Vittorio Nespeca, Delft University of Technology, Delft, South Holland, 2628
BX, The Netherlands.

# Learning to connect in action: Measuring and understanding the emergence of
boundary spanners in volatile times

Vittorio Nespeca11affiliationmark:  and Tina Comes 11affiliationmark:  and
Frances Brazier11affiliationmark:  11affiliationmark:  Delft University of
Technology, NL<EMAIL_ADDRESS>
###### Abstract

Collective intelligence of diverse groups is key for tackling many of today’s
grand challenges such as fostering resilience and climate change adaptation.
Given increasing societal fragmentation, information exchange across such
diverse groups is crucial for collective intelligence, especially in volatile
environments. To facilitate inter-group information exchange, Informational
Boundary Spanners (IBSs) as pivotal information exchange ’hubs’ are promising.
However, the mechanisms that drive the emergence of IBSs remain poorly
understood. To address this gap there is first a need for a method to identify
and measure the emergence of IBSs. Second, an Agent-Based Modelling (ABM)
framework is not available to systematically study mechanisms for the
emergence of IBSs in volatile environments through the method. Third, even
though the ability to learn who provides high-quality information is thought
to be essential to explain the emergence of IBSs, a rigorous test of this
mechanism is missing. The learning mechanism is formalized using an ABM
framework, with the model’s outputs analyzed through the proposed method for
measuring the emergence of IBSs. To illustrate both the measurement method and
the learning mechanism, we present a case study focused on information sharing
in the volatile environment of a disaster. The study shows that learning
constitutes a mechanism for the emergence of effective IBSs in (a) low-
volatility environments characterised by low uncertainty and (b) in high-
volatility environments characterised by rapid change if the number of inter-
group connections is sufficient. With the method and model, this paper aims to
lay the foundations for exploring mechanisms for the emergence of IBSs that
facilitate inter-group information exchange. This article contributes to the
field of collective intelligence by providing the essential elements for
measuring and understanding the emergence of IBSs and by exploring the effect
of learning on their emergence in volatile environments.

###### keywords:

Information management, crisis management, information diffusion, boundary
spanning, inter-organizational coordination.

## Significance statement

In today’s rapidly changing and uncertain world, effective communication and
collaboration are crucial between different groups including governmental
organizations, NGOs, and communities. This paper focuses on effective exchange
of information within and between these groups. Individual actors known as
Informational Boundary Spanners (IBSs) play a key role in this process. Yet,
there is so far no method to quantitatively measure the emergence of
individual IBSs, and as such no analytical way to systematically test the
mechanisms that drive the emergence of IBSs. Measuring and understanding the
conditions and underlying mechanisms that influence the emergence of IBSs, and
their success, is the focus of this paper.

This paper (a) proposes a method to quantitatively measure the number of
actors that take on the role of IBSs and (b) shows how this method can be used
in combination with computer simulations to study mechanisms for the emergence
of IBSs. In particular, the ability of all actors to learn which actors
provide information of high quality is explored as a mechanism for the
emergence of IBSs under different conditions.

Results show that learning can facilitate more actors into growing into the
role of IBSs that effectively convey information across groups. This process
is most effective when information is consistently provided by information
sources that are stable and do not change over time. Further, in environments
characterized by rapid change, a high number of inter-group contacts (20 or
more) is vital for the development of IBSs, to distribute the informational
exchange burden and improve communication efficiency.

These findings have two main practical implications. First, to foster
effective inter-group information exchange in volatile environments it is key
to broadly crowd-source information and widely disseminate it through stable
channels. Second, the availability of trusted connections across groups is
crucial to support effective inter-group information exchange even in
conditions of high volatility. This, in turn, mandates that trusted
connections between groups are established and maintained over time: a true
societal challenge.

##  1 Introduction

Policies and practices for ensuring a sustainable, resilient, and climate-
adaptive future rely on collective intelligence across diverse groups (Norris
et al., 2008; Malone, 2018; Rockström et al., 2023; Perrone et al., 2023).
Collective intelligence is defined as the shared problem-solving ability that
arises from the interaction and combined efforts of a group of individuals,
leading to the effective accomplishment of one or more goals (Malone, 2018;
Flack et al., 2022). Fostering collective intelligence strongly relies on the
exchange of information among the individuals belonging to the different
groups (Leonard and Levin, 2022; Ballou, 2007; Malone and Crowston, 1994;
Fiala, 2005). The need for information sharing is even more prominent in
volatile (i.e., rapidly changing and uncertain) environments, where the groups
(e.g., governmental organizations, NGOs, and communities) must continually
adapt while maintaining coordination of their activities. Disaster response
exemplifies a situation in which multiple groups operate in a volatile
environment and need to exchange information to coordinate and respond
effectively (Kapucu, 2005; Bharosa et al., 2010; Comes et al., 2020; Nespeca
et al., 2020).

