation, and the pursuit of collective or self-interests using public goods and resource allocation games.
Importance of Expectations in Shared Cognition
Expectations that members have of an interaction are an important component in many areas of study including team functioning, negotiation, and trust (Barsade & Gibson, 2012; Dawes, McTavish, & Shaklee, 1977; Diekmann, Tenbrunsel, & Galinsky, 2003; Krueger, DiDonato, & Freestone, 2012). We consider these interaction expectations as task-centric beliefs about other individuals, their potential behavior, or the nature of their interaction with others (Ladbury & Hinsz, 2013). We are particularly interested in how a shared understanding of expectations can lead to cooperative or competitive outcomes.
Expectations influence the processes by which members interact in groups (Hinsz, 1995). This premise is not foreign in traditional small group research. The theory of combinations of contributions (Hinsz & Ladbury, 2013; Hinsz et al., 1997) and the Input-Process-Outcome (IPO) framework (McGrath, 1964) posit that expectations are part of the inputs that members bring with them to the group interaction and task performance. Shared task representations and shared mental models both hold that beliefs that members have about the task and interaction influence how groups interact and perform tasks (Hinsz, 1995). Thus, expectations, as beliefs, will influence group interaction, process, and performance. We are particularly interested in how these expectations could influence tendencies for members to cooperate or compete in social dilemmas.
Kelley and Stahelski (1970) demonstrate the impact of expectations in terms of disconnected perceptions in a Prisoner’s Dilemma Game. In prisoner’s dilemmas, two participants confront a situation in which each participant’s outcomes are interdependent with the other’s outcomes. Rationally, it is always in the participant’s interest to act competitively (Komorita & Parks, 1996). A competitive participant has a tactical advantage in a prisoner’s dilemma, but most participants choose the cooperative option (Camerer, 2003). In Kelley and Stahelski (1970), participants were randomly assigned to expect that their partner would either respond cooperatively or competitively. Participants assigned to expect a competitive partner tended to be suspicious and skeptical of their partner, even if the partner began with a cooperative strategy. Over time, this led the participant to make more competitive choices. The tactical flow of the game forced the player’s partner to change from whatever strategy they began using to a competitive strategy. Changing strategies then caused the participant to misperceive the cooperative player as competitive, validating the participant’s expectation from study instructions that their interaction partner would play the game competitively. Other studies confirm the basic notion that expecting an interaction partner to be competitive increases competitive tendencies in the participant (e.g., Beersma et al., 2009; Dawes et al., 1977; Rockmann & Northcraft, 2010). Thus, when engaging with a social dilemma, each participant uses an expectation of the behavior of others to determine their own behavior. In this way, inaccurate, unshared expectations create disconnects in perception, especially when one interaction partner has expectations violated and another does not.
Predicting Group Outcomes From Individual Expectations
Studies that examine the strategically “best” way to solve social dilemmas tend to focus on individual outcomes. Focusing on individual outcomes makes sense in many cases because the research questions being addressed are usually about individuals. In addition, individual outcomes can be easily established for each participant, creating an easily operationalized and interpretable measure of behavior. However, a focus on individual outcomes leaves a fundamental question unaddressed: How do individual expectations impact collective outcomes in social dilemmas with more than the two participants? Many commonly encountered group situations have social dilemma-like qualities, for example, running red lights, donating to public broadcasting, nuclear proliferation, and trade negotiations. These are important problems with real consequences that require useful solutions. We need to understand the nature of cooperation and competition in groups to solve these problems.
As the outcomes of social dilemmas indicate, there is a large amount of interdependence associated with group interaction and performance. This interdependence can be so pervasive that it is difficult to tease apart why a particular individual would act in a particular way (Cronbach, 1955; Cronbach, Gleser, Nanda, & Rajaratnam, 1972; Gage & Cronbach, 1955). To demonstrate the interdependence, imagine the scenario depicted in the top panel of Figure 1 in which a group of four individuals all state how much they expect each of the other members of the group will contribute to a hypothetical public good, with contributions ranging from 1 to 50. When we ask why Group Member A rates Group Member D at the highest level on this measure, we as researchers run into a problem. If we look at Group Member A’s ratings of other group members, it appears that Member A rates everyone at the highest level. Member A may have a personal belief that the good the group is trying to create is valuable and useful, and also assumes that all other group members will interpret the situation in exactly the same way. However, it also appears the other group members rate Group Member D at the highest level as well. So, perhaps there is something inherent to Group Member D that is leading the others to expect high contributions from Member D. Although both descriptions for Group Member A’s rating of Group Member D are acceptable, traditional statistical techniques have difficulty separating the two possible explanations.

Hypothetical group rating all members on a hypothetical measure.
