2021

[1]Darío Blanco-Fernández These authors contributed equally to this work.

These authors contributed equally to this work.

These authors contributed equally to this work.

1]Digital Age Research Center, University of Klagenfurt, Universitätsstraße
65-67, Klagenfurt, 9020, Austria

2]Department of Management Control and Strategic Management, University of
Klagenfurt, Universitätsstraße 65-67, Klagenfurt, 9020, Austria

# Interactions between dynamic team composition and coordination

An agent-based modeling approach

<EMAIL_ADDRESS>Stephan Leitner<EMAIL_ADDRESS>Alexandra Rausch
<EMAIL_ADDRESS>[  [

###### Abstract

This paper examines the interactions between selected coordination modes and
dynamic team composition, and their joint effects on task performance under
different task complexity and individual learning conditions. Prior research
often treats dynamic team composition as a consequence of suboptimal
organizational design choices. The emergence of new organizational forms that
consciously employ teams that change their composition periodically challenges
this perspective. In this paper, we follow the contingency theory and
characterize dynamic team composition as a design choice that interacts with
other choices such as the coordination mode, and with additional contextual
factors such as individual learning and task complexity. We employ an agent-
based modeling approach based on the NK framework, which includes a
reinforcement learning mechanism, a recurring team formation mechanism based
on signaling, and three different coordination modes. Our results suggest that
by implementing lateral communication or sequential decision-making, teams may
exploit the benefits of dynamic composition more than if decision-making is
fully autonomous. The choice of a proper coordination mode, however, is partly
moderated by the task complexity and individual learning. Additionally, we
show that only a coordination mode based on lateral communication may prevent
the negative effects of individual learning.

###### keywords:

Coordination, Complex task, Dynamic team composition, Agent-based model

##  1 Introduction

The traditional perspective on dynamic team composition—i.e., the periodic
substitution of team members with different individuals—characterizes it as a
negative outcome of suboptimal organizational design choices [13, 17]. This
perspective connects dynamic team composition to the concept of organizational
turnover, leading to the common assumption that dynamic team composition
results in detrimental effects for organizations [69]. Specifically, prior
research [19, 22, 26] argues that changing the composition of a team disrupts
the development of autonomous coordination among team members—meaning the flow
and exchange of information between individuals regarding their potential
actions [9, 21, 52, 36]. This reduced coordination, in turn, leads to a
decline in task performance—i.e., in the effectiveness with which a task is
completed [13, 41, 43, 56].

The emergence of new organizational forms in recent years, however, challenges
this traditional understanding of dynamic team composition. During the past
decades, many countries have experienced a process of transition from an
industrial towards a knowledge-based economy [40]. Furthermore, these last
decades have witnessed the unstoppable advance of digitalization, impacting
almost every facet of our everyday lives [12]. Consequently, organizations and
the environment in which they operate have changed substantially. Since the
tasks and problems faced by organizations have become more complex, teams
experience higher uncertainty when handling them [60]. This increased
complexity and uncertainty require teams to be more flexible, adaptative and
agile [10, 67], decentralize decision-making [59], self-organize, be
autonomous [11, 50, 54], and establish fluid boundaries among them [3]. These
requirements often result in highly dynamic teams whose composition changes
frequently, with their members periodically moving in and out [3, 69]. Many
organizations have significantly altered their structure to adapt their
internal operations to these demands, leading to the emergence of new
organizational forms [10]. For instance, virtual or distributed organizations
employ communication technologies to connect their members even when they are
geographically dispersed [68]. This reliance on communication technologies
allows them to quickly alter their teams’ structure in response to present and
future demands [68]. Conversely, holacracies are decentralized organizations
that favour autonomous team formation and shifts in composition based on the
team members’ self-assessment of their capabilities [59]. Similarly, platform-
based organizations combine the use of communication technologies with self-
organization, functioning as a series of autonomously-formed teams that change
their composition in response to what the organization requires [10]. Finally,
organizations structured around project-based teams emphasize the creation of
temporal groups of people that disband upon completing a specific task or one
part of it, with its members moving on to other teams afterwards [45].
Consequently, we may argue that these new organizational forms often emphasize
dynamic team composition as a conscious design element [10, 69].

[10] define organizational design as ”a systemic approach to aligning
structures, processes, leadership, culture, people, practices, and metrics to
enable organizations to achieve their mission and strategy.” Each formal
design element—or choice—is a configuration of these components. While prior
research often overlooks the role of dynamic team composition as a design
choice, there has been a growing interest in investigating how dynamic team
composition can be a structural feature of organizations and how it may relate
to other design choices and task performance [3, 47, 69]. For instance, prior
research suggests that organizations employ dynamic team composition to
broaden the knowledge base of their teams and members [3, 46, 66], ensure that
teams are well-adapted to the task requirements [3, 47, 67, 69], become more
innovative [3, 67], and improve team-building efficiency over time [3, 47,
69]. Moreover, there is evidence of the effects of dynamic team composition
that contradicts the traditional perspective on the matter. For instance, [67]
argues that dynamic team composition may have a positive impact on task
performance. These positive effects, however, may only manifest themselves if
team members properly coordinate their actions [67].

This conflicting evidence between the rather traditional and modern branches
of organizational research shows that shifts in the characterization of
dynamic team composition may alter our understanding of its relationship with
coordination and task performance. Given this conflicting evidence, our aim is
to clarify how these factors—dynamic team composition, coordination, and task
performance—interrelate. To achieve this objective, we characterize dynamic
team composition as a design element consciously implemented by organizations
and examine how it interacts with selected coordination modes, influencing
task performance. From a practical standpoint, this paper aims at providing
practical advice for teams and organizations regarding their coordination mode
choices based on our results.

Design elements—such as dynamic team composition and coordination modes—have
different effects depending on the organizational context, i.e., on a
multidimensional set of components related to the organization such as its
goals, strategies, structure, external environment, tasks faced, and human
resources [9, 10]. This argument follows the contingency theory, which
suggests that there are no universally optimal organizational structures [21].
Therefore, to properly characterize dynamic team composition as a design
element and examine its interrelations with coordination, it is essential to
consider the various contextual factors that may be related to them.

The interrelations between dynamic team composition and coordination and their
joint effects on task performance may be contingent on contextual factors that
do not form part of the organization’s design, such as individual learning
[10, 13, 14]. We understand individual learning as the process by which
individuals discover new solutions and forget redundant solutions to a task
over time [61, 48]. According to the traditional perspective on dynamic team
composition, shifts in team composition trigger adaptation, forcing teams and
their members to adapt their knowledge to these changing conditions [13, 41,
42]. Conversely, dynamic team composition may be employed by teams to acquire
previously unavailable knowledge [3, 46, 62, 66]. According to prior research,
teams acquire new knowledge either through changes in their composition or the
individual learning process of their members [46, 65]. Therefore, given
standard categorizations of learning, dynamic team composition can be regarded
as an adaptation process similar to learning at the team level. Since both
individual learning and dynamic team composition appear to be highly relevant
for the adaptation process of the organization, investigating how these two
processes may interact becomes crucial. Furthermore, prior research suggests
interrelations between coordination and learning [18, 56]. Specifically,
researchers suggest that when team members coordinate properly, learning
routines emerge, improving their knowledge acquisition process [18, 56].

Task complexity is also a contextual factor that may influence the effects of
dynamic team composition and coordination on task performance [10, 57, 64,
74]. Task complexity refers to the interdependencies among the several
decisions which form an overall task [23, 72]. According to prior research,
interdependencies increase uncertainty in decision-making and decrease task
performance [38, 41, 72, 74]. To reduce this uncertainty, the mirroring
hypothesis argues that an organization’s design should fit these
interdependencies [21, 74]. From a team’s perspective, prior research suggests
that team composition should be chosen according to the interdependencies
among the decisions of the task [29]. Additionally, proper coordination among
team members should be assured to further reduce this uncertainty [21]. Thus,
task complexity, coordination, and team composition appear to be interrelated.

In summary, our objective is to clarify the relationship between dynamic team
composition, coordination, and task performance. Furthermore, and building on
prior research [6, 7], we consider two factors that might influence this
relationship: individual learning [46, 66] and task complexity [64, 74]. To
achieve our objective, we have implemented an agent-based modeling approach.
Agent-based modeling approaches are particularly helpful for studying
organizational design, as they allow researchers to simultaneously model and
study numerous design elements that interact with each other and other factors
[10, 32, 57, 64, 74]. Furthermore, simulations are especially valuable when
data is unavailable or difficult to obtain [10, 35, 75]. Specifically, we
follow previous research on organizational design by implementing a simulation
model based on the NK framework [32, 57, 64, 74]. In our approach, a
population of human decision-makers with limited capabilities—the agents of
the model—must form a team to solve tasks that we assume to differ in their
level of complexity. This team may change its composition periodically.
Additionally, the team members may employ a specific coordination mode when
making their decisions to solve the complex task [64]. Furthermore, we assume
that the agents of the model may learn about the complex task over time,
adapting their knowledge to its conditions.

We believe the NK framework is appropriate for answering our research
questions for several reasons. First, at its core, the NK framework involves
simulating and observing over time the behavior of learning agents concerning
specific interdependent elements [38, 35, 74]—in our case, the decisions of a
complex task. Second, the NK framework can be employed to simulate and observe
decision-making in small-scale teams over an extended period—see, for
instance, [24, 29, 58, 64] and [74]. Finally, the model is flexible enough to
introduce variations in team composition [6, 7, 5].

##  2 Background

###  2.1 Dynamic team composition and organizational design

Prior research on dynamic team composition may be divided into two diverging
traditions that lead to seemingly contradictory insights and suggestions. In
the branch of research concerned with more traditional organizations, teams
are assumed to be stable units that aim at maintaining the same composition
over time [69]. This line of research usually associates dynamic team
composition to organizational turnover, which is often interpreted as a cause
of organizational crises and stress [41, 42]. This negative characterization
of dynamic team composition is partly supported by prior findings. Simulation-
based research suggests that the performance of teams experiencing turnover is
significantly lower than that of stable teams [13, 41]. These insights are
also supported by experimental studies [26, 31, 43, 55] and in survey-based
research in the consulting [22], healthcare [56], and software development
[51] sectors. Additionally, simulation experiments in this branch of research
suggest a negative association between dynamic team composition and
organizational learning [13]. Evidence coming from surveys in Dutch firms [62]
and the US healthcare sector [18, 56] is in line with these insights.