Actors within these groups exchange information with each other and with
actors in other groups. Some actors do so more successfully than others: over
time they become hubs for inter-group information exchange or Informational
Boundary Spanners (IBSs) (Tushman, 1977; Ancona and Caldwell, 1992; Kapucu,
2006; Ballou, 2007; Zagorecki et al., 2009; Marrone, 2010; Altay and Pal,
2013; Altay and Labonte, 2014; Van Meerkerk and Edelenbos, 2014; Bharosa and
Janssen, 2015). Levina and Vaast (2005) find that the formal appointment of
this role as IBS, such as through a mandate, does not suffice to ensure
effective information exchange. Instead, the role of IBSs in facilitating
information sharing among groups emerges through dynamic interactions within
and between these groups. More specifically, fostering the emergence of IBSs
requires consideration of the interplay between individual group members
(micro level), their groups (meso level), and networked interactions among
groups (macro level) (Marrone et al., 2007; Marrone, 2010). This emergent
process is contingent on specific conditions at the different levels. For
example, it is key that at the micro level an IBS develops an interest in
carrying out boundary spanning. Further, the formal nomination of an actor as
an IBSs at the group (meso) level can support his/her emergence as such but is
not mandatory. And, finally, formal or informal recognition of boundary
spanners’ authority to negotiate on behalf of their group also plays as key
role in the emergence of boundary spanners when considering networked
interactions among groups (macro level).

While there are some initial empirical insights into the emergence of
informational boundary spanning at the micro, meso, and macro levels and
mechanisms that drive their emergence, there is thus far no quantitative
formalisation and analytical modeling framework that studies the emergence of
IBSs via computational experiments. This paper argues that there are three
major gaps in the literature: (i) a formalised method to quantitatively
analyse how IBSs effectively conveying information across groups emerge; (ii)
an analytical modeling framework to analyse and understand the mechanisms
behind the emergence of effective IBSs under different conditions of
environmental volatility; and (iii) a deeper understanding of the effects of
learning on the emergence of IBSs in volatile environments.

Case study research has been invaluable to study boundary spanning (Ancona and
Caldwell, 1992; Levina and Vaast, 2005; Marrone, 2010; Lifshitz-Assaf, 2018).
Yet, Agent-Based Modeling (ABM) can complement and enhance case study research
by facilitating the systematic analysis and comparison of results from several
case studies by capturing interactions from micro to macro levels within a
unified modeling framework. This is particularly relevant when investigating
emergent mechanisms resulting from complex interactions across multiple levels
(Adam and Gaudou, 2017; Antosz et al., 2022), as seen with IBSs (Marrone,
2010). For instance, by incorporating insights from case studies on individual
behavior at the micro level into an ABM, researchers can simulate a system’s
macro-level behavior, assessing whether the simulated emergent patterns
replicate and explain empirical observations from other studies (Adam and
Gaudou, 2017). This approach enables the replication, testing of consistency,
and extension of case study research findings and provides directions for
further case studies (Tubaro and Casilli, 2010; Castellani et al., 2019;
Nespeca et al., 2023).

A fundamental step in enabling a combination of case study research and ABM
when studying the emergence of IBSs is to design a quantitative method for
measuring boundary spanning on an individual or micro level. This involves
identifying individuals who emerge as IBSs by effectively providing the
information needed to the groups who need it. Identifying emergent IBSs is
vital for examining the interplay between the micro, meso, and macro level
conditions that promote such emergence (Levina and Vaast, 2005). While several
quantitative methods for IBSs have been provided for measuring informational
boundary spanning (Ancona and Caldwell, 1992; Hansen, 1999; Cummings, 2004;
Marrone, 2010; Van Osch et al., 2016), these methods typically focus on
boundary spanning at the level of one or multiple groups rather than at the
level of the individual actor. Specifically, some methods focus on assessing
the volume of boundary spanning (e.g., through the frequency of communication)
vis a vis operational performance (e.g., time required for project completion)
at the group level (Hansen, 1999; Cummings, 2004; Zagorecki et al., 2009).
Other methods, directly measure the success of IBSs in retrieving information
for their group in a timely manner (Ancona and Caldwell, 1992; Marrone et al.,
2007; Van Osch et al., 2016). Finally, Zagorecki et al. (2009) monitors
network characteristics (e.g., the average distance between nodes) and the
volume of inter-group information exchanged to study the level of
informational boundary spanning occurring among groups. However, none of these
approaches measures how many and which individual agents emerge as effective
IBSs. As such, a method to measure the emergence of effective IBSs at micro-
level is missing, leading to a lack of understanding in the mechanisms behind
the emergence of IBSs.

