Modeling Interaction in Collaborative Groups: A ect Control within Social Structure

This paper studies the dynamics of identity and status management within groups in collaborative settings. We present an agent-based simulation model for group interaction rooted in social psychological theory. The model integrates a ect control theory with networked interaction structures and sequential behavior protocols as they are o en encountered in task groups. By expressing status hierarchy through network structure, we build a bridge between expectation states theory and a ect control theory, and are able to reproduce central results from the expectation states research program in sociological social psychology. Furthermore, we demonstrate how themodel can be applied to analyze specialized task groups or sub-cultural domains by combining it with empirical data sources. As an example, we simulate groups of open-source so ware developers and analyze how cultural expectations influence the occupancy of high status positions in these groups.


Introduction
. The study of groups is one place where the fields of psychology and sociology most apparently intersect, as individual-level information processing interacts with the dynamics of a social system. In this work, we follow the common definition of a group referring to "a bounded collection of interacting individuals" exhibiting functional, cognitive (we would add, a ective), and structural interdependencies (Lindenberg , ). While in the middle of the twentieth century small-group research was an integrated research field, it subsequently fragmented into multiple specialized domains such as the study of networks, social exchange, group collaboration, collective decision making, and many others (Burke ). These subfields di er in the degree to which they focus on one or more of these interdependencies. .
However, some research questions are best tackled by an integrated approach that examines how these interdependencies are intertwined. In this vein, the present work sets out to understand how role identities and their culturally shaped a ective connotations influence the cultural acceptance of those who occupy important positions in task groups. To this end, we built an integrative computational model called ACTING (A ect Control Theory based simulations of Interaction in Networked Groups) that can realistically simulate task group interactions. ACTING takes into account all three of the aforementioned group interdependencies because each influences task groups. Task groups are goal-oriented and o en follow protocols or procedural rules to reach a shared goal (functional interdependence). They rely on shared group identities and a shared understanding of appropriate role-based identities and behaviors (cognitive-a ective interdependence). Finally, workplace interactions in a task group o en occur against the backdrop of explicit organizational hierarchies that determine who gets to interact with whom (structural interdependence). .
In the last two decades, agent-based modeling (ABM) has been developed as a fruitful knowledge-integrating approach to sociological theory building and testing, in particular for understanding how macroscopic social e ects arise from simple mechanisms operating at the individual level. ABM, therefore, naturally lends itself as a methodological framework to study emergent properties of groups, such as the emergence of cultural acceptance or rejection of status hierarchies in task groups. ABMs of group dynamics, particularly from computational organizational theories (Cohen et al. ; Prietula & Carley ; Decker ), have modeled functional, cognitive-a ective, and structural interdependencies predominantly from an information processing perspective. Although these theories have increasingly emphasized the importance of cultural knowledge and normative expectations (Carley & Hill ), the encoding of this knowledge and expectations has primarily been either as agent rules dependent largely on the researcher's knowledge and specific to a particular task domain, or as simulated knowledge of what and whom each agent knows. Consequently, with the present work we are addressing a gap in the organizational modeling literature, namely finding a tractable yet principled approach for modeling cultural dynamics. We are also addressing a gap in the group processes literature, namely incorporating identity maintenance processes into formal models of task groups. Existing models have either simulated agent's role-identities (Heise ) but ignored the network structures and associated status hierarchies they operate in; or they have focused on the formation of status hierarchies and the associated network structures (Mark et al. ), but have ignored role identities entirely or focused on broad categories such as female versus male workers which are modeled as categorical variables. .
Building on Heise's ( ) work, we propose a more general framework for modeling task groups where cultural knowledge is encoded as sentiments collected from empirical surveys. Agents in our model orient themselves with respect to the sentiments they have about concepts and behaviors, forming expectations about who should do what with whom as they engage in networked and interdependent activities. While the functional interdependence of task groups will o en be highly task-specific, we believe that a generalized model that captures the interplay of functional, cognitive-a ective and structural interdependence is feasible. The social psychological concept of identity is key to this endeavor. On the one hand, identities are focal concepts organizing an individual's goals, values, and relationships across di erent domains of daily life; on the other hand, identities are tied to structural positions in organizations and society. .
In this work, we thus extend Heise's ( ) Group Simulator, which employs a model of identity based on a ect control theory, into a more general agent based model that can simulate complex task groups. The extensions include three major contributions. First, we allow for the simulation of interactions within networked group structures. In particular, this enables us to model and investigate the alignment of a group's role identities with its organizational structure which is implemented as a directed graph G = (V, E) , where the vertices V are a set of agents and the edges E are a set of directed behavior pathways. This extension is important because the ability to manage expectations is heavily influenced by the group's organizational structure. Furthermore, networks can be connected to status hierarchies that are present in the group, allowing us to investigate the functioning of role hierarchies within a variety of formal group structures. Note that this work grew out of an e ort to model digital task-groups that collaborate online. In these settings, we repeatedly encountered interaction structures that were restricted to specific network topologies (Zöller et al. ). Moreover, we found that the possible actions of group members were o en restricted to a discrete set of behaviors, owing to the technical design of the platform on which the interactions took place. Therefore, we introduced our second innovation to Heise's ( ) model, the possibility to restrict the action space to a discrete set of behaviors. This feature is also helpful when one wants to compare simulation results to empirical data for which a discrete annotation scheme was employed such as Bales's ( ) interaction process analysis categories. Finally, task group behavior o en follows a protocol. By protocol, we mean a task structure where the completion of certain tasks requires sequential actions from group members with di erent skillsets at di erent levels of authority. This is the case not only in computer-mediated collaboration on platforms, but also in bureaucratic organizations that enforce legal or other formal prescriptions of business processes. Consequently, certain actions necessarily follow others or are only possible as a response to other actions. Thus, we added a third extension that allows the user to define behavior protocols in our model, which govern sequences of actions in the simulated groups. .
The article is organized as follows. First, we describe the theoretical basis, starting with a brief outline of relevant work about the interplay between social networks and role behavior in task groups followed by a review of A ect Control Theory. Next, we describe our ACTING model, following the established ODD protocol for ABM description (Grimm et al. ). We then turn to a series of simulation experiments aimed at understanding the network functionality of the model in the context of several stylized ideal types of network structures. We investigate how di erent network structures influence the a ective dynamics of identity management of interdependent group members. Furthermore, we demonstrate how the model reproduces well-known empirical findings about cultural expectations and status dynamics in small groups (Ridgeway & Bourg ; Ridgeway ). We then demonstrate how our framework can be used to model complex task groups that exhibit functional, cognitive-a ective, and structural interdependencies, or what Merton ( ) called role-sets, i.e "the complement of role-relationships in which persons are involved by virtue of occupying a particular social status". The last methodological step is an application of the model to di erent empirically realistic interaction structures extracted from the GitHub social graph, to show how simulations help illuminate the identity dynamics and associated status positions that occur in various types of organized collaboration.