Because of this interdependence problem, attempting to use individual metrics to predict collective outcomes is surprisingly difficult (Berri & Schmidt, 2010). This difficulty features prominently in the debate on the usefulness of the IPO conceptual framework (Ilgen, Hollenbeck, Johnson, & Jundt, 2005; Kozlowski & Ilgen, 2006). The IPO framework (McGrath, 1964) proposes that group outcomes are a function of processes that occur within the group which are themselves a function of group member inputs. Inputs can be characteristics of the members such as personality, skills, cultural dispositions, trustworthiness, and so on. The conceptual framework implies that group processes mediate between group member inputs and group outcomes. However, most statistical tools available cannot model a variable at the group level from measurements taken at the individual level. Thus, the IPO framework suggests that processes of groups are important for understanding group outcomes, such as the outcome of a social dilemma. However, there is little research that extends this set of arguments beyond saying that “process is important” (Ilgen et al., 2005).
Originally it was work by Cronbach (1955) on generalizability theory (Cronbach et al., 1972) that set the stage for describing how variance in social judgments can impact group outcomes. Importantly, ideas pertaining to generalizability theory were impressively advanced by Kenny (1994) and Kenny, Kashy, and Cook (2006) resulting in the social relations model (SRM). SRM is a powerful model that suggests that judgments by individual members of a group can be combined and partitioned into variance components that summarize underlying social processes—summaries of social processes that are predictive of group outcomes. That is, we can use the SRM to summarize social process. In particular, the metrics provided by SRM are variables that summarize underlying social process that help advance our understanding of how member expectations contribute to the prediction of group outcomes.
SRM uses dyadic data in which everyone makes judgments of everyone else (e.g., round robin). The complete set of dyadic data in a group can be used to calculate three potential sources of variance within a matrix of dyadic data. These sources of variance are (a) the individual rater may be rating all people similarly—commonly called actor effects or assimilation in the SRM literature because the ratings assimilate to a common belief held by the rater; (b) the person being rated may be rated similarly by all other group members—commonly called partner effects or consensus because it reflects a shared belief about the ratee; and (c) two individuals within the group may have unique perspectives of one another and use those perspectives to rate certain interaction partners in ways that they do not rate others—called relationship effects in SRM. When each individual’s actor, partner, and relationship effects are added to the group mean, each individual rating can be reconstructed. Most importantly, the actor, partner, and relationship effects are statistically independent of one another, allowing for differentiation between a process that occurs within the individual and a process that occurs because of a collective perception of an individual. 2
Once the individual actor, partner, and relationship effects are calculated, the variability in each effect across the members of an interacting group can be used to create group-level metrics of assimilation, consensus, and relationships. 3 In this way, the analysis takes an individual-level phenomenon and transforms it into variance at the group level.
SRM is particularly useful as a way to overcome the levels of analysis problem and index group processes based on individual inputs (Ladbury & Hinsz, 2013; Rentsch & Woehr, 2004). Essentially, the SRM variance components can be considered numerical indices of specific internal group processes. Returning to the middle panel of Figure 1, this group has a high assimilation variance and a low consensus variance. Looking across the rows, each of the four group members has expectations about what will happen in this group. Their expectations are not only uniform within an individual but also variable across individuals. Looking down the columns, the members of this group do not agree about what each individual person will do in this hypothetical situation. This combination of factors leads group members to be more confident than correct about the outcome of this hypothetical situation. The bottom panel of Figure 1 depicts a hypothetical group with low assimilation and high consensus. In this case, group members agree regarding how each other group member will respond. They also agree that the four group members would all respond differently to the situation. SRM provides a means to quantify these psychological factors as indices that can then be used to predict group-level outcomes. Hence, SRM fills a critical gap in the IPO framework by numerically indexing the sometimes difficult-to-quantify process term thought to mediate between inputs and outcomes (Ilgen et al., 2005; Weingart, 1997).
The research we conducted builds upon the ideas of shared cognition and expectations. The purpose of the study reported is twofold. First, we seek to understand how individual expectations are distributed within interacting groups completing a social dilemma with more than two members. For instance, are expectations built on considerations of each interaction partner individually based on the interaction partner’s prior behavior or are they abstracted for another source, such as the self? Second, and critically important, the study attempts to empirically demonstrate whether the distribution of member expectations alters group outcomes in various social dilemmas situations. If expectations are important for collective outcomes, and previous studies seem to indicate they are, in what way will the distribution of expectations impact which rational solution the group will pursue?
Hypotheses
Our first research question involves the source of expectations about other group members. One perspective indicates that expectations are built upon the behavior of the group members (Dawes et al., 1977; Kelley & Stahelski, 1970). This perspective implies that participant’s expectations about other group members’ behavior should generally correspond to the others’ observed behavior. In SRM parlance, this would be indicated by a self–other agreement effect. However, the social projection perspective (Acevedo & Krueger, 2005; Krueger & Acevedo, 2007; Krueger et al., 2012) predicts that expectations of the others’ behavior should generalize from an expectation of what the self will do. In SRM terms, this would be indicated by an assumed similarity effect. Therefore, Hypothesis 1 is presented as a comparative test between two potential explanations.