Such a method provides a basis to build an ABM framework enabling to simulate
inter-group information exchange and capture the simulation outputs required
to systematically analyse, test, and understand at micro-level mechanisms for
the emergence of IBSs under varying circumstances. The characteristics of the
external environment, in which the groups operate, are likely to play a
crucial role in shaping the emergence of IBSs (Aldrich and Herker, 1977; Hazy
et al., 2003). The environment consists of factors external to a group’s
boundary that affect the decisions of individuals within the group and thereby
affects the group’s ability to achieve its goals (Lawrence and Lorsch, 1967;
Duncan, 1972). Especially in volatile environments information sharing has
been shown to be essential to achieve collective intelligence and coordination
(Comes et al., 2020). Volatility is defined as the level of turbulence and
uncertainty that characterize changes in the environment, where turbulence
indicates the frequency of change (Hazy et al., 2003), and uncertainty denotes
the unpredictability in the occurrence of change (Duncan, 1972). The emergence
of boundary spanning (or lack thereof) has been primarily studied for non-
volatile environments (Ancona and Caldwell, 1992; Levina and Vaast, 2005,
2006; Lifshitz-Assaf, 2018). Even though volatile situations such as social
unrest, crises, or conflicts are increasingly common, little research is
available on the conditions that foster the emergence of IBSs in volatile
environments. Hazy et al. (2003) propose an ABM framework and use it to study
the effectiveness of different numbers of IBSs for varying levels of
environmental volatility. However, their modeling framework and study assume a
predefined number of IBSs and does not account for how and why they emerge.
Further, Zagorecki et al. (2009) propose an ABM to study the emergence of
inter-group information exchange in volatile environments. Yet, their model
does not focus on capturing the emergence of IBSs at the micro level. As such,
an ABM framework to study the emergence of IBSs at the micro level in volatile
environments in missing.

Further, several empirical studies have shown that actors in volatile
conditions actively learn who among their contacts provides high-quality
information, subsequently adjusting their information collection preferences
to align with these sources (Sutton et al., 2008; Nespeca et al., 2020).
Preliminary evidence shows that this learning behavior can lead to the
emergence of IBSs in volatile conditions (Nespeca et al., 2020). However, the
concrete mechanisms between learning and the emergence of IBSs remain poorly
understood.

In sum, there are several gaps in the understanding of IBSs. First, a method
is needed for measuring the emergence of IBSs at the micro level as key to
analyse the underlying mechanisms that drive their emergence. Second, an ABM
framework is missing to systematically study mechanisms for the emergence of
IBSs at the micro level in volatile environments. Third, a better
understanding is required of the effects of learning and the volatility of the
situation on the emergence of IBSs.

To address these gaps, this paper develops a method to measure the emergence
of IBSs at the micro-level and introduces an ABM framework enabling to study
the emergence of IBSs in volatile conditions through the method. Then, the
method and ABM framework are used to analyse and understand learning as a
mechanism that potentially results in the emergence of IBSs. To this end, two
mechanisms are introduced and compared in the ABM: in the first mechanism,
agents exchange information randomly. In the second mechanism, agents
continually learn which sources provide the most relevant information and
adjust their information collection preferences accordingly. Both mechanisms
are studied for different levels of volatility and numbers of connections
enabling information exchange among the considered groups during the response
to a disaster.