The main mechanism that drives these negative effects is the increased
uncertainty in decision-making brought by shifting team composition. According
to [42], increased turnover may disrupt the organizations’ operating
conditions, intensifying uncertainty. This increased uncertainty forces
decision-makers to act under suboptimal conditions [41] and severely restricts
the team’s ability to preplan and anticipate future needs [21]. This reduces
the team members’ decision-making capacity, decreasing task performance [21,
42].

This branch of research, however, fails to acknowledge that dynamic team
composition may be a conscious design element implemented by organizations
rather than a consequence of suboptimal design choices. [69] argue that the
emergence of new organizational forms implies that research should depart from
the traditional understanding of dynamic team composition. According to their
arguments, many modern organizations—such as holacracies, virtual
organizations, or project-based teams—rely on self-organized teams [50] with
decentralized decision-making and shifting roles, functions, and personnel
[59]. They also emphasize periodical changes in team composition as a crucial
design element [69, 76]. This dynamic team composition allows organizations to
learn how to configure the most effective possible team over time [2, 47] and
enables teams to adapt to the task’s conditions at any given time by changing
their composition [62]. This helps teams to integrate new members with
previously unavailable knowledge within their ranks [66].

The research branch that follows these suggestions provides findings that
challenge the traditional perspective on dynamic team composition and its
supporting evidence. For instance, prior simulation-based results in small-
scale teams suggest that task performance might increase when teams change
their composition periodically [6, 7]. These insights are supported by
experimental studies. For instance, [15] and [16] show that shifts in team
composition enhance innovativeness in decision-making, increasing task
performance. Survey-based research of German firms [67] and Australian R&D
teams [27] confirm these findings. This increase in innovativeness may result
from faster learning [63] and from better transfer of knowledge between team
members [16, 63]. Thus, dynamic team composition can be understood as an
exploratory process by which teams acquire new knowledge [46, 51, 66].
Exploratory processes are particularly valuable for enhancing the performance
of complex tasks, particularly during the initial stages of decision-making
[38].

In summary, both branches of research have brought forward the main advantages
and disadvantages of dynamic team composition. On the one hand, dynamic team
composition may be associated with enhanced innovativeness [16] and knowledge
transfer [63], which may lead to improvements in performance [6, 7]. On the
other hand, periodical shifts in team composition may increase uncertainty in
decision-making, reducing task performance [42]. Modern organizations that
rely on dynamic team composition might seek to capitalize on these advantages
while adopting design elements that aim at reducing its associated
uncertainty. For instance, prior research argues that implementing effective
coordination mechanisms among team members may successfully counteract
uncertainty in decision-making [21].

###  2.2 Organizational design and coordination modes

[21] suggests that organizations should alter their design when facing
significant uncertainty, either by enhancing their information processing
capacity or by decreasing the demand for it. Organizational design elements
are often divided into structure and coordination choices [10, 32, 34].
Structure choices are those related to the division of labor [10], and they
are typically used to reduce the information processing demands of the
organization [21]. Generally, organizations perform better if their structural
features eliminate the interdependencies among different decision-makers or
reduce them to their greatest possible extent [74]. This objective is
relatively easy to achieve for simple tasks with few concentrated
interdependencies. If tasks are complex—i.e., interdependencies are numerous
and widespread throughout the task—achieving this objective becomes much more
difficult [10, 64, 74].

Hence, organizations might resort to coordination choices to overcome the
limitations caused by task complexity [10]. Coordination choices encompass the
actions taken to facilitate the flow and exchange of information between
individuals, thereby increasing the organization’s information processing
capacity [9, 21, 36]. According to [52], coordination choices include informal
coordination through the establishment of incentive schemes and formal
coordination through the implementation of coordination modes111Coordination
choices and coordination modes are two separate concepts. Coordination choices
are part of organizational design and refer to those elements which ensure
that organizations combine their resources efficiently. The choice of a proper
coordination mode is a design problem in itself and part of the coordination
choices of the organization [10]., i.e., through the implementation of rules
and procedures which organize individual decision-making and assure open
communication between decision-makers [10, 37, 64, 74].

Prior research has highlighted the importance of implementing a particular
coordination mode—i.e., of establishing formal links, procedures and
communication channels—to formally coordinate the team members’ actions [21,
49, 52]. Each coordination mode has its specific functioning and
characteristics. For instance, [52] argue that when decisions are taken
sequentially, decision-makers require substantial information about the
preceding actions to act properly. Previous simulation-based research tested
this hypothesis by studying a coordination mode labeled as sequential
decision-making, suggesting that it may improve performance if tasks are
sufficiently complex [73, 74].

Conversely, establishing communication channels among team members is also
emphasized as an effective tool for achieving coordination [21, 64].
Specifically, [49] highlight two different ways of achieving coordination
following this approach. First, coordination may be achieved by mutual
adjustment, i.e., by establishing direct, unmoderated lateral communication
between team members. According to [21], this direct interaction ensures that
team members make their decisions together. [64] label this coordination mode
lateral communication. Their results suggest that, for complex tasks, lateral
communication counteracts the uncertainty associated with task complexity
better than any other coordination mode, improving task performance [64].
Second, coordination may be achieved by assuring direct, moderated
communication between team members through the establishment of liaison
devices [21, 49, 52]. Liaison devices encompass various roles which, while
having no decision-making capacity of their own, are tasked with assuring that
information flows properly between team members [49, 52]. Team members act
autonomously and fully retain their decision-making capacity, while the
liaison device ensures that they maintain communication [52, 64]. Although
they may effectively achieve their objective, prior simulation-based results
suggest that a liaison coordination mode may slow down decision-making,
reducing task performance in the long run [64].

###  2.3 Dynamic team composition and coordination

Prior research often addresses the interrelations between dynamic team
composition and coordination [18, 19, 22, 26, 51, 56]. There are, however,
diverging interpretations of the interactions between dynamic team composition
and coordination. Evidence coming from one branch of research suggests that
dynamic team composition is negatively associated with coordination. For
instance, experimental findings suggest that shifts in composition reduce
coordination among team members and, in turn, task performance [26]. Survey-
based findings in the fields of healthcare [18, 19, 56], software development
[51], and consulting [22] support these experimental results. These findings,
however, may be constrained by the traditional perspective on dynamic team
composition, which associates it to organizational turnover [47].

As dynamic team composition gains significance as an organizational design
element, it is likely that new insights will be found if research departs from
the traditional perspective on dynamic team composition, interpreting it
rather as part of organizational design [69]. For instance, the investigation
of German firms carried out by [67] leads to an alternative interpretation on
the relationship between dynamic team composition and coordination.
Specifically, their results suggest that dynamic team composition enhances
creativity and innovation within teams and improves task performance.
Nevertheless, proper coordination among team members needs to be ensured if
teams want to fully exploit these advantages [67].

##  3 The Model

In this paper, we build on the NK framework [38] and propose an agent-based
model to study the effect of coordination modes and dynamic team composition
on task performance. In contrast to experimental and empirical research, our
proposed model does not rely on observing real-life data [75]. Instead, we aim
to better understand the variables of interest by employing a simulation
approach that develops the insights found in prior research (see Sec. 2).
Three factors influence our choice of the research method. First, the NK
framework provides an opportunity for creating an artificial organization that
we can use to change its design choices and examine their effects on task
performance [72, 75]. Additionally, our adaptation of the NK framework helps
us explore the long-term dynamics of team composition [75], which is in line
with the suggestions given in prior research [47]. Second, we can modify the
NK framework to model aspects such as learning, task complexity, and agent
interaction [75]. Finally, the NK framework is a standardized approach
employed in related research [1, 72] and contrasted with other methods [4,
24]. Consequently, we believe that this model is the best choice for our
research.

The following four subsections correspond to the four building blocks of the
model and follow the sequence of events during each simulation (see Fig. 1).
In this agent-based model, several human decision-makers are entrusted with
solving a complex task (see Sec. 3.1). These agents must form a team to solve
this complex task; the process of team formation is repeated periodically to
account for dynamic team composition (see Sec. 3.2). Once the team is formed,
team members follow a specific coordination mode to implement a solution to
the complex task (see Sec. 3.3). At the end of each period, all agents update
their knowledge by going through a learning process (see Sec. 3.4).
Subsequently, depending on the parameter configuration, the process returns to
either team formation or the decision-making phase.

Figure 1: Sequence of the model.

Section 3.5 discusses the parameter settings. Appendix A provides a discussion
on the technical aspects of the model and the simulation.

###  3.1 Task environment and agents

We model the complex task as a vector of $N=12$ binary decisions. Each
decision, denoted by $d_{n}$, contributes $c_{n}$ to the overall task
performance, which we calculate as the average of all contributions (see Eq. 1
and Appendix A.1). Each vector of $12$ binary values is a solution to the
complex task and has an associated task performance. The mapping of each of
the $2^{12}=4,096$ possible solutions to their associated performance is the
performance landscape [38] (see Appendix A.1 for additional details).
Following the NK framework, we incorporate task complexity by making the
decisions interdependent [23, 38, 72]. Thus, the contribution to task
performance $c_{n}$ depends on the decision itself $d_{n}$ and $K$ other
decisions. A larger value of $K$ indicates more interdependencies and, thus, a
higher task complexity. When there are no interdependencies, i.e., $K=0$, only
one optimal solution to the complex task exists, which is easily achievable.
As $K$ increases and approaches $N-1=11$, several suboptimal solutions appear,
making it increasingly challenging to reach the optimal solution [38, 58].

Furthermore, task complexity has significant implications for the decision-
making agents. To solve a complex task, it is often necessary to combine
different complementary skills that are typically not found in a single
individual [29]. Consequently, a single agent cannot solve a complex task by
themselves, as they have limited capabilities concerning the complex task they
face [20]. Instead, complex tasks are usually solved by teams of different
experts [23, 29, 57]. To account for these limited capabilities, we divide the
$12$-dimensional task into $M=3$ subtasks, each consisting of four decisions.
Each subtask corresponds to an area of expertise [29]. We randomly assign each
agent of the model to one of these areas of expertise, i.e., they can only
solve one of the three subtasks. Additionally, agents are not aware of the
complete set of solutions to their assigned subtask from the beginning.
Instead, we initially endow each agent with one random solution to their
assigned subtask. This characterization of limited capabilities follows the
difficulty assumption as described by [39], ensuring that agents do not have
the complete set of solutions to their assigned subtask at their disposal from
the beginning.