Our second hypothesis concerns the variance in the members’ expectations within groups.
Group members are hypothesized to be able to recognize when a group member is consistently cooperative and when they are consistently competitive based on that feedback. Indeed, many theories of group effectiveness note that the creation of a “working consensus” (Swann, Milton, & Polzer, 2000) regarding each group member is an important first step toward optimal group performance (Bushe & Coetzer, 2007).
Significant assimilation and consensus variance are predicted by Hypotheses 2a and 2b. Assuming they are found, assimilation and consensus variance are hypothesized to predict group-level outcomes in public goods and resource allocation games. The specific direction of this prediction depends on the theoretical formulation. According to theory that social projection is an important process in cooperation (Krueger et al., 2012), the following pattern is anticipated.
Furthermore, if social projection is the key variable in influencing behavior in these social dilemmas, an individual’s level of assimilation should be correlated with that individual’s expectation of how cooperative he or she will be during the dilemma—a variable termed self-expectation.
Consensus represents a belief shared by teammates about how a specific group member behaves. Without consensus, some members would have inaccurate expectations of their interaction partners. An actual cooperative member may be viewed as competitive, even if that group member acts in a cooperative manner during the first few rounds. Rather than increasing cooperation among partners, the cooperative behavior of a member may increase suspicion and doubt by partners. Because consensus features prominently in theories of effective group interaction, and previous empirical work shows that inaccurate beliefs tend to increase competition (Diekmann et al., 2003; Kelley & Stahelski, 1970), we predict the following:
Method
Participants and Design
Undergraduate students (N = 148) participated in this research and received course credit for completing the study. Each participant was placed in a group of four individuals for a total of 37 groups. As this research involves a new application of the SRM, effect sizes of the relationships do not exist, nor could they be used to determine appropriate estimated sample sizes. Therefore, we used the central limit theorem as a guideline for recruiting approximately 30 experimental units (in this case, groups) into the study.
Each group played five iterated rounds of both a resource allocation and public goods game with the order of each game counterbalanced. One group was not able to complete the public goods game due to technical difficulties that kept their data from being recorded. A second group had their data from both the public goods and resource allocation game removed because they communicated during the experimental session, even after several reminders that communication was not allowed.
Social Dilemmas
Participants were told at the beginning of each game (i.e., public goods or resource allocation game) that every 100 points they accumulated individually would be worth one entry into a lottery in which they could win prizes of US$100 or US$50. For the public goods game, each participant began the game with an endowment of 125 points. The participants were informed that each person could contribute up to 50 points per round to a central resource pool. If the entire group contributed 125 points or more to the central resource pool, each member of the group would receive a bonus of 75 points. Group members would receive this bonus regardless of how many points each group member contributed. After each round, the participants were given feedback regarding each participant’s contributions to the resource pool. After receiving feedback, the next round began with the same restrictions as the previous round, but participants were contributing resources from their existing pool rather than the initial pool of 125 (i.e., if the participant contributed 50 points to the resource pool during the first round and the bonus was not given, she or he had only a pool of 75 points to draw from for the second trial). This procedure was repeated for five rounds.
The resource allocation game proceeded in a similar manner. However, in the resource allocation game, a pool of 500 points was provided to the group at the beginning of the game. They were told each group member could harvest up to 50 points from the pool. If the total harvest by the group was 75 points or less, they received a bonus of 75 points per group member regardless of how much each one harvested. The participants harvested resources from the same pool during the next round. Thus, if all four group members harvested 50 points during round one, they would harvest from a pool of 300 points for the second round. After the participants made their decisions, they were given feedback regarding the amount of resources each person harvested. This procedure was repeated for five rounds or until the pool of resources was completely depleted. During the actual experiment, no group completely exhausted the resource pool before the fifth round.
Procedure
Each group was randomly assigned to complete either the public goods game or the resource allocation game first. Before involvement in the games, participants completed measures of familiarity regarding their interaction partners and social value orientation (Messick & McClintock, 1968; Van Lange, Otten, De Bruin, & Joireman, 1997). Familiarity with their interaction partners and social value orientation did not impact any of the dependent variables and will not be discussed further.
Once participants had been placed in their assigned groups, they completed a team building exercise so they would have some basis for making judgments during the study. The team building exercise took the form of a survival scenario in which the group had to reach consensus regarding what materials would best allow them to survive a plane crash in sub-zero weather (“SURVIVAL: A Simulation Game,” n.d.). After completing the team building exercise, participants completed the social dilemmas as described above.
Before each round began, participants’ expectations of their group members’ contribution or harvesting behavior were assessed using a single question, “How many points do you expect Group Member 1 to contribute/harvest during the next round?” Participants were asked to report on every other group member. The expectations measure was asked at the beginning of each round. Participants were also asked to report, at the beginning of each round, how many points they expected to contribute or harvest during the following round (self-expectation).