Background
. Sociality and cognition are inextricably linked (Donald ; Dunbar ). Groups provide arenas for social learning and skills transmission (Hobaiter et al. ). Learning to join and work in groups is critical for children to develop a theory of mind and a sense of agency (Piaget ; Corsaro & Molinari ). The social networks of social animals (the patterns of relations between group members) influence behaviors related to reproduction, cooperation, conflict, and tool use (Kappeler ; Connor et al. ; Hobaiter et al. ). In humans, they influence patterns of reciprocation (Cook & Emerson ), perceptions of risk (Molm et al. ), and group solidarity (Markovsky & Lawler ). Finally, groups are where dominance relations are sustained and reproduced (Fararo & Skvoretz ; Skvoretz et al. ; Mark et al. ).

Status dynamics in task groups
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Because task groups are important in the allocation of social goods (Bales & Slater ; Berger et al. ), they have long been the focus of scholars interested in the reproduction of status inequality. By status, we mean both ascribed (e.g., gender and race) and achieved (e.g., a post-secondary degree) characteristics that confer prestige across multiple group settings. Merton ( , p. ) observed that status and roles serve to connect culturally defined expectations with the patterned conduct and relationships that make up a social structure. He focused on the reproduction of status in work settings through the enactment of role sets. Role sets describe role identities such as doctors, nurses and interns that not only imply a set of attributes such as good or potent but also a set of logical relations such as directing and reporting.

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Bales and colleagues (Bales & Strodtbeck ; Bales ) found that groups whose members were presumably initially equal in status, nevertheless exhibited inequalities in participation and influence. This empirical puzzle was the launching point for the expectation states research program in social psychology (Berger et al. ; Ridgeway , ). The expectation states literature includes a variety of theories; but, central to them all is the notion that goal oriented groups when they form confront an information problem -they do not know who is competent. Group members, thus, must infer competence from social cues such as wealth and prestige. If a correlation exists between resources and nominal characteristics such as race or gender in the population, even if this correlation is spurious, a self-reinforcing pattern of interaction can arise that associates competence with the given characteristic (Ridgeway ). These di erential expectations create a self-fulfilling prophecy (Merton ) whereby higher-status group members are more influential and receive disproportionately more positive evaluations and rewards. .
Demonstrating how such an endogenous mechanism might operate and testing theoretical assumptions regarding this process has included pioneering simulation studies examining the formation of dominance hierarchies (Skvoretz et al. ; Grow & Flache ), the exercise of weak power through social exclusion (Markovsky et al. ), the attribution of status value to nominal characteristics (Mark et al. ; Lynn et al. ), and the formation of trust and cooperation (Flache & Macy ). In all of these simulation studies, status hierarchies have been defined and quantified through network properties. For example, Skvoretz et al. ( ) identify dominance hierarchies by analyzing the directionality of ties. Similarly, Lynn et al. ( ) use in-degree centrality of a deference network as the metric for status ranking. Centrality measures have a long-standing tradition as useful metrics in sociological theory building (Friedkin ). Examples are Hubbell's measure of sociometric status (Hubbell ), Coleman's measure of power (Coleman ), and Burt's measure of prestige (Burt ). Freeman ( ) identified three di erent families of centrality that imply three competing theories of how centrality might a ect group processes. It is, therefore, important to note that while in most cases a useful metric of group status can be defined in terms of network properties, the exact form will always depend on the specific context and the meaning of ties and nodes in the network. A general review about network theory and small groups can be found in (Katz et al. ). .
In the simulation studies conducted as part of the expectation states program cited above, status characteristics such as gender are typically operationalized as categorical variables that influence an individual's opportunities to participate in group activities. Role identities such as CEO, supervisor, secretary or intern are not taken into account. However, by jettisoning role identities, an important factor in the relationship between perceived competence and status characteristics is lost. For example, gender scholars (Fiske & Stevens ; Rudman ; Moss-Racusin et al. ; Connor & Fiske ) have found that female leaders experience more scrutiny because gender expectations and role expectations are misaligned (the warmth versus competence dilemma). Thus, they are at greater risk of being unable to leverage their present status in future group interactions (Ridgeway & Smith-Lovin ). .
In our present study, the focus is on how role expectations that are encoded in a ective identities integrate with explicit organizational hierarchies to influence the impressions group members have about one another. Specifically, our focus is to distinguish between group settings where agents are likely to be able to manage expectations given their role, traits, and structural position from settings where this is less likely. By examining the interaction of these factors, we are able to re-integrate role performance as a determinant of status within a generative model using a parsimonious but flexible representation of task groups. To generate the role expectations, we define task groups as role systems where each agent is assigned an identity. We assume that group members seek to fulfill their role identities and behave accordingly, where role identity can be understood as "internalized social positions and their meanings" (Owens et al. ). Because behaviors are o en definitional to role identities (e.g., teaching and teachers, sentencing and judges, programming and so ware developers, etc.), we compare situations where agents are able to draw on a wide array of behaviors to a irm their roles, and situations where behaviors are circumscribed by the task or institutional domain. Essentially, we assume that group members orient themselves with respect to a ective meanings during group interactions. To develop this claim, we briefly describe a ect control theory as it applies to group interaction.