There are $P=30$ agents in our model. Agents are utility-maximizing, and they
experience utility by participating in the team and solving the complex task.
A team member’s utility is the average of their own performance contributions
and the remaining members’ performance contributions—i.e., the performance
contributions of the residual decisions. (see Eq. 2 and Appendix A.2) In
addition to the aforementioned limited capabilities, agents also have
restricted cognitive capacities, which prevent them from pursuing long-term
objectives. Instead, agents are myopic and aim at maximizing their immediate
utility.222This ensures that agents behave analogously to a hill-climbing
process on the performance landscape. This is a defining feature of the NK
framework, see Appendix A for additional details.

###  3.2 Team composition

We assume that one team of three members—one per area of expertise—is
sufficient to solve the entire complex task.333Team member $1$ deals with
decisions $1$ to $4$, member $2$ with decisions $5$ to $8$, and team member
$3$ with decisions $9$ to $12$. Following the increasing reliance on self-
organization that characterizes modern organizations [54, 59], we set up a
team formation mechanism in which agents autonomously come together to create
the team. As [59] notes in his study of holacracies, members of modern
organizations often decide autonomously whether to join and leave teams by
assessing their own expertise and potential contributions. Additionally, team
members often take a proactive stance towards self-improvement and the upgrade
of the team’s operations [53]. To apply this modern approach to self-
organization, the agents in our model follow a signaling mechanism for team
formation that aims at integrating the best available experts within the team
[6, 7].

We work on certain assumptions about the agents’ behavior to avoid any
strategic behavior. First, we assume that agents know perfectly how the team
composition is chosen. Additionally, we assume that agents do not cheat during
team formation. Finally, we omit any communication between agents during the
team formation process.

Team formation works as follows: Each agent, who knows a specific set of
solutions, estimates the utility associated with these solutions (see Eq. 3
and Appendix A.3). Agents cannot, however, anticipate the residual decisions
for the incoming period or communicate to obtain information on them, since
these decisions are located outside their area of expertise. Instead, they
assume that the residual decisions from the previous period will not change
for the incoming period. Furthermore, agents may commit small miscalculations
which range between 1 and 10 percent, reflecting the average error rate in
reporting according to prior research [70]. Each agent then sends a signal
equivalent to the highest estimated utility available. The agent with the
highest signal for each subtask joins the team.444In the case of a draw, the
team member is randomly chosen from the top signalers. Consequently, the team
is formed by the three agents who are supposed to be the best-available
experts in their respective subtasks.555Non-members wait on the sidelines
until the next team formation process, earning utility equal to 0.

The team is always formed in the first period. Afterwards, agents periodically
change the team composition by repeating the team formation process every
$\tau$ periods. $\tau$ is a design parameter that can be understood in terms
of the team’s lifetime: A higher (lower) value of $\tau$ indicates that team
formation occurs less (more) frequently, which implies a long-term (short-
term) team composition.

###  3.3 Decision-making and coordination modes

Once the team is formed, the three team members propose solutions to their
assigned subtasks. These proposals are combined to create an overall joint
solution to the complex task. Following prior research [64, 74], we define
three coordination modes. The choice of the coordination mode determines how
team members evaluate their solutions, which criteria they follow to make
their proposals, how these proposals are shared between team members, how
proposals are combined to form candidate solutions, and how team members agree
on implementing an overall task solution [10, 64, 74]. These coordination
modes differ in three aspects [64]: The team members might

  * •

evaluate their solutions privately before making proposals.

  * •

control in which order their proposals are considered.

  * •

have veto power over the remaining members’ proposals.

Additionally, we define a benchmark scenario without coordination. In this
benchmark scenario, we study a fully autonomous team in which decision-making
is entirely decentralized, without communication between team members [64,
74]. This highly decentralized structure corresponds to a congregation of
loosely connected individuals with mutual interests [28] that can be found,
for example, in professional bureaucracies like schools [49]. Furthermore,
this fully autonomous team reflects the need for rapid action and innovation
that drives many organizations. It also reflects their strong reliance on full
self-organization and decentralization [52]. In this scenario, each team
member estimates the utility of each solution they know as outlined in Sec.
3.2 (see Eq. 3 and Appendix A.3). Then each member chooses the solution to
their subtask which reports the highest estimated utility, and the overall
task solution for the current period is the concatenation of all members’
proposals.

Teams often attempt at simplifying the process of solving complex tasks by
partitioning them into multiple steps and addressing them sequentially [9,
49]. When there are corresponding interdependencies among team members, this
creates a sequential reliance among them, as they must be aware of prior
decisions to act accordingly [49, 52]. This is evident, for instance, in ass
production factories [49] or in activities such as the processing of checks in
banks [52]. Following [74], we transfer these insights onto the sequential
coordination mode. In this coordination mode, the proposals are made
successively according to the subtask order [74]. This coordination mode,
thus, includes individual evaluation, but members cannot veto other proposals
or control the order of choice. The team member associated with the first
subtask makes a proposal and reports it to the following members, who update
their residual decisions accordingly. This process is repeated for each member
until they all have made their proposals. Thus, the team member associated
with the first subtask chooses according to previous period residual
decisions, while the remaining team members choose according to their updated
residual decisions. The overall solution is then the concatenation of all
these sequential proposals.

Organizations that rely on decentralized decision-making and self-organization
often encounter challenges when establishing communication channels among
their members [49]. Consequently, liaison devices are particularly relevant in
modern organizations such as holacracies [59] and adhocracies [64]. A liaison
device involves establishing a mediator which handles communication among team
members, who in turn retain their decision-making power [21]. Liaison devices
rely on direct meetings between team members to discuss their current
information and future intentions [49]. We follow [64] and model these
insights in the liaison coordination mode, which retains decentralized
decision-making while introducing direct communication between the team
members. The liaison coordination mode includes individual evaluation, veto
power, and control of the order in which proposals are considered, and works
as follows [64]. Each member ranks each solution known in terms of their
estimated utility. Then they present their two highest-ranked proposals in a
coordination session.666As [64] show, the number of proposals selected by
decision-makers does not improve performance significantly for a liaison
coordination mode. Two candidate solutions are formed, one by concatenating
the team members’ preferred proposals and other by concatenating their second-
preferred proposals.777[64] show that increasing the number of candidate
solutions that decision-makers evaluate improves performance significantly for
a liaison coordination mode. We keep the candidate solutions restricted to two
to retain the same processing power for the liaison and lateral communication
coordination modes, see footnote 8 later on. Each team member evaluates the
two candidate solutions according to their estimated utility. Team members
accept the candidate solution if its estimated utility is higher than the last
achieved utility. Otherwise, they veto the candidate solution. If both
candidate solutions are vetoed, the overall solution from the previous period
remains unchanged. Conversely, if all team members accept one candidate
solution, it becomes the overall solution for the upcoming period.

Since fast decision-making and innovation is often demanded in organizations,
teams may reject the establishment of liaison devices while retaining broad
communication among their members [52]. Thus, team members may coordinate
their actions by mutual adjustment, i.e., by communicating directly and
without moderation [49]. Mutual adjustment implies that team members retain
their decision-making capacity, but they must exchange information before
taking any action [49]. According to [21] this results in team members jointly
agreeing on decisions. These insights are transferred onto the lateral
communication coordination mode [64]. This coordination mode retains the team
members’ veto power, but they cannot evaluate their solutions privately or
consider the proposals in their preferred order [64]. The lateral
communication mode works as follows: Each member randomly chooses two
solutions to their assigned subtask from the set of known
solutions.888According to [64], the number of proposals selected by team
members does not impact performance significantly for a lateral communication
mode. The team members take their two proposals to a coordination session. In
this session, two candidate solutions are formed by randomly concatenating the
team members’ proposals.999In contrast to the liaison mode, the number of
candidate solutions evaluated by team members does not impact performance
significantly for a lateral communication mode [64]. We keep the number of
candidate solutions evaluated to two to retain the same processing power for
the lateral communication and liaison coordination modes, see footnote 6
earlier on. Similarly to the liaison mode, team members then veto or accept
the candidate solutions depending on their estimated utility. The team
implements a candidate solution if all members accept it. Conversely, if the
members veto both candidate solutions, the overall solution remains unchanged
from the previous period.

###  3.4 Individual learning

Recall that, due to their limited capabilities, agents do not know the
complete set of solutions to their assigned subtask from the beginning (see
Sec. 3.1). Instead, agents gradually learn about the complex task and adapt
their knowledge—i.e., their set of available solutions—over time
[20].101010Learning occurs for all agents, team members or others. According
to [48], learning is a process limited by the amount of knowledge that
individuals can retain. Thus, as agents discover new things, they tend to
forget prior knowledge which was not considered relevant in that particular
time frame [48]. As [61] argue, forgetting is a process in which the agents’
knowledge gradually deteriorates. Hence, prior research suggests that learning
should be considered the combination of multiple interrelated processes,
including discovering, forgetting, and recalling, rather than just discovering
[48]. Our characterization of individual learning follows the insights given
by [61] and [48] and consists of two processes: discovering and forgetting [6,
7].111111Agents may forget and rediscover the same solution multiple times
during a simulation.

Each agent may discover a solution to their assigned subtask at the end of
every period with probability $\mathbb{P}$. This solution is chosen randomly
from all unknown solutions. Each solution has a certain likelihood of being
discovered that is influenced by the agent’s beliefs about it (see Appendix
A.5 for additional technical details). These beliefs are periodically updated
according to their experience and following a Bayesian updating rule [32, 71].

The updating process works as follows. Each time a team member implements a
solution to their assigned subtask, they experience a particular utility.
Then, the team member compares this utility with the utility experienced in
the previous period. If this solution represents an improvement in their
utility compared to the previous period, its likelihood of being discovered
will increase. Conversely, this likelihood will decrease if it reduces the
team member’s utility compared to the previous period. We formalize this
process in Eqs. 5a and 5b in Appendix A.5.121212Non-member agents cannot
update their solutions regarding the discovery process, as they cannot
implement them.