Once the group finished both games, they were debriefed on the purpose of the study. At the conclusion of data gathering, the drawing for the cash prize was conducted and those who were due the US$50 and US$100 received their rewards.
Data Analysis
Unless otherwise specified, expectation data were analyzed using the SoReMo software package available online at http://davidakenny.net/srm/srmp.htm. Raw data were entered into text files which were then read into SoReMo. To test the statistical significance of SRM variance components, all data were entered into a single text file and analyzed together. To test the relationships between SRM variance components and outcomes, each group had their assimilation and consensus variance calculated separately. The resulting variance components were entered into SPSS to conduct the regression analyses.
Results
Rates of Contribution and Harvest
Across all rounds of the public goods dilemma, the mean group contribution was just above the threshold needed to receive the cooperation bonus (M = 125.02, SD = 23.60), with the mean individual contributions ranging between 31.51 (SD = 9.49) in Round 2 and 30.95 (SD = 9.98) in Round 5. Remember that larger contributions indicate more cooperative behavior and a greater likelihood of receiving the bonus in the public goods dilemma. On average, groups tended to contribute enough resources to receive the cooperation bonus during about three of the five rounds (M = 3.05, SD = 1.61).
During the resource allocation game, the average level of harvesting across all rounds was slightly larger than the threshold needed to receive the cooperation bonus (M = 76.49, SD = 23.30), with the mean individual harvests ranging between 20.06 (SD = 11.99) in Round 1 and 17.69 (SD = 9.16) in Round 5. Remember that smaller harvests indicate more cooperative behavior in the resource allocation dilemma. For this game, groups also received the cooperation bonus after more than three of the five rounds (M = 3.14, SD = 1.80).
Order Effects
Order of the two social dilemma games was counterbalanced within the study. To test whether order influenced cooperative or competitive behavior, the number of bonuses the group received was entered into a 2 (Order: public goods first vs. resource allocation first) × 2 (Game: public goods vs. resource allocation) ANOVA with Game as a repeated measures factor. The analysis revealed no main effects of either order, F(1, 35) = 0.01, p = .91, or game, F(1, 35) = 0.09, p = .76. The interaction effect between order and game was not significant, F(1, 35) = 3.24, p = .08. Thus, order of the games did not significantly impact cooperative behavior as measured by the number of bonuses the group received.
The contributions given during each round of the public goods game and the harvests taken during each round of the resource allocation game were also analyzed for order effects. Contributions during each single round of the public goods game were entered into a regression equation as a dependent variable with order—either public goods game first or resource allocation game first—entered as a dummy coded predictor. Order did not predict contributions during any round of the public goods game (all Fs < 2.46, all ps > .13). Similarly, harvests during each round of the resource allocation game were subjected to the same analysis with order as a dummy coded predictor. One order effect emerged. Groups that completed the public goods game first tended to harvest fewer points during the first round of the resource allocation game than groups that completed the resource allocation game first, F(1, 35) = 6.59, p < .05, B = −22.08, t = −2.57, p < .05. Because this was the only effect of order for either game for any of the rounds, little consideration will be given to this unstable order effect and the effect of order will not be discussed further.
Self-Expectations With Assimilation and Consensus Effects
Public goods game self-expectations
Prior to establishing the participant’s expectations for the other members of the group, participants answered how much they expected they would contribute to the public good in the following round. These data were used to test Hypothesis 1. Self-ratings were correlated with the degree to which the individual expected similar contributions from the rest of the group members (assimilation effects). This correlation establishes assumed similarity 4 (Kenny et al., 2006), that is, the belief that everyone else will contribute a similar amount as the person. Assumed similarity correlations were significant across all rounds (see Table 1). In general, the results are consistent with a social projection perspective that participants believed their interaction partners would contribute a similar number of points as themselves.
Relative Percentage of SRM Variance Components and Correlations With Self-Expectations.
Note. Bold values indicate variance significantly different from 0, p < .05. n = 35 groups for public goods game and n = 36 groups for resource allocation game. Assumed similarity and self–other agreement are partial correlations of self-expectation with assimilation effects and self-expectation with consensus effects, respectively, corrected for measurement error. SRM = Social Relations Model.
Self-expectations can also be correlated with consensus effects to determine whether or not the participants’ expectations for themselves match the expectations other group members have regarding that person. This correlation is termed self–other agreement. Correlations in this case are numerically substantial but not significant (see Table 1), most likely due to the restricted range and limited variability within the consensus effects for the expectation measures. SoReMo corrects the numerical value of these correlations for measurement error. However, the significance test is run on the non-corrected magnitudes (Kenny et al., 2006). Thus, the correlations can be large but nonsignificant if there is a large amount of measurement error in the data. Table 1 shows that very little self–other agreement is indicated by the data.