A ect Control Theory
. A ect Control Theory (ACT) is a quantification of classic symbolic interactionist and cultural constructionist ideas about social interaction as based on linguistic meanings of social objects. The theory conceptualizes culture as a collectively shared representation of identities, social behaviors, and modifiers such as personality traits and emotional states (Heise ). These concepts are assumed to populate a three-dimensional a ective space that spans the three base dimensions of evaluation (how good vs. bad is the person, behavior, or modifier?), potency (how powerful vs. weak is it?), and activity (how active and noisy vs. passive and quiet?). These dimensions, collectively referred to as EPA, have been shown in decades of research to structure the semantic relations of social concepts in psycholinguistic rating studies, and are hypothesized to reflect crosscultural universals of socio-emotional behavior and experience (Osgood et al. ). The empirical basis of ACT accordingly consists of databases of fundamental a ective meanings (denoted F in subsequent equations) of usually many hundred to a few thousand social concepts, assessed in population surveys which tend to show considerable consensus about these meanings within linguistic communities (Ambrasat et al. ). .
Descriptions of social reality require conceptual combinations. E.g., we expect a "cynical manager" or a "lazy worker" to act di erently than a "manager" or a "worker" as such, respectively. These so-called a ective amalgamations can be modeled with weighted regression equations that take the fundamental a ective meanings of the constituent concepts as input and return an experientially quite accurate EPA vector as output (Averett & Heise ). The regression weights come from vignette experiments where participants provide EPA ratings of conceptual combinations. Similarly, ACT scholars have modeled the impressions resulting from specific behaviors such as "a manager scolding a worker" or "a worker ignoring a manager". Again, vignette experiments provide the empirical basis for parameterizing regression equations that take EPA vectors for actor, behavior, and object as input and return a vector for the transient impressions (denoted τ in subsequent equations) resulting from the described social event as output (Gollob ).
. In a given culture, role identities entail normative expectations of behavior. E.g., we would expect a manager to train, supervise, or interview a worker but find it inappropriate if they demeaned, ridiculed, or discouraged them. Mathematically, such expectations are modeled as deflection d = (F − τ ) 2 , an inverse measure of the degree to which transient impressions from a social event confirm the fundamental a ective meanings of the involved role identities (Heise ; Morgan et al. ). ACT is a control theory precisely because it assumes that people are motivated to keep deflection to a minimum; hence, intuitively aligning their social actions with the normative order of their culture. This fundamental principle is in line with a large body of work in social psychology and cognitive science emphasizing the need to maximize cognitive and emotional coherence of thought and action (Hoey et al. ; Powers ; Thagard ). Much empirical work in the ACT research tradition has shown that the deflection-minimization principle predicts the perceived likelihood of verbally described social events, actual verbal and nonverbal behavior in experiments, and even EEG parameters related to expectation violation (e.g., Schauenburg et al. ; Schröder & Scholl ). .
Because of ACT's unique capacity to quantify the symbolic content of social cognitions and their behavioral consequences, the theory lends itself as a conceptual and empirical basis for social simulation. INTERACT (Heise , p. ) is a legacy program written in Java that allows one to model sequences of a dyadic interaction. A more recent probabilistic implementation of ACT as a partially observable Markov decision process called BayesACT (written in Python) has been used to simulate the e ects of uncertainty and multiple role identities on the emergence of social structure (Schröder et al. ). Most relevant for the present article is Group Simulator, an agent-based model of small-group dynamics written in Netlogo, whose individual agents act according to the a ect-control principle of minimizing deflection (Heise ). Heise's simulation results yielded remarkable agreement with empirical behavior distributions of jury deliberations from classical empirical studies of group dynamics. In the present paper, we build on the Group Simulator to study the alignment of network structures and role identities in work groups.

ACTING Model
. We name the agent-based model presented here ACTING (A ect Control Theory based simulations of Interaction in Networked Groups). The model was implemented in Python using the mesa library for ABM (Masad & Kazil ), and the source code for the model and Jupyter notebooks with all simulations presented in this article can be found at https://github.com/nikozoe/ACTING. Here, we present a shortened version of the model description following the ODD (Overview, Design concepts, Details) protocol (Grimm et al. ). The complete, detailed version, including all design principles and submodel descriptions is provided in the Supplementary Material. .
The overall purpose of our model is to simulate task group interactions in order to understand and analyze the interplay between role identities, role expectations, status hierarchies, and the group's interaction structure. Specifically, we are addressing the following question: Based on their role identities, which team members are more or less likely to occupy high status positions? The formalization of how the e ort to maintain role identities translates into role expectations and behaviors is guided by a ect control theory (ACT). Thus, another purpose of the model is to bridge the sociological theories of ACT and status characteristics. To consider our model realistic enough for its purpose, we use patterns in behavior distributions and formation of status hierarchies.
. The model is grounded in empirical data and it is adaptable to task groups that operate in specific subcultures. For this purpose, a small survey has to be conducted to obtain ratings of central role identities and behaviors. We demonstrate this process by modeling teams of open source so ware developers, where the interaction structures are derived from empirical observations (Zöller et al. ).

Entities, state variables, and scales .
The model includes the following entities: agents which represent members of a task group, a group object (optional) which represents the group identity, and the global environment which is either provided by the GroupModel or by the ProtocolGroupModel. An overview about all entities and their state variables can be found in Table . Variable name  .

Group members:
All agents in the model are initialized with a fundamental identity F , which remains constant during a simulation run, and an event-driven transient identity, τ , which changes through interactions with other agents in the group. Both consist of -dimensional arrays [E, P, A] with values for evaluation, potency and activity. An agent's deflection d = (F − τ ) 2 represents the a ective dissonance an agent experiences between their situational and their fundamental identity.
. Group object: Lawler et al. ( ) find that emotions produced through the interactions of group members are attributed in part to relevant social units. The group identity consequently forms over time through repeated and consistent interactions between its members. Depending on which kind of a group situation one wants to model, it may or may not be sensible to include a group object. Therefore, our implementation of the model makes the integration of a group object optional. In some of the simulations presented in this paper, it is included while in others it is not, depending on the group setting and the focus of the research question. When included, it is simulated as a pseudo agent that like the group members holds a fundamental and a transient identity. The group object can be acted upon, but can not act itself.
. Global environment: In our implementation, the global environment inherits from the Model class of the Python package mesa (Masad & Kazil ). It is either constituted by the GroupModel or its extension Pro-tocolGroupModel. GroupModel keeps track of the current time step, the order of agents at each time step, who is acting on whom and also the data collection. Parameter settings of the global environment regulate which actions are available (discrete_actions), how o en actions are reciprocal (reciprocity_rate), how o en an action is performed on the group object (action_on_group) and who can act on whom (network_structure). If the simulated task is made up of a predescribed sequence of actions, the global environment is best represented by the ProtocolGroupModel. ProtocolGroupModel lets the researcher define a protocol in which the global environment changes over time including all aforementioned parameters. Most importantly, this allows the researcher to define di erent sections of the protocol of di erent length (n_iterations) for which only a discrete set of actions is available (discrete_actions) to the group members. Further customizations options (select_actor, code) make the ProtocolGroupModel very general and expressive, so that it can be adapted to specific work flows of specialized task groups. .
As for the spatial and temporal resolution and extent of the model: Each time step corresponds to an action that is performed by one of the group members. The model does not represent physical space, but instead it represents EPA space in which fundamental and transient identities of agents are located as well as behaviors.
Process overview and scheduling .
The most important process, which is repeated every time step, is an action being performed by one agent (actor) on another agent (object). First the actor is determined. This is generally the group member with the highest deflection unless the action is probablistically determined to be reciprocal. Next, the object and behavior are determined according to the chosen object selection criterion and ACT principles (see Equation ). Finally, the action is performed, the resulting changes to the transient identities of all involved agents are applied and the resulting deflection is calculated. There is a chance that the action is directed towards the whole group determined by the model parameter group_action_rate. In this case, all group members except the actor experience the action as if they had been the object.

Design concepts .
The most important design concepts of the model are principles, objectives and interaction which we present here in some detail. For additional design concepts, see the Supplementary Material.