Thus, a belief is only updated when an agent knows and implements a solution
to their assigned subtask. Beliefs, however, specifically affect the
likelihood with which solutions are discovered and are only relevant to
unknown solutions.

Agents may forget one known solution at the end of each period with the same
value of probability $\mathbb{P}$. The forgotten solution is randomly selected
from the set of known solutions. Again, agents form beliefs regarding these
solutions that determine their likelihood of forgetting. This likelihood may
change as time passes and agents update their beliefs. Each time a team member
implements a solution to their assigned subtask, they update their associated
belief by comparing the utility experienced in the current and the previous
period. The likelihood of forgetting this solution will increase if it reduces
their utility compared to the previous period. Conversely, if this solution
improves the team member’s utility, the likelihood of forgetting it decreases.

Additionally, forgetting is related to the passing of time [8]. We introduce a
memory factor in the agents’ updating process, which reflects that agents tend
to forget solutions because they have stored them in their memory for too long
[61]. In our model, all agents—team members or not—update the beliefs of the
solutions they know at the end of every period, increasing the likelihood of
forgetting each solution as time passes. We provide the general updating rule
for all beliefs regarding forgetting in Eqs. 7a and 7b in Appendix A.5.

In conclusion, by implementing solutions and updating their beliefs, agents
ensure that they retain those solutions perceived as beneficial and discard
those perceived as harmful or irrelevant.

###  3.5 Parameters and scenarios

As outlined in Sec. 3.1, we study a task formed by $N=12$ binary decisions
divided into $M=3$ subtasks of length $S=N/M=4$. The group is formed by three
team members out of a population of $P=30$ agents. Regarding task complexity,
we consider two levels: Low ($K=3$) and moderate complexity ($K=5$).
Additionally, we take into account six different interdependence structures.
These structures reflect which contributions depend on which decisions and,
thus, the degree of task decomposability [58] (see Appendix A.1 for additional
details). According to prior research, the interdependence structure also
determines the performance landscape’s shape and, consequently, the team’s
performance [58]. We represent the six interdependence structures studied in
Fig. 2:

  * •

Block diagonal: We allocate the interdependencies in squares of size $K+1$.
For low complexity, this structure reflects a perfectly decomposable task in
which there are no cross-interdependencies between subtasks.

  * •

Centralized: Interdependencies are located within the first $K+1$ decisions.
In low-complexity tasks, only the first team member influences the other
members’ contributions. In tasks of medium complexity, the power to influence
others is shared between the first and the second member.

  * •

Dependent: This structure reverses the idea of the centralized structure:
instead of making one team member very influential, we make one member highly
dependent on the other members’ decisions.

  * •

Hierarchical: Each decision influences the $N-n$ following contributions but
not the preceding $n-1$.

  * •

Local: Each decision affects the following $K$ contributions. If there are no
following contributions, interdependencies fall back to the beginning of the
task (see Fig. 2, Local).

  * •

Random: We randomly allocate the interdependencies throughout the task.
Consequently, each member partly affects the other members’ contributions.

Figure 2: Interdependence matrices. Interdependencies between each
contribution and each decision are highlighted in grey with an X.

Regarding dynamic team composition, we define $\tau$ in Sec. 3.2 as the number
of periods between each instance of team formation. There are three scenarios
depending on $\tau$:

  * •

A team with a long-term composition maintains the same composition during the
observation period. We represent this scenario by $\tau=\infty$.

  * •

A team with a medium-term composition changes its composition every $\tau=10$
periods.

  * •

A team with a short-term composition changes its composition in every period,
so $\tau=1$.

Concerning individual learning, we set equal probabilities for discovering and
forgetting. This reflects the agents’ limited capabilities and ensures that
they discover and forget solutions at the same rate. This reduces the
likelihood that each agent simultaneously knows all available solutions to
their assigned subtask.131313This is based on the difficulty assumption. More
details are provided in [39]. In our analysis, we study probabilities between
$\mathbb{P}=0$ and $\mathbb{P}=1$ in intervals of $0.1$.

We summarize the main parameters of the model and their values in Tab. 1. For
our analysis, we simulate 1,584 scenarios, each consisting of 1,500 simulation
rounds of 100 periods.141414We fix the number of simulations following an
analysis of the variance of the results; see [44].. The dependent variable in
our analysis is the observed task performance at each period. To assure
comparability between scenarios, we normalize this observed task performance
by the maximum achievable performance in each simulation round. We then
calculate the mean normalized performance at each period for the 1,500
simulation rounds. This measure is formalized in Eq. 8 in Appendix A.6.

Table 1: Parameters Type | Variables | Notation | Values
---|---|---|---
Independent variables | Task complexity | $K$ | {3, 5}
Interdependence structure | Matrix | See Fig. 2
Team composition | $\tau$ | {$\infty,1,10$}
Learning probability | $\mathbb{P}$ | $\\{0:0.1:1\\}$
Time period | $t$ | $\\{1:1:100\\}$
Coordination mode | - | See Sec. 3.3
Dependent variable | Task performance | $C(\mathbf{d_{t}})$ | $[0,1]$
Other parameters | Number of decisions | $N$ | 12
Population of agents | $P$ | 30
Number of subtasks | $M$ | 3
Simulation round | $\phi$ | $\\{1:1:1,500\\}$
Error term | $e$ | $e\sim N(0,0.1)$

##  4 Results

This paper aims at examining the interrelations between selected coordination
modes and dynamic team composition. Additionally, we investigate whether there
are moderating effects of task complexity and individual learning. We present
the results in the following three subsections. In Sec. 4.1 we outline the
general effects of dynamic team composition on task performance and its
interrelations with the coordination mode implemented. In Sec. 4.2 we
differentiate our results by task complexity and the interdependence structure
and, finally, by individual learning in Sec. 4.3.

###  4.1 General effects of dynamic team composition

In this subsection, we report two performance measures: The mean performance
of the $100$ periods of each simulation—see Eq. 9 and Appendix A.6—and the
final performance, denoting the performance achieved on average at $t=100$.
Table 2 reports the mean and final performances for each team composition and
coordination mode studied. We also report the confidence limits below each
performance at a 0.01% confidence level and highlight in bold the highest
performance achieved for each team composition considered.

Table 2: General effects of dynamic team composition

| Mean performance | Final performance
---|---|---
| Long | Medium | Short | Long | Medium | Short
Fully autonomous | 0.8296 | 0.8531 | 0.8792 | 0.8435 | 0.8680 | 0.8921
($\pm$0.0029) | ($\pm$0.0030) | ($\pm$0.0026) | ($\pm$0.0029) | ($\pm$0.0030) | ($\pm$0.0026)
Sequential | 0.8390 | 0.8668 | 0.8982 | 0.8510 | 0.8794 | 0.9095
($\pm$0.0022) | ($\pm$0.0026) | ($\pm$0.0022) | ($\pm$0.0022) | ($\pm$0.0026) | ($\pm$0.0022)
Liaison | 0.7601 | 0.7835 | 0.8120 | 0.7689 | 0.7987 | 0.8283
($\pm$0.0024) | ($\pm$0.0028) | ($\pm$0.0032) | ($\pm$0.0024) | ($\pm$0.0028) | ($\pm$0.0032)
Lateral | 0.8504 | 0.8774 | 0.9075 | 0.8816 | 0.9189 | 0.9410
($\pm$0.0019) | ($\pm$0.0020) | ($\pm$0.0018) | ($\pm$0.0019) | ($\pm$0.0020) | ($\pm$0.0018)

The results of Tab. 2 suggest that more frequent team formation is generally
associated with higher mean and final performances. Depending on the scenario
studied, each decrease in $\tau$ generally increases mean performance by
approximately $2$ to $3$ percentage points and final performance by
approximately $3$ to $4$ percentage points. These differences, although small,
are statistically significant at a 0.01% confidence level. Hence, our results
are closer to the modern view of dynamic team composition [3, 69] than to the
traditional perspective on the matter [13, 14, 17, 42]. Specifically, these
results suggest that dynamic team composition is not a negative consequence of
suboptimal design choices, as we find no negative effects of increasing the
frequency of team formation. Instead, our findings support the
characterization of dynamic team composition as a design element consciously
implemented by organizations [69]. Team composition becomes more efficient
when it is periodically reorganized, as [2] and [47] argue. The mechanism
behind this improved efficiency lies in the increased exploration of the
solution space attributed to dynamic team composition [46, 66]. As prior
research argues, this enhaced exploration increases the number of solutions
available to the team, thus resulting in the team being more innovative [15,
16, 27, 63, 67]. Our results show that this increased innovation improves both
mean and long-term performance. From a practical standpoint, these findings
suggest that organizations should consider incorporating dynamic team
composition in their design. As a design element that promotes exploration,
this guidance may be particularly relevant for organizations seeking to
generate new value, establish a competitive advantage in a particular area, or
modernize their structure [60].

Regardless of the frequency of team formation, our results suggest that the
highest mean and final performances are associated with the lateral
communication mode, followed by the sequential coordination mode, the fully
autonomous team, and, finally, the liaison coordination mode (see Tab. 2).
Differences in performance between the lateral communication, sequential and
fully autonomous modes are quite small, ranging approximately from 1 to 2
percentage points for mean performance and from 3 to 5 percentage points for
final performance. All these differences are significant at a 0.01% confidence
level. Conversely, there are significantly larger performance gaps between the
lateral communication and liaison coordination modes. Specifically, this gap
is of approximately 9 percentage points for mean performance and 12 percentage
points for final performance.

These findings follow prior insights into coordination and task performance
[10, 57, 64]. In particular, previous results suggest that a proper
coordination mode should achieve a balance between autonomy with stability in
decision-making [10, 57]. Autonomous decision-making allows team members to
intensively explore their available solution space [64], and reflects the
demand for rapid change and decision-making often encountered in organizations
[52]. In contrast, stability redirects the team members’ focus toward
exploiting their available solutions [64], which allows them to fully take
advantage of their knowledge [60]. Excessive autonomy, however, might result
in overexploration [60], reducing task performance in the long run [64]. This
is exemplified in our results by the fully autonomous team. Conversely,
excessive stability might slow down decision-making [52], which also decreases
task performance [64]. Our results show that this occurs in the case of the
liaison coordination mode. Conversely, the lateral communication and
sequential coordination modes balance autonomy and stability in decision-
making. The lateral communication mode, for instance, puts more weight on
stability but retains a certain degree of autonomous decision-making in the
form of the veto power (see Sec. 3.3). The sequential coordination mode, in
contrast, focuses more on autonomy but retains some stability in the form of
successive decision-making. This balance explains why for these two
coordination modes, performance is generally higher than in the fully
autonomous team. Consequently, our results suggest that organizations should
consider how their coordination choices balance autonomy and stability in
decision-making before taking any action.