Another analysis involving self-expectations tested whether a participant’s self-expectation for how much she or he would contribute during a round was related to her or his actual contribution during that round. Self-expectations were significantly correlated with actual contributions during all five rounds of the public goods game (see Table 2, diagonal values). However, the correlations are not as substantial as one may expect given that the assessment of expectations occurred minutes before the actual behavior (r = .41 across all rounds). This correlation indicates that, while self-expectations relate to actual behavior, there is some adjustment between the assessment of self-expectations and actual behavior.
Correlations Between Actual Behavior and Self-Expectations Across All Rounds (N = 148).
Note. Bold values indicate significance, p < .05.
The potential differences between self-expectations and actual behavior raise interesting additional questions. If self-expectations and behavior differ, how and why do the differences occur? Do participants believe they will be more generous when making their expectation judgments than they decide to be when actually making their contribution? Or do participants believe they will be more competitive when assessing their expectations and change their actual behavior to be more group oriented? To answer these questions, the number of points the participant expected to contribute was subtracted from the number of points the participant actually contributed. The difference scores were not significantly different from zero, but the means tended to be positive numbers indicating that they were more cooperative in their actions than in their expectations (see Table 3).
Means, Standard Deviations, and Mean Differences Between Self-Expectations and Behavior (N = 148).
Note. Bold values indicate significance, p < .05.
Resource allocation game self-expectations
Participants were also asked how many resources they expected they would harvest for themselves during the next round of the resource allocation game. These measures were correlated with assimilation and consensus effects to establish assumed similarity and self–other agreement. Assumed similarity occurred during all rounds of the resource allocation task (see Table 1). As with the public goods game, participants generally expected their interaction partners to harvest a similar number of points as they expected they would harvest themselves.
Correlations between the self-expectations and consensus effects were also calculated to see if the participant and the rest of the group agreed on how many points the participant would harvest from the pool during that round. Similar to the results in the public goods game, some of the correlations were numerically substantial, but none achieved significance (see Table 1). Again, the rest of the group had very little agreement with the participant regarding how many points that participant would harvest.
As with the public goods game, self-expectations of harvests during each round were correlated with actual harvests during that same round (see Table 2). The correlations in this case were again significant (r = .41 across all rounds), but not as extensive as might be expected given the limited time between the assessment of self-expectations and actual behavior. Expectations in both games are related to actual behavior but there is room for adjustment between measurement of expectations and actual behavior.
The difference score between actual harvest and self-expectations was also calculated for harvests during each round for the resource allocation game. The difference between self-expectations and harvests was negative and significantly different from zero during Rounds 1, 2, and 5. The negative sign indicates that actual harvests were smaller than expectations for harvests, indicating that participants were more cooperative when asked directly for harvests than when assessing expectations.
SRM Variance Components
Using the SoReMo software, it is possible to decompose the pattern of responses of group members for each trial in each game. The decomposition provides variance components that are indices for assimilation (i.e., the degree that raters provide similar ratings for all other groups members) and for consensus (i.e., the degree that group members are rated consistently by others).
Public goods game
In the public goods game, there was significant assimilation variance at the group level for Rounds 1 to 4 (see Table 1), showing support for Hypothesis 2a on this task. In general, group members expected everyone else in the group would contribute a similar amount of points to the public good, but there was variation within the group regarding what the expected contribution level would be. As can be seen in Table 1, actor variance has a downward trend, as Hypothesis 2b implied, but assimilation variance does not diminish entirely. Consensus variance was minimal and nonsignificant for all rounds of the public goods game (see Table 1) suggesting that groups did not achieve consensus on which group members would contribute many resources and which would contribute few, even after being provided accurate feedback after each round. The prediction of Hypothesis 2b that consensus would build as the game progressed was not supported.
Resource allocation game
For the resource allocation game, significant variance in the SRM variance components at the group level was found for all rounds. Assimilation variance was significant across all rounds of the dilemma and consensus was significant for Rounds 2, 3, and 5. These findings indicate that in the resource allocation game—much like in the public goods game—group members generally believed that each of their interaction partners would act similarly, but there was disagreement regarding what the actual level of harvesting should be. However, as the resource allocation game progressed, there was some increase in the degree of agreement reached across participants regarding what each individual may do during the subsequent round. In this way, Hypotheses 2a and 2b were supported for the resource allocation game. 5
SRM Variances Associated With Expectations Predicting Contributions and Harvests
For the preceding analyses, all groups were entered into a single model assessing the experiment-wise level of assimilation and consensus variance. For the following analyses, each individual group had their assimilation and consensus variances calculated separately. Assimilation and consensus variances calculated from participants’ expectations of their group members’ behavior were entered as predictors into a regression equation with total contributions given by all group members during a single round as the dependent variable. This analysis tests the predictions of Hypothesis 3a and 3b that either assimilation or consensus variance would predict higher levels of cooperation. For these analyses, absolute variances rather than relative variances were used as they more closely approximated a normal distribution. Separate regression equations were calculated for each round of the game.