Basic principles
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The model, modifying and extending Heise's ( ) Group Simulator, conceptualizes a small group as a "team" in which individuals are committed to helping each other maintain their identities. The formalization of how this e ort to maintain role identities translates in role expectations and behaviors is guided by A ect Control Theory, a mathematically specified theory of symbolic interaction (Heise ).
. An event in ACT consists of an actor A that directs a behavior B towards an object O. A er an event, the transient impressions of the actor, object and behavior are changed according to empirically parameterized impression formation equations: where τ is a vector that holds the EPA representations of the transient impressions of actor A, behavior B and object O which as the result of an event becomes τ af t respectively. The vector t is calculated from τ and contains not only the transients of A, B and O but also all possible products of their E, P and A components up to first order in A, B and O. M is a matrix with prediction coe icients that were estimated through a regression analysis of survey data. In these studies, participants rate the evaluation, potency, and activity of concepts both outof-context (e.g, the worker) and when combined as vignettes triples (e.g., the worker questions the boss). The equations predict how the E, P, and A values of each event element change as a result from being combined with the other elements based on the out-of-context ratings. The coe icients used in our simulations are the same as those used in Heise's ( ) study, and were originally obtained from a survey of North Carolina undergraduates.

Objectives .
The agents' objective is to choose the action that will most confirm their own fundamental identity and the fundamental identities of others. In this regard, the model follows the ACT principle stating that people seek to verify cultural knowledge about the social order (Heise ). Formally, this means that agents choose their behavior in order to minimize event deflection D which is defined as where F is a vector that holds the fundamental identities of actor, behavior, and object person, which remain constant. If the actor and object have been determined, the minimization conditions for deflection can be solved for the optimal behavior B which may then be calculated from M , F and the transients τ before the event. .
For the full mathematical form of B and its detailed derivation, see part II Mathematics of A ect Control Control theory in Heise's book Expressive Order (Heise ).
Actor and object selection: In each step of a simulation run, only one actor gets to act on one object which is either another agent or, if applicable, the group object. When an actor and an object are determined and their fundamental and transient identities are known, ACT provides a framework to calculate the optimal behavior which follows cultural norms, preserves role identities, and minimizes a ective dissonance to the greatest possible extent (see Objectives). However, ACT provides no clear guidance on how to select an actor or an object in a group setting. This is not surprising since the ACT equations are derived from dyadic vignette experiments. Realistically, who acts upon whom in task groups is o en task specific. Nonetheless, we assume that a ective reasoning influences actor and object selection because it has an e ect on the amount of a ective dissonance experienced within the group which agents seek to minimize as per a ect control theory's control principle. .
In our model, we follow Heise ( ) and assume that the agent who experiences the most deflection will be the next to act. This means that a ective dissonance is the only driving force in turn-taking, which in the absence of task-specific information seems sensible. There are other options available in the model implementation like for example random actor selection that might be more accurate depending on the group and the task one wants to model.

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A er an actor is determined, the object selection criterion regulates how the object that the actor will act upon is chosen. One possible criterion is minimum event tension which was also used in Heise's ( ) study to model juries. The minimum event tension criterion works as follows: once the actor is set, for each object candidate the optimal behavior is determined according to ACT. Subsequently, the action is carried out hypothetically and the resulting a er-event deflection is calculated, which involves only the fundamentals and the transients a er the event for the actor, object and behavior. Finally, the actual object is chosen so that this a er-event deflection is minimized. .
The minimum event tension criterion has the short-coming that it only considers the situational deflection of the actor, object and behavior triple a er the event. However, Heise points out himself in the article (Heise ) introducing his original model that it aims at integrating Go man's ( ) suggestion that "a small group operates as a team in which individuals are committed to helping each other maintain their identities (faces)". Furthermore, Heise claims that "an individual motivated to action selects as object the group member who provides an optimal basis for creating a tension-reducing action that will confirm the fundamental a ective meanings of actor and object". However, this tension reduction is not properly taken into account by the minimum event tension criterion. We therefore introduce a di erent object selection criterion that, in our opinion, adheres even more closely to the control principle. We term the criterion maximum deflection reduction, because it tries to reduce overall a ective deflection instead of only causing a minimally deflective event. It works as follows: once the actor is set, for each object candidate the optimal behavior is determined based on ACT's impression change equations and subsequently the hypothetical a er-event deflection is calculated. But this is now compared to the overall deflection before the event from which the a er a er-event deflection is subtracted. Object and behavior are then chosen such as to maximize this di erence, i.e. the deflection reduction. This means that both the transient identities and the overall deflection before and a er the event are taken into account.
. Action space: Past ACT models have assumed a continuous connotative action space along the dimensions evaluation, potency and activity, where each point can be mapped to a denotative label, i.e. the name of a behavior in natural language. In our model, the user can specify either a continuous action space, or define a discrete and finite set of possible actions. A discrete action space can be helpful in at least three ways. First, empirical data is o en annotated using categorical taxonomies to describe the observed actions (Bales ). Although other behaviors might be possible, it is sensible to restrict simulation behaviors to the empirical annotation scheme in order to increase comparability. Second, there is a binning problem when mapping back in hindsight from connotative space to a categorical behavior set in denotative space because the volume that is mapped to each behavior might vary. This in return can lead to biased behavior distributions. Third, in many situations, agents simply only have a limited set of actions at their disposal. This might be due to institutional procedures or limited capabilities that are not captured by role identities. An obvious example where this is the case is the digital sphere. Behaviors might simply be restricted by a graphical user interface or a limited set of possible actions in an application. In our implementation, the action space is limited through passing a list of allowed behaviors in the environment parameter discrete_actions.

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Interaction structure: In the model, the default setting is that every agent can act on every other agent. But, in many real world situations, who can interact with whom is governed by institutional hierarchies or organizational procedures. Therefore, the user can impose restrictions on who can interact with whom through passing the model a network structure in the form of an adjacency matrix. This means that an agent can only act on another agent if there exists a directed edge from the former to the latter in the network.
. Protocols: Many task groups are structured by sequential protocols in which some actions necessarily have to follow others in order to complete a task. To allow for a realistic simulation of these groups, we include the possibility to parse such a protocol to the model in the form of a list in which each item represents one part of the protocol. What behaviors are available and how many actions should be carried out is specified for each step. Optionally, di erent settings for model parameters can be parsed before the beginning of each part as well as custom python code that should be executed before or a er the protocol step. This flexibility makes the model expressive and allows one to customize the simulations to specific tasks and work flows of interest.

Simulations
. We describe here a series of simulation experiments conducted with the ACTING model. First, we replicate Heise's ( ) study simulating juries, which provides a baseline validation of our modified Group Simulator model and allows us to appraise the e ects of the added features on model behavior. Second, we systematically explore the impact of di erent network topologies on a ective dynamics of small groups according to the model, demonstrating how the model can be used to study how structural and cognitive-a ective interdependencies interact in small groups. Third, we show how the model systematically reproduces empirical findings about status dynamics in groups following the expectation states research program in social psychology reviewed above. Lastly, we use the model to analyze interactions in teams of so ware developers on GitHub, based on a recent empirical study (Zöller et al. ), with the intention to show the practical usefulness and domain-specific adaptability of the model.