The remainder of this paper is structured as follows. Section 2 introduces our
case study of disaster response in Jakarta as an example of a situation that
requires collective intelligence. Section 3 introduces the method proposed for
measuring the emergence of IBSs based on existing literature. Section 4
formulates three propositions concerning learning mechanisms for the emergence
of IBSs and their impact on inter-group information exchange in volatile
environments. Section 5 describes the development of an ABM that captures
inter-group information exchange and provides the output required to study the
emergence of IBSs through the proposed method. Section 6 illustrates the model
parametrization and experimental design aimed at testing the method for
capturing the emergence of IBSs and study the propositions through the ABM.
Section 7 presents the results of the experiments. Section 8 discusses the
implications of these results, leading to considerations regarding the
correctness of the method proposed for measuring emergent IBSs, the extent to
which the results support the formulated propositions, and what the findings
imply for information management and collective intelligence in volatile
environments. This section also presents directions for future research.
Section 8 concludes the paper.

##  2 Case study: Disaster response in Jakarta

In disaster response, typically multiple and loosely connected organizations
(e.g. governmental organizations and NGOs) and groups (e.g. communities)
collectively operate in a highly volatile environment. These groups need to
exchange information to respond effectively (Kapucu, 2005; Altay and Green
III, 2006; Bharosa et al., 2010; Comes et al., 2020; Nespeca et al., 2020).
Information exchange in these conditions is particularly challenging as, given
the sheer volume and frequency of new information produced during a disaster,
the actors are likely to become overloaded with information, which impairs
their ability to share and retrieve relevant information (Van de Walle et al.,
2016; Comes, 2016). Further, disaster response is typically characterized by
high uncertainty, meaning it is often difficult to predict when and from which
sources relevant information will become available. As such, disaster response
presents an ideal case study to understand the emergence of IBSs in volatile
environments.

This research focuses on the case study of Jakarta, Indonesia. Situated on the
northwest coast of Java, the world’s most populous island, Jakarta is subject
to frequent flooding, primarily attributed to its rapid subsidence and ongoing
urbanization processes (Abidin et al., 2011, 2015). Jakarta also hosts diverse
stakeholders including governmental organizations, NGOs, and community
initiatives that need to coordinate, collaborate, and exchange information
effectively. Additionally, Jakarta was chosen because, during the data
collection period in 2018, numerous international organizations were present
in response to the humanitarian response to the Sulawesi Earthquake. The
details on the case study including data collection, analysis, and discussion
are available in (Nespeca et al., 2020).

##  3 Measuring the emergence of informational boundary spanners

While several functions can be attributed to boundary spanning including
information processing, external representation, negotiation, and brokering
(Aldrich and Herker, 1977; Ancona and Caldwell, 1992; Fleming and Waguespack,
2007), this paper focuses on information processing. Information processing or
informational boundary-spanning is defined as the activity of searching for
information that lies outside the boundary of a group (i.e. that originates in
the group’s external environment) to find, process, and share new and relevant
information that can enhance the knowledge of the group (Bharosa, 2011;
Lindgren et al., 2008; Ancona and Caldwell, 1992; Van Osch et al., 2016).
Boundaries are the delimitation of a group or organization from its
environment (Scott, 1992). Often external information needed by a group is
available from other groups. As such, performing the informational boundary
spanning function entails fostering the exchange of information among groups.

IBS candidates (actors that can become IBSs), are those who have connections
across group boundaries, or ’inter-group ties’. As such, they can potentially
search, find, process, and share information across groups, thus performing
the informational boundary spanning function.

One approach to measuring the emergence of IBSs may be to simply count the
number of IBS candidates that carry out the informational boundary-spanning
function. However, while this function may be performed occasionally by many
or all potential IBSs, only a few of these actors consistently perform this
function and thus contribute significantly to fostering the exchange of new
and relevant information across groups (Levina and Vaast, 2005). As such,
simply counting the number of IBS candidates that perform the informational
boundary-spanning function occasionally (e.g. once or a few times) is expected
to overestimate the number of IBSs that emerge. Then, measuring the emergence
of IBSs requires identifying those actors that not only carry out the
informational boundary spanning function but also do so with sufficient
consistency to significantly enhance the exchange of new and relevant external
information among groups.

##  4 Understanding the emergence of informational boundary spanners

This section presents insights from the literature and the Jakarta case study
(Nespeca et al., 2020) that were used to formulate propositions and design the
ABM for testing the propositions.

###  4.1 Mechanisms for the emergence of informational boundary spanners

Insights regarding potential mechanisms for the emergence of IBSs were gained
in the case study of Jakarta. In the words of an information management
officer interviewed by (Nespeca et al., 2020):

> ”I was becoming a reference for everyone asking about mailing lists, who is
> working in a certain area, or what sort of maps are available. So that’s the
> role that I have played”. UN-OCHA Information Management Officer. Collected
> in October 2018.