Public goods game
Results indicate assimilation variance predicted the total contributions during Rounds 1, 3, and 4 of the public goods game (see Table 4), but not entirely in the manner predicted by Hypotheses 3a and 3b. Hypothesis 3a predicted that assimilation variance would lead to cooperative outcomes. This hypothesis was not supported and, in fact, the opposite was shown. Group-level assimilation variance significantly predicted lower levels of contributions except during Round 3 where the effect p value is .06. Stated differently, belief within a group that all group members would contribute a similar number of points to the public good combined with divergent views of what the contribution should be was indicative of less cooperative behavior. This pattern is depicted in the top half of Figure 2. Note that across nearly all rounds, groups that were 1 standard deviation above the mean on assimilation variance tended to fall short of the bonus threshold, whereas groups that were 1 standard deviation below the mean in assimilation variance tended to exceed the threshold.
Regression Tables for Assimilation and Consensus Variance Predicting Group-Level Contributions in the Public Goods Game.
Note. Bold values indicate significance, p < .05, n = 35 groups for Public Goods, n = 36 groups for Resource Allocation.

Predicted contributions (top half) and harvests (bottom half) of groups that are 1 SD above and 1 SD below the mean on assimilation variance.
Hypothesis 3b (Consensus Leads to Group Cooperation) was not supported, most likely because group members cannot be shown to have developed any level of consensus across the five rounds of the public goods game. Thus, the impact of consensus on cooperation in public goods dilemmas remains an open question.
Resource allocation game
Paralleling our findings with the public goods game, assimilation and/or consensus variance were shown to be significant predictors of the total number of harvests each group made during all five rounds. Again, assimilation variance was the primary predictor of group-level harvests. In this case, the more variable the individual assimilation scores were, the more the group tended to harvest during any given round. The belief within the group that everyone would harvest a similar number of points combined with divergent views of what the harvest was expected to be was associated with less cooperative behavior (see Table 4). The bottom half of Figure 2 shows this pattern. Groups that are 1 standard deviation above the mean on assimilation variance tend to exceed the harvesting threshold and do not receive the bonus. Groups that are 1 standard deviation below the mean tend to harvest within the threshold and receive the bonus.
It is also important to note that consensus, which was expected to be the driving force behind cooperative behavior, showed almost no ability to predict contributions or harvests. In the public goods game, consensus’s lack of predictive ability may be due to the very low levels of consensus observed. That is, group members were unable to agree on which group members would contribute more or less during the game which could contribute to consensus’s lack of predictive power. However, in the resource allocation game, groups were able to develop some consensus during Rounds 2, 3, and 5. Nevertheless, even under these conditions, the effects of consensus are inconsistent. During Round 2, consensus significantly predicts smaller harvests. During Round 3, the effect is nearly significant but in the opposite direction. The effect during Round 5 is decidedly nonsignificant. Thus, Hypothesis 3b is not supported for either game.
Discussion
The results of this study demonstrate how group processes associated with member expectations can influence outcomes within social dilemmas. Participants in public goods and resource allocation games generally expect that all group members will act similarly to how the participant will act with regard to contributions and harvests. Moreover, participants achieve little consensus regarding which group members are more cooperatively oriented and which are more competitively oriented during five iterations of the games. The pattern of expectations fits with a social projection perspective regarding how individuals perceive their partners when completing social dilemmas. Most notably, the present study uses the SRM to demonstrate that assimilation and consensus variance within the group predicts group-level outcomes within social dilemmas. The expectations that individuals bring with them into the task are shown to be a key variable for understanding cooperation in social dilemmas.
Distribution of Expectations Within Groups
Expectations of group members’ behavior in social dilemmas followed the general consensus pattern of expecting all interaction partners to act similarly when confronted with the social dilemma situation. In addition, the large correlations between self-expectations and assimilation effects indicate that individual group members believe that their interaction partners will all act similar to the way the individual acts.
There was very little consensus variance associated with measures of expectations in the public goods game, indicating that group members do not agree regarding which group members contribute more or fewer resources. This is true even after five rounds of the public goods game in which group members were given accurate feedback of what each group member contributed on the previous round. Consensus does appear to some extent in the resource allocation game. The amount of agreement is small but statistically significant for three of the five rounds of the game. Limited consensus variance indicates that most participants failed to substantially update their understanding of their group members and instead persisted with assimilating their expectations of group members’ contributions based on an expectation of what the participant themselves would do.
The repeated, consistent belief that group members will respond similarly during each round of the game may appear to be a case of belief perseverance (Lepper, Ross, & Lau, 1986) at best or a failure to fully respond to feedback. However, the data show that the continued belief in similar responses from the group members is a necessary but not sufficient step toward group cooperation. In this way, ignoring diagnostic information about the behavior of fellow group members may have social benefits not previously demonstrated by empirical research.