Application: Jury deliberations .
The purpose of this section is two-fold. On the one hand, we reproduce Heise's ( ) legacy study in which he simulated jury deliberations and compared the results to empirical data reported by Strodtbeck & Mann ( ).
This serves as a sanity check for the basis of our model implementation. On the other hand, while reproducing these simulations, we explore two of the new features, examining how including these features influences Heise's original model. First, we explore how including a discrete action space that restricts the behaviors available to the agents influences the model. Second, we explore how a new object selection criterion that aims at maximum deflection reduction instead of only minimizing a er-event deflection influences agent behavior.
We conducted all simulations with the exact parameters used by Heise's ( ). For convenience, we briefly state the model parameters here. All simulations modeled groups of agents, holding the fundamental identity of male jurorF = [0.8, 1.6, −0.5] and the fundamental identity of a female jurorF = [1.2, 0.7, 0.0]. The individual EPA values were based on the same survey as the IPA categories (Smith-Lovin & Heise ) and the conjoint identities of male and female juror were obtained with amalgamation equations (Averett & Heise ), which model how EPA connotations combine in conceptual combinations of nouns (here: juror) and adjectives (here: female). A group object initiated with the average fundamental and transient identities of all group members was included. Parameters for individuality and initial tension were set to . , the action-ongroup rate was set to . and the reciprocity rate was set to . . For the rationale of these parameter settings, please refer to Heise ( ). All results shown here were averaged over simulations, which ran for steps each. .
We simulate six di erent settings that we evaluate subsequently against the empirical data. Three object selection criteria, minimum event deflection, random and the novel maximum deflection reduction, are simulated crossed with a continuous action space versus the newly introduced discrete action space. To compare the simulated and empirical data, we calculate the behavior distributions in terms of IPA categories and compute the correlations with empirical data, following Heise ( ). Note that in the case of a discrete action space, the EPA labels of the IPA categories (Table ), i.e. the annotation scheme of the empirical data, are passed as the set of possible discrete actions. In the case of a continuous action space, an observed action is binned to the IPA category to which it has the smallest euclidean distance.
. Figure (a) shows the IPA distributions for all observed behaviors and (b) the observed gender di erences in these distributions for all simulated model settings and the empirical data respectively. Table summarizes all correlations between simulations and the empirical data set. First of all, we see that for all simulation settings high correlations between simulated behavior distributions and empirical data are achieved . This is equally true for the observed di erences in behavior between male and female jurors. With a correlation of . , the best agreement between the simulation and empirical data is reached using a discrete action space in combination with the new object selection criterion of maximum deflection reduction.
. A discrete action space increases the correlations with the empirical data for all object selection criterions. For the di erent object selection criteria, we cannot identify a clear "winner" in terms of correlations with the empirical data. But regarding Figure , we see that for the newly introduced criterion of maximum deflection re-duction, the average level of deflection per agent is indeed notably lower than for the other criteria. There are many factors that influence turn taking. O en, these are task-related and dictated by a sequence of actions in which a task necessarily has to be performed to be completed successfully. They might also depend on cultural conventions or specific role configurations that are not captured in the formalization of ACT as presented here. But if one assumes that agents have full understanding of the a ective consequences of their actions and choose their objects in a manner to minimize deflection in the group, then maximum deflection reduction would be the adequate object selection criterion to implement.

Figure :
The plot compares empirical data from jury trials with data generated by simulations with di erent settings. The highest correlation is obtained for a simulation with discrete behaviors and the object selection criterion "max deflection-reduction".

Restricted group interaction structure: Toy network experiments .
In many situations, a group's interaction structure is restricted such that not every group member interacts with every other. Instead, interaction occurs only along a specific network topology. There are a variety of reasons why this can be the case: the interaction restriction might be by design via a top-down approach, arise from organizational procedures, result from task-specific necessities, or emerge naturally from a given roleidentity structure. In real-world scenarios, several reasons might be overlapping and di icult to disentangle when observing interactions. To make the simulation of such groups feasible, we enable the user to model these kinds of restrictions using a static network topology that defines which agent can interact with whom. At a theoretical level, this enhanced model allows one to study the complex interactions between structural and cognitive-a ective interdependencies in groups.

.
In the following simulation experiments, we analyze how a restricted interaction structure influences the situational identities occupied by group members, and the level of a ective deflection they experience. To uncover the basic e ects of di erent network topologies, we focus on the least complex group structures possible which still exhibits rich di erences in their network properties. Thus, we simulate groups of only three agents. There are in principle di erent connected and directed network topologies with three nodes, but we need each node to have at least one outgoing edge which means that the agent at that position will have a possibility to act on another agent. Of the remaining topologies, we restrict the experiments to the four networks depicted in Figure because they let us investigate di erent basic network properties we are interested in. a) is the fully connected base line, b) implies no hierarchy but nodes di er in terms of the number of incoming edges, c) implies a clear hierarchy and d) exhibits transitivity, i.e. a cyclic flow of actions. The remaining three topologies that we don't analyze here are mere combinations of these basic properties. .
In a task group setting, the topologies in Figure might be interpreted as follows: Network a) resembles an egalitarian team in which all group members can act on one another. Network d) also corresponds to an egalitarian group but is best interpreted as a task group in which the task requires circular iterative sequential actions from the team members. In network b), agent occupies a particular position, but it is somewhat ambiguous what that means in terms of status hierarchy since the existing arrows are reciprocal. We could interpret the setting as a formally egalitarian team in which agent is more in demand, and thus more stressed than the other team members. Finally network c) provides a clear status hierarchy in which agent is the leader who directs agents and . Figure : The network typologies we are simulating. .
To ensure that observed e ects result from di erent network topologies and not from the role-identity structure of the agents, we initialize all agents in each simulation with the same typical fundamental identity of a female with an EPA value of [1.78, 0.83, 0.84], but allow for random fluctuations in fundamental and initial transient identities through setting the parameters for individuality and initial tension to 1.0. Furthermore, we do not include a group object in this simulation, and in the subsequent toy network simulations for two reasons. First, we are interested in the e ects a restricted interaction structure and the related implicit status hierarchy have on group dynamics. We, thus, do not want to blur the e ects caused by the network topology by compounding them with actions on the group. Second, in the presence of a restricted interaction structure, it seems implausible that an action on the group object would simply translate in e ect to the equivalent of a dyadic action on all group members in equal parts, particularly when the network structure implies a clear status hierarchy.
In all the plots, we see that a er an initial relaxation phase the sentiments quickly approach a stable plateau. This initial relaxation can be interpreted as the agents' adjustment to the group situation and their negotiation of their role identities in the group setting. In the symmetric network structures a) and d), we see that all agents have on average the same transient identities. This is, of course, what we expect since no agent holds a more advantageous network position, and all agents are on average initialized with the same fundamental identities. We notice that the circular interactions in network d) do not have a noticeable e ect (compared to the fully connected network a), on either the transient identities or on the deflection levels of the agents. This finding hinges on the fact that all agents hold the same fundamental role identities, and would otherwise be di erent if this was not the case. .
In the simulations of the asymmetric network structures b and c, the average transient identities as well as the average deflection levels di er among the agents. This clearly indicates that the network topology influences the a ective dynamics of the group. In network b, agent can interact with both of the other agents, but she also gets to be acted upon more o en than either agents or . Being the object of an action more o en diminishes the potency of an agent which in return causes higher levels of deflection. In network c, on the other hand, actor can act on both agents and while they can only act on each other. This results in higher E,P and A values for agent which are closer to her fundamental identity, and therefore results in less deflection. Since network c is the only network that has a clear status hierarchy, we conclude that agents whose network positions provide more opportunities to act are able to choose more identity-conforming actions resulting in lower levels of deflection; this e ect is particularly pronounced along the potency dimension.