Additionally, our results suggest that coordination somewhat helps teams
exploit the potential positive effects of dynamic composition on task
performance. We can observe this by comparing the mean and final performances
between a long- and a short-term team composition in Tab. 2. Differences in
mean and final performances between a short- and a long-term team composition
are slightly higher for a sequential and a lateral communication mode,
approximately amounting to 6 percentage points, than for the fully autonomous
team, with around 5 percentage points. This implies that the positive effects
of the lateral communication and sequential coordination modes on task
performance increase modestly with the frequency of team formation. Rather
than dynamic team composition reducing coordination, as prior research often
suggests [18, 19, 22, 26, 51, 56], our results indicate a positive—though
modest—correlation between these two design elements. Thus, our results are
partly in line with those provided by [67], suggesting an alternative
interpretation of the relationship between dynamic team composition and
coordination that departs from the traditional perspective on the matter. From
a practical standpoint, our results indicate that organizations should ensure
that team members effectively coordinate their actions when changes in team
composition are frequent, even if the gains in performance are modest.

###  4.2 Moderating effects of task complexity

Table 3: Differentiated effects - Low complexity

|  | Block | Centralized | Dependent | Hierarchical | Local | Random
---|---|---|---|---|---|---|---
Long-term | Fully autonomous | 0.9344 | 0.8813 | 0.8573 | 0.8591 | 0.8431 | 0.7970
($\pm$0.0029) | ($\pm$0.0036) | ($\pm$0.0019) | ($\pm$0.0031) | ($\pm$0.0026) | ($\pm$0.0029)
Sequential | 0.9343 | 0.9156 | 0.8548 | 0.8650 | 0.8483 | 0.8089
($\pm$0.0029) | ($\pm$0.0035) | ($\pm$0.0018) | ($\pm$0.0029) | ($\pm$0.0027) | ($\pm$0.0027)
Liaison | 0.8427 | 0.7736 | 0.8134 | 0.7698 | 0.7765 | 0.7474
($\pm$0.0028) | ($\pm$0.0017) | ($\pm$0.0020) | ($\pm$0.0016) | ($\pm$0.0016) | ($\pm$0.0019)
Lateral | 0.9156 | 0.8706 | 0.8877 | 0.8656 | 0.8522 | 0.8322
($\pm$0.0025) | ($\pm$0.0038) | ($\pm$0.0028) | ($\pm$0.0038) | ($\pm$0.0027) | ($\pm$0.0045)
Medium-term | Fully autonomous | 0.9572 | 0.9104 | 0.8876 | 0.8858 | 0.8720 | 0.8187
($\pm$0.0034) | ($\pm$0.0035) | ($\pm$0.0024) | ($\pm$0.0030) | ($\pm$0.0030) | ($\pm$0.0027)
Sequential | 0.9571 | 0.9156 | 0.8863 | 0.8928 | 0.8806 | 0.8361
($\pm$0.0034) | ($\pm$0.0034) | ($\pm$0.0025) | ($\pm$0.0029) | ($\pm$0.0031) | ($\pm$0.0028)
Liaison | 0.8822 | 0.8110 | 0.8448 | 0.7988 | 0.8059 | 0.7664
($\pm$0.0030) | ($\pm$0.0029) | ($\pm$0.0027) | ($\pm$0.0026) | ($\pm$0.0026) | ($\pm$0.0023)
Lateral | 0.9435 | 0.9039 | 0.9166 | 0.8960 | 0.8843 | 0.8576
($\pm$0.0033) | ($\pm$0.0042) | ($\pm$0.0035) | ($\pm$0.0042) | ($\pm$0.0042) | ($\pm$0.0046)
Short-term | Fully autonomous | 0.9694 | 0.9327 | 0.9057 | 0.9087 | 0.9010 | 0.8502
($\pm$0.0033) | ($\pm$0.0031) | ($\pm$0.0025) | ($\pm$0.0027) | ($\pm$0.0029) | ($\pm$0.0026)
Sequential | 0.9695 | 0.9375 | 0.9059 | 0.9155 | 0.9123 | 0.8732
($\pm$0.0033) | ($\pm$0.0030) | ($\pm$0.0025) | ($\pm$0.0027) | ($\pm$0.0030) | ($\pm$0.0027)
Liaison | 0.9266 | 0.8570 | 0.8810 | 0.8396 | 0.8413 | 0.7893
($\pm$0.0032) | ($\pm$0.0028) | ($\pm$0.0029) | ($\pm$0.0025) | ($\pm$0.0028) | ($\pm$0.0023)
Lateral | 0.9631 | 0.9334 | 0.9419 | 0.9266 | 0.9189 | 0.8910
($\pm$0.0035) | ($\pm$0.0040) | ($\pm$0.0037) | ($\pm$0.0040) | ($\pm$0.0043) | ($\pm$0.0045)

Table 4: Differentiated effects - Medium complexity

|  | Block | Centralized | Dependent | Hierarchical | Local | Random
---|---|---|---|---|---|---|---
Long-term | Fully autonomous | 0.8150 | 0.8191 | 0.7817 | 0.8254 | 0.7783 | 0.7638
($\pm$0.0037) | ($\pm$0.0040) | ($\pm$0.0027) | ($\pm$0.0036) | ($\pm$0.0032) | ($\pm$0.0031)
Sequential | 0.8283 | 0.8332 | 0.7931 | 0.8369 | 0.7965 | 0.7835
($\pm$0.0033) | ($\pm$0.0035) | ($\pm$0.0024) | ($\pm$0.0033) | ($\pm$0.0028) | ($\pm$0.0029)
Liaison | 0.7490 | 0.7233 | 0.7422 | 0.7266 | 0.7319 | 0.7249
($\pm$0.0022) | ($\pm$0.0015) | ($\pm$0.0022) | ($\pm$0.0014) | ($\pm$0.0022) | ($\pm$0.0021)
Lateral | 0.8348 | 0.8391 | 0.8326 | 0.8398 | 0.8182 | 0.8163
($\pm$0.0049) | ($\pm$0.0050) | ($\pm$0.0050) | ($\pm$0.0046) | ($\pm$0.0049) | ($\pm$0.0051)
Medium-term | Fully autonomous | 0.8384 | 0.8460 | 0.8030 | 0.8504 | 0.7950 | 0.7723
($\pm$0.0034) | ($\pm$0.0038) | ($\pm$0.0025) | ($\pm$0.0033) | ($\pm$0.0027) | ($\pm$0.0025)
Sequential | 0.8576 | 0.8634 | 0.8205 | 0.8661 | 0.8225 | 0.8026
($\pm$0.0033) | ($\pm$0.0027) | ($\pm$0.0026) | ($\pm$0.0033) | ($\pm$0.0029) | ($\pm$0.0027)
Liaison | 0.7660 | 0.7392 | 0.7560 | 0.7496 | 0.7471 | 0.7344
($\pm$0.0023) | ($\pm$0.0019) | ($\pm$0.0022) | ($\pm$0.0022) | ($\pm$0.0022) | ($\pm$0.0020)
Lateral | 0.8618 | 0.8657 | 0.8558 | 0.8668 | 0.8419 | 0.8348
($\pm$0.0049) | ($\pm$0.0050) | ($\pm$0.0048) | ($\pm$0.0046) | ($\pm$0.0048) | ($\pm$0.0048)
Short-term | Fully autonomous | 0.8698 | 0.8800 | 0.8326 | 0.8800 | 0.8307 | 0.7895
($\pm$0.0032) | ($\pm$0.0014) | ($\pm$0.0024) | ($\pm$0.0031) | ($\pm$0.0028) | ($\pm$0.0025)
Sequential | 0.8937 | 0.9012 | 0.8585 | 0.8979 | 0.8676 | 0.8457
($\pm$0.0031) | ($\pm$0.0032) | ($\pm$0.0025) | ($\pm$0.0030) | ($\pm$0.0029) | ($\pm$0.0027)
Liaison | 0.7846 | 0.7617 | 0.7720 | 0.7794 | 0.7648 | 0.7462
($\pm$0.0023) | ($\pm$0.0022) | ($\pm$0.0022) | ($\pm$0.0023) | ($\pm$0.0023) | ($\pm$0.0018)
Lateral | 0.8941 | 0.8953 | 0.8870 | 0.9010 | 0.8746 | 0.8631
($\pm$0.0047) | ($\pm$0.0047) | ($\pm$0.0047) | ($\pm$0.0045) | ($\pm$0.0048) | ($\pm$0.0047)

In general, our results suggest that both task complexity and the
interdependence structure influence the choice of a proper coordination mode,
similarly to the results reported in [64]. When subtasks are not
interdependent (for low complexity and a block diagonal structure, see Fig. 2,
Block diagonal (A)), neither of the three coordination modes improves task
performance significantly (see the first column of Tab. 3). We report similar
results for tasks of low complexity, centralized structure, and teams with a
medium- and short-term composition (see the second column of Tab. 3); and for
low complexity, hierarchical structure in teams with a long-term composition
(see the fourth column of Tab. 3). When interdependencies are concentrated in
one subtask (see Fig. 2, Centralized (A) and Hierarchical (A)), the demand for
coordination with the remaining team members decreases, as they have no
control of the interdependencies.