Distribution of Expectations Related to Outcomes
Indices denoting the assimilation and consensus variances are quite good at predicting task-oriented outcomes. In particular, assimilation variance significantly predicts the amount of resources contributed in the public goods game and the amount of resources harvested in the resource allocation game during most rounds of each game. In both cases, increased assimilation variance within the group results in reduced cooperative behavior among group members. Essentially, the groups that are least cooperative are the groups in which all group members believe that everyone will respond similarly but the expectations of what the contribution or harvest will be varies across group members. Participants in these least cooperative groups share an expectation that everyone will act the same way. However, they do not share the particular details of those actions. In this way, when the final results are shown, everyone in these least cooperative groups has their expectations violated. Similar to Kelley and Stahelski (1970), violation of expectations leads to less cooperative behavior.
However, there is another perspective one can use to interpret the pattern surrounding assimilation variance. If all participants expect each group member will be highly cooperative, the group tends to respond with increased contributions or decreased harvests. If all participants expect each group member will be very individualistically or competitively oriented, more group cooperation is again the result. Competitive behavior is not observed until the expectations are similar within a single participant but variable across group members.
Understanding why variability in assimilated expectations generates competitive behavior is aided by two additional findings. First, the correlations between self-expectation and actual contributing behavior are significant but smaller than might be expected across the five rounds of both games. The size of the correlations indicates that there is definite correspondence between self-expectations and actual behavior, but in the time between assessing expectations and acting, participants may be considering the implications of their contribution or harvest. Second, if each group member’s self-expectation is subtracted from his or her final action, the mean difference is negative during most rounds of the resource allocation game, meaning that harvests taken are smaller than expectations. This indicates that participants may be willing to attempt a cooperative action in that game even though they fully expect the group to act competitively. If all group members choose to follow such a strategy, they may find themselves pleasantly surprised that more of their group appears willing to act in the best interest of the collective.
The pattern of results demonstrates very clearly that variability in the expected level of contributing or harvesting across the entire group engenders competition. For example, imagine during the public goods game a group in which one member believes the group will respond entirely cooperatively, another group member expects the group will respond entirely competitively, and the two remaining group members fall along a continuum between the two extremes. Further imagine that all group members act in accordance with their expectations during the game. In this case, a situation would arise in which one group member contributes a large number of points to the good, one contributes the minimum number of points, and the other two would contribute some points, but below the maximum. Under these conditions, the bonus threshold is unlikely to be attained and participants that contribute large numbers of points will find themselves losing points. This pattern of responding may initiate a cycle in which the cooperative participant attempts to protect against further exploitation and reduces future contributions. The competitive participant would find his or her expectations fulfilled and would be reinforced for contributing little to the public good. The two players in between would be forced to choose between contributing more points, gaining the possibility of receiving more group bonuses but risking being exploited, or contributing fewer points, receiving fewer group bonuses but protecting themselves from exploitation. Given that placing oneself at risk of exploitation is highly irrational, it is very unlikely that the former scenario would occur (Komorita & Parks, 1996) unless a system exists to punish free-riders (Yamagishi, 1986).
Shared Representations
The current study investigates, in a general way, how shared representations in regard to expectations of the behavior of others impact cooperative and competitive behavior. The data show that there may be two different strategies regarding getting a group to “be on the same page” with a shared representation. Importantly, which strategy is used can result in different outcomes. For convenience purposes, we will refer to these as the social projection strategy and the other-focused strategy.
The other-focused strategy would seem to be the most intuitive. Shared representations are created by building consensus regarding a task situation. Research has considered cognitive consensus as a metric of shared task representations and shown important gains in decision satisfaction and use of informational resources (Mohammed & Ringseis, 2001; van Ginkel & van Knippenberg, 2009), though this research typically looks at consensus regarding the requirements of the task rather than consensus of expectations. Our data show that building consensus based on expectations has inconsistent effects on cooperative behavior, at least in the resource allocation game where we can reliably say that consensus was created. During Round 2 of the game, consensus led to more cooperative behavior, but in the very next round, consensus was marginally related to competitive behavior. More research should focus on the effect of expectation consensus on cooperative behavior to understand this link.
The social projection strategy, on the contrary, is potentially the more reliable but also more dangerous strategy of mediating the link between a shared representation and a behavioral outcome. One could create a shared representation by encouraging assimilation and simultaneously reducing the variability in assimilated expectations. The image of a drill sergeant consistently berating all subordinates regardless of skill, ability, or behavior comes to mind. The goal would be to get everyone in the group to believe all group members are exactly the same. According to our data, this strategy would reduce competitive behavior within the group. Importantly, reducing competitive behavior should not be construed as the same thing as increasing cooperative behavior.
The sign associated with the assimilation variance term in the regression equations in Table 4 is in the competitive direction for both games. This means that the most cooperative outcome would result if the assimilation variability term was equal to zero. Any increase in assimilation variance above zero would lead that group in a competitive direction.