Expectation states theory .
Here, we show that the model reproduces well-known theorizing and empirical findings about status dynamics in groups. Expectation states theory (EST) o ers an explanation for how status hierarchies form and are reproduced in task groups (for review, see Ridgeway & Smith-Lovin ). According to EST, the absence of knowledge about their coworkers' competence leads team members to take di use status characteristics such as race or gender as signifiers of ability, providing some group members with both more opportunities to contribute, and to have their contributions more favorably evaluated because group members are inclined to believe that they are good. Given di erences in opportunities, asymmetries in status and prestige can quickly follow. Gender remains an important status characteristic that informs expectations about behavior. These expectations, in turn, organize social relations between men and women that result in system-level inequalities in access to resources and opportunities, resulting in a wide range of economic and social disparities (Ridgeway & Bourg ). Status structures in groups can be thought of as the building blocks of these macro-level structural inequalities. For example, to the extent that status processes make it less likely for women in work groups to become and be accepted as leaders, in the aggregate we will observe that more men than women will hold leadership positions in organizations (Correll & Ridgeway ). .
Our simulation experiment is driven by the hypothesis that the status-related group dynamics described in the EST research program emerge from a ect-control mechanisms in the interdependence of individual group members. To develop this argument, we demonstrate in simulation that our implementation of a ect control theory in combination with networked interaction structures is capable of reproducing the structural gendered inequality that men are more culturally accepted in leadership positions than women. To this end, we interpret a ective deflection in our simulations as a metric for how well cultural expectations are met. We interpret lower average levels of deflection in a group as the group configuration adhering more closely to cultural norms. .
The experimental setup is as follows: We simulate task groups of three agents with an interaction structure corresponding to network c) from the previous section which exhibits a clear status hierarchy of one agent in a leadership position and two agents with an equally subordinate status. We are interested in the interplay between status and gender in a setting when group members have no prior explicit knowledge about the actual merit or competence of their team members. We model this by simulating mixed groups of simple female (EP  uga.edu/act/usa-2015). We then systematically vary which identity is in the leadership position and which gender constitutes the majority of the group. This results in experiments with di erent setups: . A male leader with two female subordinate coworkers. . A female leader with one female and male subordinate each. . A male leader with one female and male subordinate each, and . A female leader with two male subordinate coworkers.
. . We observe that a male majority in the groups raises the overall level of deflection. This can be attributed to the fact that cultural norms, expressed in the fundamental male identity EP A = [1.07, 2.01, 1.05], entail the expectation of males to be particularly potent. Universally high potency is di icult to meet in group settings because role performance consists of performing the task while also confirming ones role identities. As subordinates, male agents have few opportunities to do this because they are acted upon far more o en than they act, resulting in a loss of potency.
. More importantly, we find that a female agent in the leadership position results in significantly higher levels of deflection compared to a group with the same role composition, but with a male leader. This is exactly what expectation states theory asserts. Since leadership is associated with potency and the male identity is culturally framed and thus perceived as being more potent than their female counterparts, male group leaders are culturally more accepted than female leaders in the absence of additional competence markers. People generally try to perform their role identities in accordance with cultural expectations, which in turn explains at least partially, why disparities remain between men and women in executive and upper management positions.

A Real-World Network Example: Online Collaboration on GitHub
. In the preceding section, we demonstrated that network restrictions on a group's interaction structure can influence transient identities and the amount of deflection experienced by agents in di erent network positions. Subsequently, we investigated the interplay between status encoded in a network structure and di use status characteristics such as gender that are implied by the agents' role identities. In this section, we study the e ect of specific status characteristics, how they interact with more realistic networked interaction structures, and what that means for a task group's management of roles and cultural expectations. A specific status characteristic indicates that a person, regardless of social group, has some instrumentality to the specific task goal at hand.
. As a real world example, we examine interaction structures found on GitHub, the world's largest online platform for social coding and collaborative so ware development. The open source so ware community is o en described as a skill-based meritocracy (Scacchi ; Eckhardt et al. ). Although there have been findings of gendered behavior and gender bias (Terrell et al. ; Vedres & Vasarhelyi ) in open source projects as well, the predominant value system in the community is meritocratic. Major motivational factors for developers to contribute to open source projects are the accumulation of reputational status and peer recognition they receive in return, which leads to strong norms for giving credit to authors where credit is supposedly due. This means that developers in leadership positions are presumably selected based on the quality of their contributions and their commitment to a project. Role assignments are of primary importance for programmers' task groups because perceptions of competence determine who assumes which role (Bianchi et al. ). .
In the process of collaborative so ware development on GitHub, a central interaction between developers is the acceptance and rejection of pull requests (PRs). If a developer wants to contribute to a project, she usually forks it (i.e., creates a local copy of the code base), commits changes to it, and then sends a pull request to the original project. These code changes are subsequently reviewed and discussed within the group. A developer with the necessary administrative rights, o en one of the maintainers, then either accepts or rejects the PR. If it is accepted, the changes are merged into the project's code base. This work flow is an example of a sequential protocol in which the goal of the task group can only be reached when certain actions are performed in a given order. Zöller et al. ( ) found di erent types of groups present on Github, categorized in terms of the network topologies spanned by the history of a project's accepted PRs. The di erences in interaction topology corresponded with di erences in productivity, popularity, resilience and language use. In order to shed light on the interplay between topology of the interaction structure, status, role expectations and identity management in collaborative online so ware development, we take two representative example networks ( Figure ) of the most di erent and clear-cut clusters of this study as the starting point for our analysis. Figure a) shows an example of a complex interaction topology that exhibits clustering, reciprocity, several high-status developers who have the administrative rights to merge PRs, as well as several lower-status contributors who do not have the right to merge PRs. Figure b), in contrast, depicts a very clear-cut hierarchical interaction topology with a single maintainer responsible for merging all of the PRs. Figure : Examples of typical pull request interaction structures found on github as identified by Zöller et al. ( ).