As interdependencies spread throughout the task, the demand for coordination
increases, as reported in prior research [64]. Specifically, employing either
lateral communication or sequential decision-making becomes more advantageous
in terms of task performance. In columns three to six of Tab. 3 we observe
that coordination by sequential decision-making or lateral communication
slightly improves task performance in 11 out of the 12 structures. Differences
range between approximately 0.5 percentage points for the local
interdependence structure and 5 percentage points for the random structure,
and increase modestly with the frequency of changing composition. These
differences are significant at a 0.01% confidence level. Among these 11
scenarios, the lateral communication mode is the sole best performer in seven
of them. This result is reinforced if we look at tasks of medium complexity,
in which there are always interdependencies between subtasks (see Fig. 2).
Regarding the 18 scenarios of Tab. 4, the lateral communication mode shares
the highest performer status with the sequential mode in 10 out of them and is
the sole highest performer in the remaining eight. Overall, performance
increases approximately from 1 percentage point for the hierarchical
interdependence structure to 7.5 percentage points for the random
interdependence structure. Furthermore, these improvements in task performance
are slightly higher for more frequent changes in team composition, and
significant at a 0.01% confidence level. Overall, our findings suggest that
lateral communication is the best option for improving task performance when
there are interdependencies between subtasks, although in some specific cases
sequential decision-making is also an efficient choice.

Prior findings suggest that the interdependence structure has important
implications for task performance, as it shapes the performance landscape
[58]. We build on these insights by showing that the interdependence structure
also affects the choice of the coordination mode. To explain this result, we
shall go back to the balance between stability and autonomy in decision-making
[57]. As outlined in Sec. 2, as interdependencies spread throughout the task,
uncertainty in decision-making increases, which in turn harms task performance
[38, 41, 72, 74]. Decision-makers need to counteract this uncertainty by
making design choices that ensure stability, i.e., by focusing on coordination
choices [21, 64]. Among these, lateral communication is usually the most
efficient, although sequential decision-making may also be an optimal choice
in certain cases. From a practical perspective, our results imply that
organizations should carefully review the nature of the tasks they face and
evaluate how different coordination modes may fit their demands.

These differentiated results also reinforce the insights discussed in Sec. 4.1
regarding the interrelations between coordination and dynamic team
composition. Specifically, while both task complexity and the interdependence
structure moderate the demand for coordination, they do not affect the
fundamental relationship between coordination and dynamic team composition.
Again, to illustrate this we examine the performances for the fully autonomous
team and compare it to the three coordination modes, both for a long- and a
short-term composition. Results show that for all kinds of tasks considered
teams that follow a specific coordination mode gain slightly more from
changing their composition periodically than fully autonomous teams. Thus, the
results of Sec. 4.1 regarding the interrelations between coordination and
dynamic team composition are robust to variations in task complexity and the
interdependence structure.

###  4.3 Moderating effects of individual learning

Figure 3: Mean performance for each probability of learning and team
composition.

In Fig. 3, we plot the mean performances achieved by each team depending on
the coordination mode and the learning probability, i.e., $\mathbb{P}$.
Additionally, we differentiate the results by team composition. In general,
increasing the learning probability has more significant effects the less
frequently teams change their composition. For example, task performance in a
fully autonomous team with a long-term composition increases from 0.7617 at
$\mathbb{P}=0$ to 0.8381 at $\mathbb{P}=1$ (see Fig. 3(A)). When the fully
autonomous team has a short-term composition, however, performance increases
from 0.8680 only to 0.8827 (see Fig. 3(C)). This pattern is robust to all
coordination modes and consistent with prior results [6, 7].

For the lateral communication mode, the sequential coordination mode, and the
fully autonomous team, Fig. 3 shows how performance increases significantly
when agents start to learn, i.e., when $\mathbb{P}$ increases from 0 to $0.1$.
For instance, in the lateral communication mode, performance increases by
approximately 6.5, 4, and 3 percentage points for a long-, medium-, and short-
term composition, respectively. These differences in performance are
statistically significant at a 0.01% confidence level. An increase in the
learning probability beyond $0.1$ improves task performance with decreasing
marginal effects. Once the learning probability reaches a certain threshold,
performance slightly falls if team composition is dynamic for the sequential
coordination mode and the fully autonomous team (see Fig. 3(B) and (C)). The
cumulative negative effects are around 1 percentage point and lack statistical
significance at a 0.01% confidence level. Although these negative effects are
not significant, it is worth noting that they do not appear in the lateral
communication mode. Instead, we can observe a slightly steady increase in
performance—approximately 1 percentage point in total—as the learning
probability increases above $\mathbb{P}=0.1$.

Conversely, we can observe a different relationship between individual
learning and task performance in the liaison coordination mode. For a long-
term team composition, there is an increase in task performance when agents
start learning (see Fig. 3(A)). As the learning probability increases further,
however, performance declines steadily. In total, performance declines around
3 percentage points between $\mathbb{P}=0.1$ and $\mathbb{P}=1$, which is
statistically significant at a 0.01% level. This steady decline in task
performance is also observable for a medium-term composition (see Fig. 3(B)),
also adding up to approximately 3 percentage points. For a short-term team
composition (see Fig. 3(C)), we observe a slight decrease in performance when
agents start to learn. The performance then stabilizes as the learning
probability increases. Finally, performance declines once the probability
reaches $\mathbb{P}=1$. Overall, performance declines by approximately 1.25
percentage points, which is statistically significant at a 0.01% level.

Our findings show that coordination choices influence the interrelations
between individual learning and dynamic team composition, and their effects on
task performance. The impact of learning is lower in dynamic teams because, as
[66] notes, dynamic team composition and individual learning are exploratory
processes with similar effects. Specifically, they are both mechanisms that
increase the number of solutions available to the team. Thus, if one is
already present, the marginal effect on performance of the other is reduced
[6, 7]. Furthermore, excessive individual learning may result in decreases in
task performance. As [60] note, overexploration may result in long-term
problems for organizations. For instance, financial resources may be reduced
if innovation is not associated with significant improvements in performance
[60]. From a practical perspective, this means that organizations should
consider the balance among the different exploration processes that take
place—i.e., individual learning and dynamic team composition—as our results
show that this is a highly relevant issue. Organizations in which dynamic team
composition is prevalent may not gain from investing in individual learning,
and vice versa.

To prevent this overexploration, prior research suggests various methods to
shift resources towards the exploitation of current knowledge [25, 60]. Among
all methods, prior research emphasizes the establishment of coordination among
decision-makers as one of the most relevant methods [25, 60]. Our results are
consistent with these insights, as they show that teams (i) employing either
lateral communication or sequential decision-making and (ii) maintaining a
long-term team composition experience greater advantages from individual
learning. Coordination, thus, may enable teams to exploit the beneficial
effects of individual learning on task performance. This exploitation is
particularly relevant for stable teams, although dynamic teams may also
benefit from implementing coordination (see Fig. 3(C)). Not all coordination
choices, however, have the same effects. Suboptimal coordination choices can
decrease task performance, as results for the liaison coordination mode
suggest. Conversely, lateral communication eliminates the decline in task
performance associated with excessive learning, even when teams change their
composition very frequently (see Fig. 3(A)-(C)).

##  5 Conclusion

In this paper, we employ an agent-based modeling approach to study the
interrelations of dynamic team composition, coordination, and task
performance. Furthermore, we investigate the moderating role of task
complexity and individual learning. Our results depart from the traditional
perspective on dynamic team composition, which interprets it as a result of
suboptimal design choices that reduce coordination and decrease task
performance. Instead, we show that dynamic team composition may be
characterized as a design element that improves the innovative capacity of
teams. According to our results, this improves task performance.

Characterizing dynamic team composition as a design element enables us to
study how it interacts with another design element, namely the coordination
mode. Departing from the traditional perspective on dynamic team composition
allows us to find new insights regarding these elements and their interplay.
According to our results, coordination helps teams to exploit the positive
effects of dynamic team composition on task performance. This is particularly
relevant for complex tasks, as coordination reduces the uncertainty in
decision-making associated with complexity. Specifically, we find that both
lateral communication and sequential decision-making improve task performance,
while liaison devices reduce it.

Based on our results, we can argue that organizations increasingly rely on
dynamic team composition because it allows teams to adapt to the task
environment over time, improving task performance in the process. Thus, we can
study how dynamic team composition interrelates with other adaptation
processes, such as individual learning. Our results suggest that combining
dynamic team composition with individual learning may lead to overexploration,
and performance may not increase significantly. To reduce these effects,
organizations may resort to coordination choices. For instance, our results
indicate that lateral communication may successfully prevent the negative
effects of excessive exploration.

Nevertheless, our research is not without limitations. First, we work under
the implicit assumption of zero coordination costs [64, 74]. Future research
could consider them. Second, we do not study the potential effects of changing
the agents’ incentives and the interrelations between these incentives and the
coordination mode [64]. Finally, we employ a classic approach to
organizational design, taking the design choices as given and studying their
effects over time. Further extensions of our research could employ an
evolutionary perspective to organizational design in which design choices
emerge over time [33, 74].

## Declarations

### Funding

Does not apply.

### Conflict of interest/competing interests

The authors declare that they have no conflict of interest.

### Availability of data

Simulation data is available https://figshare.com/articles/dataset/Datasets_-
_RMSC/24598278

### Code availability

The code is available
https://figshare.com/articles/software/Source_code/24598290

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##  Appendix A Technical aspects of the model

###  A.1 Task environment and performance landscape

We model a complex task as an $N$-dimensional binary vector such that
$\mathbf{d}=\left(d_{1},\dots,d_{N}\right)$. Each decision $d_{n}$ contributes
$c_{n}$ to the overall task performance $C(\mathbf{d})$. Task performance is
the average of all contributions, such that:

$C(\mathbf{d})=\frac{1}{N}\sum_{n=1}^{N}c_{n}.$ (1)

There are $2^{N}$ different solutions to the complex task, each with an
associated performance. The mapping of each of the $2^{N}$ solutions to its
associated performance is the performance landscape. The performance landscape
can be conceptualized as a multidimensional space in which the $N$ decisions
are represented in the horizontal axis and their associated performances in
the vertical axis [58]. The concept of performance landscape is analogous to
that of the fitness landscape of evolutionary biology [30]. In its original
formulation, [30] sought to explain the population dynamics of a certain
organism and the fitness of its characteristics to a particular environment.
In this formulation, an organism is formed by $N$ interdependent genes that
evolve over time. Periodically, the organisms below a certain fitness
threshold are assumed to have not survived the environmental conditions. As an
agent-based modeling approach, the original formulation of the NK framework
examines how the different behavior of multiple individuals—in this case,
assumed to be organisms formed by a set of genes—lead to emergent properties
at the collective level—in this case, the population dynamics of the organism
in a particular environment [30]. [38] adapted the idea of the NK framework
and the fitness landscapes to explain the population dynamics of organizations
and their evolution based on each organization’s initial conditions, whereby
$N$ represents the different design elements of an organization rather than
genes. Thus, the overall fitness achieved by an organization determines its
likelihood of survival. Similarly to its biological counterpart, [38] examines
how the different design choices of each individual organization eventually
lead up to alterations in their population.