Following from our data, the social projection strategy would have more reliable results, but paradoxically would also be more subject to failure. For example, assume a situation where the ultimate goal is cooperative group action but the incentives of the situation might lead the individual group members away from that ideal. A basketball team fits this situation quite well in that team wins—the collective benefit—are more often the result of passing to open shooters for high efficiency scoring attempts, but individual players get noticed and rewarded for large individual scoring efforts which they can make more likely by taking more inefficient shots (Berri, Brook, & Schmidt, 2011). Furthermore, basketball teams generally have a coach outside the situation that influences tasks completed on the court and influences team member expectations. The coach may generally believe that successful teams have a shared representation of one another (Reimer, Park, & Hinsz, 2006). The coach may also be led by experience to believe that if the team is going to be successful, team members must have assimilated expectations, as this is the reliable effect found in this study. If the coach chooses to create a shared task representation in the group by encouraging assimilated expectations, the coach must also seek to reduce all variability in those expectations. Any deviation from that course or failure to implement both assimilated expectations along with zero variability in those assimilated expectations will result in the coach being more likely to see competitive or individualistic behavior within the team.
The current study suggests that all shared task representations are not created equal. If one builds a shared representation based on consensus, different behavioral outcomes will result than if one builds a shared representation based on eliminating assimilation variability associated with expectations. Leaders need to be particularly careful when choosing a method of creating a shared representation depending on whether increased cooperation or decreased competition is the desired goal.
Using SRM to Index Process in an IPO Framework
This study also presents a general methodology that we hope will become more established in group research. The IPO theoretical framework (McGrath, 1964) has been a dominant model of group functioning since it was proposed (Kozlowski & Ilgen, 2006). However, a problem within the model persists: How does one define the term “process” and how can one quantify the amount of a particular group process occurring within a group (Ilgen et al., 2005; Weingart, 1997)? The use of the SRM methodology helps to solve a number of analytical problems within the IPO framework (Ladbury & Hinsz, 2013) and—in this study in particular—confirms and advances previous findings on the distribution of expectations within a group.
It should be noted that we maintain that the variance components of SRM can be treated as indices of group process. By this we mean that the variance components represent how an interdependent group is likely to approach a situation. If a group is composed of members that all believe the group members are “on the same page” but everyone in the group has a different idea regarding what page they are actually on, the group will have a large assimilation variance and, according to our results, be poised for conflict. This does not mean that the large assimilation variance represents conflict. Rather, it establishes that this group has a potential for conflict on interdependent tasks that constrain communication. SRM indices are useful to the IPO framework because they numerically represent both the absolute level and the distribution of an expectation within a group. By using both sources of data, SRM allows for better predictions of the processes involved in group interaction during the task than previous methods.
Conclusion
This study demonstrates that the expectations that individuals have for their own behavior and that of their teammates can be aggregated in particular fashions to predict the nature of group interaction. As such, this article is aligned with a strong and long-standing tradition in social cognition research that considers how individual expectations drive individual behavior; however, in this research, we examine member expectations as predictors of group behavior. In general, the current study establishes the utility using SRM variance components as indices of group process. This allows for a numerical understanding of the degree of consensus and assimilation occurring within groups and allows for predicting group outcomes based on those processes. We demonstrate that processes associated with expectations have important implications for whether or not groups will display more or less cooperative behavior.
This study also establishes an unexpected relationship between the distribution of expectations and outcomes of social dilemmas. By establishing that assimilation variance is a significant predictor of competitive behavior in social dilemmas, the current study demonstrates that variability in expectations is a driving factor when considering whether or not a group will choose a cooperative solution to a social dilemma. Eliminating variability in assimilated expectations resulted in more cooperative solutions. In this way, a group may arrive at a cooperative solution even though every group member expects all other group members to act competitively.
This leads us back to our initial discussion of traffic lights. Even though collectively drivers in this city flaunt the rules of safe driving, the shared belief that everyone will do so creates the opportunity for a less competitive solution to be reached. We can all agree that one or two cars will likely drive through the red light and alter our behavior to match that situation. Checking for clear intersections before advancing on a green light may seem unnecessary to a tourist unfamiliar with drivers in this city, but that exact variability in expectations is what creates the opportunity for accidents and property damage. Expecting drivers to run red lights can be irritating, but it is also an adaptive expectation that allows everyone to get to their destinations safely and efficiently.
Supplementary Material
Supplementary Material, ladbury_online_appendix – How the Distribution of Member Expectations Influences Cooperation and Competition in Groups: A Social Relations Model Analysis of Social Dilemmas
Supplementary Material, ladbury_online_appendix for How the Distribution of Member Expectations Influences Cooperation and Competition in Groups: A Social Relations Model Analysis of Social Dilemmas by Jared L. Ladbury and Verlin B. Hinsz in Personality and Social Psychology Bulletin
Footnotes
Declaration of Conflicting Interests
The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.
Funding
The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This research was conducted as part of a doctoral dissertation by Jared L. Ladbury, Department of Psychology, North Dakota State University, and supported in part by a Presidential Fellowship awarded by the Graduate School of North Dakota State University to the first author.
Notes
Supplemental Material
Supplementary material is available online with this article.
References
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