Formalization of the examples .
In the example graphs depicted in Figure , the directed edges point from the developer who submits to the developer who accepts the PR. But when submitting a PR, a developer does not necessarily know in advance who is going to review it. Hence, to simulate the network structure, we reverse all edges because accepting a PR is without a doubt a directed action towards the submitter while submitting a PR is more accurately modeled as an action on the whole group. Therefore, we include a group object in this simulation setup and allow actions on the group. .
Although the network structures at hand were derived from accepted PRs, we assume that the majority of actions are carried out along the same topology. We, thus, feed the adjacency matrices of the reversed graphs into our model as restrictions that govern both pull-requests and group discussion. During the group discussion, actions on the group object are possible in order to adress the whole group. Note that we ignore any occuring self loops . .
In the simulation, we want to mimic the sequence of actions we observe in real Github repositories, i.e. the sequence of submitting a PR, discussing it in the group and it being accepted or rejected by a maintainer. We, therefore, enforce a cyclic protocol in the model that consists of the following sequential actions: . An agent submits a PR which is interpreted as an action on the group. . The group discusses the PR. This is simulated via a sequence of freely chosen actions that are performed along the network topology or on the group object. The length of the sequence is determined randomly to be between and actions. . An agent with merge rights who shares a link with the submitter (specified via the network topology), either accepts or rejects the PR. The agent that actually gets to act is the one that experiences the most deflection among the candidates that come into consideration.
. To obtain the EPA labels of relevant concepts in the subculture of so ware developers, we conducted a minisurvey among N = 17 proven Github users , in which participants rated concepts along all three dimensions on a continuous scale ranging from −4.3 to +4.3. The resulting mean EPA values for these concepts are shown in  (Heise ) .
To investigate the interplay between specific status characteristics that are encoded in role identities, network positions that imply status, and cultural expectations that mediate between the two, we essentially run four di erent experiments for each network structure in Figure . • All agents are initialized with the fundamental identity of "experienced developer".
• All agents are initialized with the fundamental identity of "novice developer".
• All agents who have higher status and can accept PRs ( i.e. who have an incoming edge in Figure ) are initialized with the fundamental identity of "experienced developer". All other agents are initialized with the fundamental identity "novice developer".
• Agents are randomly initialized with either the identity "experienced developer" or "novice developer" independent of their network position, but with the same numbers of experienced/novice developers as in setup c).
. For all four conditions, we set the action-on-group rate and reciprocity rate to zero to have as little overlapping/distracting additional e ects as possible. Furthermore, when initializing the model, fundamental identities are drawn from a clipped normal distribution with standard deviation (individuality) . , centered on the target fundamental. All results shown in the subsequent section are averaged over model runs for each experimental setup.    .

Figure
In the star shaped interaction topology, there is only one project maintainer with a clear network advantage that is higher in status and contributors that have all the same symmetrical network positions with lower status. We see from Figure a) and b) that whether we simulate a group of experienced developers or a group of novice developers, in both cases the developer in the high status network position (agent ) exhibits a higher value of potency. However, Figures a) and b) reveal that, for experienced developers, this increase in potency leads to less deflection while for novice developers it leads to more deflection. The reason for this is that an increased potency aligns more closely with the potent fundamental identity of the experienced developer while it is not role-confirming for the novice developer. .
The simulation results suggest that experienced developers experience more deflection than novice developers which holds true for both the star-shaped topology and the more complex interaction structure. In an ACT simulation framework, this is generally the case for agents with more potent identities because they experience a higher level of deflection when acted upon or when they are unable to perform role conforming behavior on less potent agents. Therefore, to illuminate the interplay of role identities with network positions, we keep the simulation settings as comparable as possible in experiments c) and d) and include the same number of experienced and novice developers in the groups. Unexpectedly, agent exhibits lower potency than the other experienced developers in high status network positions, even though no other agent can directly act on her. The reason for this finding is that agent can only directly act on agent who is also an experienced developer. Because agents try through their actions not only to confirm their own identity but also the identities of the others, agent has to routinely compromise by choosing actions that lead to lower potency and higher evaluation and activity values than would be the case if agent was inexperienced. The potency of agent , in return, is lowered as well because she is acted upon regularly by agent . For both agents and , this translates into slightly higher deflection values which can be seen in Figure c). This interplay is a nice example of the complex, non-linear dynamics that can quickly arise in a ective space when modeling complex role-identity and network cofigurations.
. Compared to experiment d) in which the agents are randomly assigned to network positions, the matching in experiment c) leads to a lower mean deflection in the group when averaged over the deflection of all agents. This holds true for the star-shaped topology (Figure ) and for the more complex interaction network ( Figure  ) where the e ect is even stronger due to the more balanced numbers of experienced and novice developers in the group. Comparing the two group cofigurations, lower average deflection levels in one group signify that the assignment of role identities to network positions is culturally more accepted in this group than in the other. Hence, the simulations confirm the repeated statements in the literature that meritocratic values in the form of deference to experienced skilled individuals plays a strong role in the open source so ware development community. This result may seem trivial, since it might be considered common sense that experienced developers are culturally more accepted in leadership positions than novice developers. However, our model sheds light on how these cultural expectations arise. Specific (and di use) status characteristics translate into role identities that imply normative a ective meanings. People then choose their actions according to cultural norms, and in such a way as to perform their role identity to confirm its a ective meaning, as well as to confirm the a ective meanings of the role identities of their fellow team members. Furthermore, the simulations demonstrate that a ect control theory as a generic social theory in combination with networked interaction structures and protocol sequences is capable of sensibly reproducing observations from specific occupational fields such as so ware development.