Further adaptations of the NK framework have abandoned this emphasis on
population dynamics and focus on aspects such as departmental decision-making
[64, 74], incentive systems [32], and decision-making in teams [4, 6, 7, 23].
Rather than modeling and observing the behavior of large organizations that
operate in an environment, the scope is reduced to examine human decision-
makers—the agents of the model—that operate in a team or in an organization
and face a complex task. In these adaptations, the term fitness landscape is
often replaced by the term performance landscape to emphasize that their
primary focus is not on population dynamics. We follow these further
adaptations, characterizing $N$ as the interdependent decisions of a task that
have an associated task performance.

The core concept underlying the NK framework is the investigation of adaptive
search processeses [72]. This implies that studies employing the NK framework
normally model a set of agents who engage in a neighborhood search process on
the performance landscape, looking for new solutions to the complex task that
improve task performance [38, 58]. The neighborhood search process works as
follows [38]. Agents randomly change the value of one of the $N$ decisions and
observe its associated performance. This new decision is adopted if it
improves task performance compared to the previous period. Conversely, this
decision is rejected if performance declines. As this development continues,
the agents follow a hill-climbing process on the performance landscape. This
process stops when none of the immediate alternatives improve task
performance, i.e., when agents reach a peak. Depending on the shape of the
performance landscape, this peak may be global—i.e., the optimal decision—or
local—i.e., a suboptimal decision.

The shape of the performance landscape is influenced by task complexity [38,
58]. Each contribution $c_{n}$ depends on its associated decision $d_{n}$ and,
due to the existence of interdependencies, on $K$ other decisions. This means
that $c_{n}=f(d_{n},d_{i_{1}},\dots,d_{i_{K}})$, where
$\\{i_{1},\dots,i_{K}\\}\subseteq\\{1,\dots,n-1,n+1,\dots,N\\}$ and $0\leq
K\leq N-1$. If there are no interdependencies, i.e., $K=0$, the performance
landscape is single-peaked. The landscape becomes more rugged as $K$ increases
and approaches $N-1$ [38, 58]. Rugged landscapes are characterized by several
local optima where agents might get stuck [38, 58]. This characterization of
complexity is a crucial feature of the NK framework. Specifically, the NK
framework allows for the the control and manipulation of task complexity [72].
This, in turn, allows the modeler to observe the changes in behavior of
individual agents that result from altering $K$—and, thus, the shape of the
performance landscape.

Furthermore, [58] argue that not only the number of interdependencies—i.e.,
$K$—influences the shape of the performance landscape, but also the
interdependence structure. The interdependence structure is reflected in the
interdependence matrix, which is a $N\times N$ matrix that represents
contributions in one axis and decisions on the other. Interdependencies are
usually marked with an x (see Fig. 2 in Sec. 3.5). The interdepedence
structure often varies depending on the task’s nature [58]. As prior results
show, the number of local peaks decreases when interdependencies concentrate
on few decisions, making the global peak more accessible for agents [6, 58].

###  A.2 Agents

Approaches based on the NK framework usually assume that agents have limited
capabilities and are thus rationally bounded [72, 75]. Specifically, it is
often assumed that the agents’ information processing-power and their access
to it are limited [65]. This assumption implies that, rather than looking
immediately for an optimal solution, agents search locally and step-wise on
the performance landscape [72, 75]. Furthermore, it is often assumed that
agents are heterogeneous in one or more aspects [72, 75]. To reflect the
limited capabilities of agents and their heterogeneity, we partition the
$N$-dimensional task into $M$ subtasks of equal size $S=N/M$ and randomly
assign each agent to one of them. Each subtask is denoted by
$\mathbf{d}_{m}=(d_{S\cdot(m-1)+1},\dots,d_{S\cdot m})$. Additionally, agents
do not start with full knowledge of the solution space. Instead, we endow each
agent with one random solution to their assigned subtask $\mathbf{d}_{m}$, and
they learn new solutions over time (see Sec. 3.4 and Appendix A.5).

The $P$ agents of the model are utility-maximizers and myopic, experiencing
utility only when they are part of the team. Specifically, a team member
assigned to subtask $m$ maximizes the following utility function:

$U(\mathbf{d}_{mt},\mathbf{D}_{mt})=\frac{1}{2}\cdot\left(C(\mathbf{d}_{mt})+\frac{1}{M-1}\sum_{\begin{subarray}{c}{r=1}\\\
{r\neq m}\end{subarray}}^{M}C(\mathbf{d}_{rt})\right)~{},$ (2)

where $C(\mathbf{d}_{mt})$ is the performance contribution coming from the
agent m’s own area of expertise. Additionally, $C(\mathbf{d}_{rt})$, where
$r=\\{1,\dots,M\\}\subset\mathbb{N}$ and $r\neq m$, is the contribution from
the residual decisions
$\mathbf{D}_{mt}=(\mathbf{d}_{1t},\dots,\mathbf{d}_{\\{m-1\\}t},\mathbf{d}_{\\{m+1\\}t},\dots,\mathbf{d}_{Mt})$,
i.e., the contribution of the decisions located outside subtask $m$.

###  A.3 Team formation

Agents self-organize in a team to solve the complex task. They follow a
signaling mechanism for team formation that works as follows. Agent $m$ knows
a set of solutions denoted by
${\mathbf{S}}_{m}=\\{\hat{\mathbf{d}}_{m1},\dots,\hat{\mathbf{d}}_{mI}\\}$
where $\hat{\mathbf{d}}_{mi}$ is a solution to subtask $\mathbf{d}_{m}$,
$i=\\{1,\dots,I\\}\subset\mathbb{N}$ and $1\leq I\leq 2^{S}$. Each agent
estimates the utility associated with each solution they know, i.e.,
$\forall\hat{\mathbf{d}}_{mi}\in{\mathbf{S}}_{m}$. Since agents cannot predict
the residual decisions for the next period, they assume that the residual
decisions from the previous period $\mathbf{D}_{m\\{t-1\\}}$ will not change.
Agent $m$’s estimated utility is then:

$EU(\mathbf{d}_{mt},\mathbf{D}_{m\\{t-1\\}})=\frac{1}{2}\cdot\left(C(\mathbf{d}_{mt})+\frac{1}{M-1}\sum_{\begin{subarray}{c}{r=1}\\\
{r\neq
m}\end{subarray}}^{M}C(\mathbf{d}_{r\\{t-1\\}})\right)\cdot\left(1+e\right)~{}\mathchar
24635\relax\;$ (3)

where $e$ is an error term that reflects the miscalculations that agents might
make. Prior research estimates that, on average, error rates range between 1
and 10 percent [70]. To reflect this, the error term follows a normal
distribution with a standard deviation of $0.1$, i.e., $e\sim N(0,0.1)$. This
formulation is consistent with the NK framework. Specifically, [38] assumes in
his adaptation of the NK framework that the agents of the model—i.e., the
organizations—are able to identify the fitness value of each solution. [38]
introduces and examines the concept of noisy search, which occurs when agents
can commit errors in the identification of the fitness values. We follow a
similar approach in our formulation by assuming that the agents are able to
estimate the utility each solution reports, although they may commit small
errors.

Each agent then sends a signal equivalent to the highest estimated utility
available, i.e., their signal is
$U(\hat{\mathbf{d}}^{*}_{mt},\mathbf{D}_{m\\{t-1\\}})$, where
$\hat{\mathbf{d}}^{*}_{mt}:=\operatorname*{arg\,max}_{\mathbf{d}^{\prime}\in\mathbf{S}_{mt}}~{}U(\mathbf{d}^{\prime},\mathbf{D}_{m\\{t-1\\}})$.
The agent with the highest signal for subtask $\mathbf{d}_{m}$ joins the team.
Consequently, the team is formed by $M$ agents.

###  A.4 Decision-making and coordination

We model three coordination modes and one benchmark scenario without
coordination. In this benchmark scenario we model a fully autonomous team in
which decision-making is completely decentralized and team members do not
communicate. Each team member estimates the utility for each solution they
know, i.e., $\forall\hat{\mathbf{d}}_{mi}\in\mathbf{S}_{mt}$, following Eq. 3.
Then, each member proposes the solution to their subtask associated to the
highest estimated utility, $\hat{\mathbf{d}}^{*}_{mt}$. The overall task
solution for the current period is the concatenation of all members’
proposals, denoted by
$\mathbf{d}_{t}:=\hat{\mathbf{d}}^{*}_{1t}\frown\dots\frown\hat{\mathbf{d}}^{*}_{Mt}$.

In the sequential coordination mode, the proposals are successively made. The
team member associated with subtask $m$ chooses a solution to their subtask
and reports it to the $M-m$ following members, who update their residual
decisions accordingly. They repeat this process until the $M$ members have
made their proposals. The team member associated with the first subtask makes
their proposal according to previous period residual decisions
$\mathbf{D}_{1\\{t-1\\}}$, while the other team members make their proposal
using their updated residual decisions as a basis for their estimations
$\mathbf{D}_{m}=(\mathbf{d}_{1t},\dots,\mathbf{d}_{\\{m-1\\}t},\mathbf{d}_{\\{m+1\\}\\{t-1\\}},\dots,\mathbf{d}_{M\\{t-1\\}})$,
where $m\neq 1$. The concatenation of all the sequentially-made proposals
forms the overall solution to the complex task, i.e.,
$\mathbf{d}_{t}:=\hat{\mathbf{d}}^{*}_{1t}\frown\dots\frown\hat{\mathbf{d}}^{*}_{Mt}$.