Summary and Discussion
. In this work, we developed and implemented an agent-based model to simulate interactions in complex task groups in constrained environments. To this end, we extended an existing model based on a ect control theory by Heise ( ) in three important ways. First, we allow the analyst to specify a network topology that restricts possible action pathways in the group which can be used to model hierarchical role configurations. This extension was motivated by observations in online task groups whose interactions occurred solely along network structures. Second, we allow the analyst to specify a discrete set of actions for agents to choose from, which caters to the fact that in many group situations only a limited number of behaviors are admissible, acceptable or available. Third, we allow the analyst to specify sequences of actions that have to be carried out in order. These protocols are o en observed in task groups where the completion of a task requires several steps of role-based division of labor.
. In a series of simulations, we found that network positions have an influence on agents' experienced a ective deflection and their transient identities, particularly along the dimension of potency. This finding highlights the interconnection between structural properties of groups and group members' cognitive-a ective representations of group interactions. By expressing status hierarchies in terms of node positions in a network topology and interpreting deflection as a metric for cultural acceptance, we were able to build a bridge between expectations states theory and a ect control theory that can contribute to new theoretical developments in both literatures. In particular, we succeeded at reproducing central results from the expectation states framework (Ridgeway ) in simulations of groups whose actions were driven by the a ect control principle. The simulations of idealized, mixed-gender task groups suggested that, regardless of actual competence, men were on average culturally more accepted in leadership positions than women, which in the simulations could be traced back to the encoding of cultural norms in a ective identity labels. Agents chose their behaviors in such a way as to align them with the cultural expectation from the group towards their role identity, but for female agents in leadership positions the average deflection in the group was significantly higher compared to male agents in leadership positions. This result suggests that in order to promote gender equality sustainably, the cultural norms in which female identity is generally perceived to be less powerful and more positive than the male identity would have to be adjusted. From a symbolic interactionist point of view, cultural meanings arise and are consolidated through interactions. Consequently, by continuously promoting and normalizing female leadership and by increasing its visibility, the perception of the normative female identity can possibly be changed in the long-term future through changes in the cultural a ective meanings of female identities. .
As an example of a realistic complex task group, we modeled in a series of experiments groups consisting of open source so ware developers with their domain-specific work flows. We extracted network structures from GitHub, the largest platform for open source so ware development, and conducted a small survey among verified Github users in which we had the most important role identities and task related behaviors rated on affective scales. This subculture and domain-specific data served as an empirical basis to parameterize the simulation model. The simulations showed that in these groups average deflection was significantly lower if highstatus network positions, signifying more responsibility and the power to accept or reject proposed changes to the code base, were filled with experienced developers instead of novice developers. This result is in accordance with the presumed meritocratic value system in the open source so ware development community, which is essential for the process of self-organization in groups that are not backed by a larger organization.
. We believe that this is a good example for how our model can be adapted and generalized to the study of groups in other domains and subcultures which we think is a promising use case of the model for future research. An adaptation process will generally consist of the following steps. First, one will have to research the task domain and its subculture of the groups of interest. This might include the identification of an organizational structure that typically guides group interactions. Furthermore, this is likely to include the identification of important role identities and behavior sequences that are characteristic or necessary for completing core tasks or conducting other focal interaction protocols in the group. Second, one can then design a mini-survey to collect a ective ratings of these concepts. These empirical findings can subsequently be injected into the simulation setup which can then be used to illuminate the a ective group dynamics, generate hypotheses, or compare di erent role constellations. In this way, it is possible to systematically analyze the interplay between status characteristics, role identities, and cultural norms and expectations. .
There are several limitations in our model that we briefly want to discuss: The ACT equations are derived from dyadic vignettes, but have not been tested empirically in group settings (Heise ). We assume that as long as the actions in a group are mostly of a dyadic nature, our model will be accurate, but corrections to the theory and model implementation might be necessary in groups where the focus is on the collective aspects of the group like joint behaviors by or on several agents or towards the group as a whole. In this context, the implementation of the group object should also be reviewed. We followed Heise ( ) in how we implemented the group object as a pseudo-agent, but we have the impression that both ACT as a theory as well as its implementation in a simulation model would benefit from a rigorous empirical investigation about how to formalize the group identity within an ACT framework. .
Another consequence of the dyadic structure of ACT's impresssion change equations is that the theory originally did not include propositions about the mechanisms that guide turn taking. Like Heise, we assumed for the most part that taking the initiative to act was guided by deflection levels and only in the simulation of Github groups sometimes the actor was determined by other factors like the administrative rights encoded in the network structure. Note that we tried to shed some light on the di erences between possible object selection criteria in the reproduction of the jury simulation experiments, but we did not find tremendous di erences in the agreement with the available empirical data set between the di erent criteria. But the amount of available empirical data was both limited and domain-specific. What we did find, however, was that the newly introduced object selection criterion of maximum deflection reduction did significantly reduce deflection in the group. In any case, we believe that the mechanics of turn taking in groups and its interplay with ACT should be further investigated. This includes the specific micro-interactions group members use to negotiate and signal who is the next person to act. Our current model implementation, where each group member has full and consensual information about each other group member's state of mind is clearly unrealistic given the bounded rationality of the human brain. A more realistic assumption would be a social-comparison mechanism where the tension experienced by a group member translates into nonverbal cues which are then recognized by other agents, but it remains for future work to model such a mechanism. In addition, a group member's ability to recognize and understand a ective group dynamics might vary and depend on each individual's communication skills and ability to empathize with others, which are related to the "collective intelligence" (Woolley et al. ) of the group as a whole.
. An interesting step in the direction of modeling individual di erences not only in terms of agents' observations but also in terms of agents' ability to manage several roles simultaneously is Bayesian a ect control theory (Schröder et al. ), which models dyadic interactions via partially observable Markov decision processes. Observations might also play a role in turn taking. It is plausible to imagine group situations in which a group member might intervene and take the initiative a er observing the actions of other group members even when they have not been the target of any action themselves. .
In addition, a ect control theorists have started to model the interplay of identity maintenance processes and other goals (Hoey, MacKinnon, and Schröder ); this work has important implications for modeling task groups as group members frequently must balance between meeting immediate task goals, advancing their own social status, and ensuring the group's mid to long-term functioning by supporting both the group's collective identity and the identities of the group members. Successful identity performance is critical to leveraging social capital at a later point in time, which means that a irming and seeking advancement are not necessarily mutually exclusive. However, we believe that the two processes operate on di erent time scales. While our model is designed to simulate situational task group settings, an agent's career advancement is an important long-term strategic goal that is currently not taken into account. The amount of tension between these di erent objectives is largely influenced by whether personal long-term goals align with the goals of the group. Future group models will ideally include a utility function that enables the modeling of several kinds of objectives and time scales. .
Most of the aforementioned limitations could be systematically addressed with a series of networked online experiments that monitor group interaction processes while at the same time controlling the experimental conditions. Combined with a survey among participants this would be a promising branch of future research that could both advance theoretical aspects of group processes research, and at the same time provide an invaluable source of data to directly evaluate simulation models.

Model Documentation
The ACTING model was implemented in Python . using the Mesa library for ABM (Masad & Kazil ), and the source code for the model and Jupyter notebooks with all simulations presented in this article can be found at https://github.com/nikozoe/ACTING. The source code is also available through the CoMSES Computational Model Library as: ACTING (A ect Control Theory based simulation of Interaction in Networked Groups)" (Version . . ), https://www.comses.net/codebases/fe554877-a041-4fb4-91e5-8400ebec573c/releases/1. 0.0/.
Note that while implementing the model in Python we discovered a bug in the implementation of the object selection that was present in Heise's original Netlogo version of group simulator. This bug by coincidence slightly increased the correlation between experimental data and Heise's simulation results (min-event-tension + continuous action space Heise ). A er the fix, this correlation dropped from . for all behaviors and . for the gender di erences to . and . , respectively. We conjecture that Heise calibrated the other parameters, i.e. action-on-group rate and reciprocity rate such as to maximize this correlation, which would explain the drop a er the fix.
For this example, the type of identity we model is not important because our goal here is to isolate the e ect that the network topology has on the agents' transient identities and deflection levels.
Self loops correspond to developers merging their own pull requests.
While N= might seem small, note that we are measuring cultural consensus not variation. The error on the mean sentiment is reduced by a factor of 1/ √ N * compared to an individual rating. Standard deviations of . on Evaluation, . on Potency, and . on Activity are reasonable general estimates of error when a single respondent is being employed to assess cultural sentiments (Heise ).