The liaison coordination mode works as follows: Each member ranks each
solution known in terms of their estimated utility. Then, they choose their
two highest-ranked proposals, $\hat{\mathbf{d}}^{(1)}_{mt}$ and
$\hat{\mathbf{d}}^{(2)}_{mt}$, taking them to a coordination meeting. During
this meeting, two candidate solutions are created: the first by concatenating
the team members’ top-choice proposals and the second by combining their
second-choice proposals, such that
$\mathbf{d}^{(j)}_{t}:=\hat{\mathbf{d}}^{(j)}_{1t}\frown\dots\frown\hat{\mathbf{d}}^{(j)}_{Mt}$
where $\hat{\mathbf{d}}^{(j)}_{mt}$ is agent $m$’s $j^{th}$ preferred choice.
These candidate solutions are evalutated by the team members according to
their estimated utility. Team members accept the candidate solution if they
estimate that their utility will increase, i.e., if
$EU_{m}(\mathbf{d}^{(j)}_{t})>U_{m}(\mathbf{d}_{t-1})$. Otherwise, they veto
the candidate solution. In case both candidate solutions are vetoed, the
overall solution does not change from the prior period, so
$\mathbf{d}_{t}=\mathbf{d}_{t-1}$. Conversely, if one candidate solution is
accepted, it is implemented in the upcoming period, such that
$\mathbf{d}_{t}=\mathbf{d}^{(j)}_{t}$.

Finally, in the lateral communication mode each member randomly picks two
solutions to their assigned subtask from the set of known solutions
${\mathbf{S}}_{mt}$ and brings them to a coordination session, i.e., picking
$\hat{\mathbf{d}}^{(1)}_{mt},\hat{\mathbf{d}}^{(2)}_{mt}\sim
U(\mathbf{S}_{mt})$. Then, two candidate solutions are formed by randomly
concatenating the team members’ picks, i.e.,
$\mathbf{d}^{(j)}_{t}:=\hat{\mathbf{d}}_{1t}\frown\dots\frown\hat{\mathbf{d}}_{Mt}$
where $\hat{\mathbf{d}}_{mt}\sim
U\left(\hat{\mathbf{d}}^{(1)}_{mt},\hat{\mathbf{d}}^{(2)}_{mt}\right)$. Then,
each team member accepts or vetoes the candidate solutions based on their
estimated utility, i.e., depending on whether
$EU_{m}(\mathbf{d}^{(j)}_{t})>U_{m}(\mathbf{d}_{t-1})$ or not. The candidate
solution is implemented if all members accept it. Conversely, if both
candidate solutions are vetoed, the overall solution remains the same as in
the previous period.

###  A.5 Learning

Following the principles of the NK framework, our agents cannot observe the
complete set of solutions to their assigned subtask $\mathbf{d}_{m}$ from the
beginning. Instead, they learn step-wise, adapting their set of known
solutions ${\mathbf{S}}_{mt}$ over time. Individual learning consists of two
processes: discovering and forgetting. Agent $m$ discovers a solution to their
subtask with probability $\mathbb{P}$. This solution is randomly picked from
all unknown solutions. The distribution of the probabilities with which the
solutions are discovered is based on agent $m$’s beliefs. Agent $m$ updates
these beliefs according to a Bayesian updating rule.We denote agent $m$’s
belief about solution $\hat{\mathbf{d}}_{mi}$ by:

$p^{(i)}_{mt}=\frac{\alpha^{(i)}_{mt}}{\alpha^{(i)}_{mt}+\beta^{(i)}_{mt}}~{},$
(4)

where $\alpha^{(i)}_{m1}=\beta^{(i)}_{m1}=1$ so that $p^{(i)}_{m1}=0.5$. This
means that, in the beginning, all solutions have equal beliefs, i.e., that the
initial probability distribution with which solutions are discovered is
uniform. Beliefs, however, may change as time passes, altering this
probability distribution. Each time agent $m$ implements solution
$\hat{\mathbf{d}}_{mi}$, they experience utility $U_{m}(\mathbf{d}_{t})$.
Then, they assess this utility and compare it to the utility they experienced
in the previous period $U_{m}(\mathbf{d}_{t-1})$. If solution
$\hat{\mathbf{d}}_{mi}$ improves agent $m$’s utility compared to the previous
period, $\alpha^{(i)}_{m}$ will increase by one. This, in turn, increases the
probability of discovering solution $\hat{\mathbf{d}}_{mi}$. Conversely,
$\beta^{(i)}_{m}$ will increase by one if solution $\hat{\mathbf{d}}_{mi}$
decreases agent $m$’s utility compared to the previous period. The probability
of discovering solution $\hat{\mathbf{d}}_{mi}$ decreases as a result. We
formalize this process in Eqs. 5a and 5b.

$\alpha^{(i)}_{mt}\begin{cases}\alpha^{(i)}_{m\\{t-1\\}}+1\textrm{ if
}U_{m}(\mathbf{d}_{t})\geq U_{m}(\mathbf{d}_{t-1}),\\\
\alpha^{(i)}_{m\\{t-1\\}}\textrm{ otherwise.}\end{cases}$ (5a)
$\beta^{(i)}_{mt}\begin{cases}\beta^{(i)}_{m\\{t-1\\}}+1\textrm{ if
}U_{m}(\mathbf{d}_{t})<U_{m}(\mathbf{d}_{t-1}),\\\
\beta^{(i)}_{m\\{t-1\\}}\textrm{ otherwise.}\end{cases}$ (5b)

Thus, a belief $p^{(i)}_{mt}$ is only updated when agent $m$ knows and
implements solution $\hat{\mathbf{d}}_{mi}$.

Agents may forget one known solution with probability $\mathbb{P}$. The
forgotten solution is picked randomly from the pool of known solutions
${\mathbf{S}}_{mt}$. The corresponding probability distribution with which
solutions are forgotten is based on agent $m$’s beliefs. Specifically, agent
$m$’s belief about solution $\hat{\mathbf{d}}_{mi}$ follows:

$q^{(i)}_{mt}=\frac{\lambda^{(i)}_{mt}}{\lambda^{(i)}_{mt}+\delta^{(i)}_{mt}}~{}.$
(6)

Initially, at $t=1$, all solutions have equal beliefs, such that
$\lambda^{(i)}_{m1}=\delta^{(i)}_{m1}=1$ and $q^{(i)}_{m1}=0.5$. This means
that agents forget solutions with a uniform probability distribution. This
probability distribution, however, may change as time passes and agents update
their beliefs. Each time agent $m$ proposes solution $\hat{\mathbf{d}}_{mi}$,
they update belief $q^{(i)}_{mt}$ by evaluating the current utility and
comparing it to the one experienced in the previous period.
$\lambda^{(i)}_{m}$ will decrease by one if solution $\hat{\mathbf{d}}_{mi}$
reduces agent $m$’s utility compared to the previous period. Consequently, the
probability of forgetting solution $\hat{\mathbf{d}}_{mi}$ increases.
Conversely, if solution $\hat{\mathbf{d}}_{mi}$ improves agent $m$’s utility,
$\delta^{(i)}_{m}$ increases by one, and the probability of forgetting
solution $\hat{\mathbf{d}}_{mi}$ decreases.

Additionally, we incorporate a memory factor into the agents’ updating
process, taking into account that agents tend to forget solutions that have
been stored in their memory for an extended period. This means that the
probability of forgetting each solution increases as time passes, i.e.,
$\forall\hat{\mathbf{d}}_{mi}\in\mathbf{S}_{mt}:\lambda^{(i)}_{mt}=\lambda^{(i)}_{m\\{t-1\\}}+1$.

Thus, if agent $m$ implements solution $\hat{\mathbf{d}}_{mi}$ and their
utility decreases, $\lambda^{(i)}_{mt}$ will increase by two.
$\lambda^{(i)}_{mt}$ increases by one because one period has passed and,
additionally, by one because utility has decreased. This double increase makes
it more likely to forget $\hat{\mathbf{d}}_{mi}$. We provide the general
updating rule for belief $q^{(i)}_{mt}$ in Eqs. 7a and 7b.

$\lambda^{(i)}_{mt}\begin{cases}\lambda^{(i)}_{m\\{t-1\\}}+2\textrm{ if
}U_{m}(\mathbf{d}_{t})<U_{m}(\mathbf{d}_{t-1}),\\\
\lambda^{(i)}_{m\\{t-1\\}}+1\textrm{ otherwise.}\end{cases}$ (7a)
$\delta^{(i)}_{mt}\begin{cases}\delta^{(i)}_{m\\{t-1\\}}+1\textrm{ if
}U_{m}(\mathbf{d}_{t})>U_{m}(\mathbf{d}_{t-1}),\\\
\delta^{(i)}_{m\\{t-1\\}}\textrm{ otherwise.}\end{cases}$ (7b)

###  A.6 Performance measures

Our dependent variable is the observed task performance at each period,
$C(\mathbf{d_{t\phi}})$, where $\phi\in[0,...,\Phi]$ corresponds to the
current simulation round. To compare the different scenarios, we normalize
$C(\mathbf{d_{t\phi}})$ by the maximum achievable performance in each
simulation round, i.e., $C^{\ast}_{\phi}$. We calculate the mean normalized
performance at each period for the 1,500 simulation rounds, $\bar{C}_{t}$.
This measure is formalized in Eq. 8.

$\overline{C}_{t}=\frac{1}{\Phi}\sum_{\phi=1}^{\Phi}\frac{C\left(\mathbf{d}_{t\phi}\right)}{C^{\ast}_{\phi}}~{}.$
(8)

In our results (see Sec. 4), we report two performance measures. The first
performance measure corresponds to the mean performance of the $100$ periods
of each simulation, and it follows:

$\overline{\overline{C}}_{t}=\frac{1}{T}\sum_{t=1}^{T}\overline{C}_{t}~{},$
(9)

where $\overline{C}_{t}$ comes from Eq. 8 and $T=100$ is the last observable
period. The second performance measure is the final performance, which is the
performance achieved on average by a team at $t=100$, i.e.,
$\overline{C}_{100}$.

###  A.7 Other technical details

We implemented and ran the model in Python 3.7.4. using the Spyder software,
version 5.0.0. Two laptops were employed in the simulations: One with 16GB of
RAM and a 1.90 GHz Intel Core i7 Processor and the other with 8GB of RAM and a
3.30 GHz AMD Ryzen 5 5600H with Radeon Graphics processor. Each simulation
takes between 10 and 40 minutes, depending on the device and the settings.