This quote shows that an actor can emerge as an IBS not because of direct
choice, but through an emergent process resulting from the collective choices
and adjustments in the information collection preferences of a multitude of
actors. This finding hints at the ability of actors to learn the contacts that
consistently provide relevant information and adjust their information
collection preferences to match such contacts over time. This learning process
constitutes a mechanism that occurs at the micro (agent) level, and can lead
to the emergence of ’information hub roles’ (here termed IBSs) at the macro
level (Nespeca et al., 2020, pp 9-10). Such a mechanism is referred to as
’LearNing’ or LN in the following. In this study, learning is compared to
another mechanism in which actors collect information randomly among their
contacts without developing information collection preferences (called ’Random
Collection’ or RC).

Agents relying on LN develop a preference for collecting from contacts that
share relevant information frequently. This significantly increases their
chances of finding relevant information. For IBS candidates with inter-group
contacts, these preferences tend to favor external contacts, who provide
access to external information not readily available within the their own
groups. Consequently, IBS candidates relying on LN are more likely to engage
with sources outside their group boundaries, accessing new and relevant
information more effectively than those using RC, who lack such targeted
preferences. Therefore, IBS candidates influenced by LN are more likely to
fulfill the informational boundary spanning function (Cf. Section measuring
the emergence of IBSs) and emerge as effective IBSs compared to those that
rely on RC. This has two consequences. First, a larger portion of IBSs
candidates become emergent IBSs, resulting in a higher number of emergent IBSs
with LN compared to RC. Second, as a whole, the IBSs that emerge are more
effective in finding external information that is relevant and new for their
groups with LN compared to RC. The following proposition is formulated.

Proposition 1 (Learning VS Random Collection):When actors learn by adjusting
their preferred information sources based on the past quality of information
provided by such sources, a higher number of informational boundary spanners
emerge that are more effective in retrieving external information than in the
case in which actors collect information randomly among their contacts.

###  4.2 The effect of environmental uncertainty

In disaster response, there are typically two types of events in a group’s
external environment that need to be detected by individuals belonging to the
group to inform decision making, namely shocks and announcements (Nespeca et
al., 2020, 2023). Shocks are unexpected disruptive events such as cascading
effects generated by infrastructural failures (e.g., blackouts), riots, or
natural disasters. Announcements represent the release of information that is
produced and consistently shared by particular groups or agencies such as
flood early warnings (Watts et al., 2019; Nespeca et al., 2018), evacuation
orders (Adam and Gaudou, 2017), or needs assessments.

In this study, uncertainty can be associated with the event itself (e.g.,
concerning the nature and timing of the event) and the source from which
information regarding the event is released or made available (i.e. the
information origin). Shocks and announcements differ in terms of their
uncertainty in the source of information associated with them. In the case of
shocks, it is not known when and where a shock will occur, and who will be
affected and communicating about it. Consequently, the origin (or source) of
information becomes uncertain. As such, shock-related information has an
unstable origin. In contrast, announcements are consistently generated from
the same source within an information exchange network (e.g., weather
forecasting agency in the case of early warnings, or the village leader in the
case of evacuation orders). As such, while the time and type of announcement
is still uncertain (it is not known when an early warning will be necessary),
the source of announcement information is known. Therefore, announcement
information is referred to as information with a stable origin.

The combined effect of the stability in information origin and learning on the
emergence of IBSs can be conceptualized from the perspective of information
flow paths. Information flow paths (or simply information flows) represent the
contact-to-contact information exchanges through which information spreads
within and across groups. These paths originate once information is created
from unstructured data, and then routed to one or more of the actors belonging
to the groups considered (as shown in Figure 1).

Figure 1: Information flow paths illustrating the spread of information from
its origin (i.e. node in the network in which new information is introduced)
through a series of information sharing activities carried out by the network
nodes representing the actors.

The configuration of information flows and whether they reach groups depend on
several factors. This study accounts for the following three: (1) information
flows depend on the structure of the network through which information can be
exchanged within and across the boundaries of different groups (as introduced
by (Zagorecki et al., 2009; Altay and Pal, 2013)). In this case, the network
is considered to be constant. (2) information flows are affected by the
locations of the network, in which new external information is introduced i.e.
the origin of the information. The origin of information can be stable
(announcements), or unstable (shocks). (3) The paths depend on the information
exchange behavior and preferences of the actors constituting the nodes in the
network.

Whether learning impacts the emergence of IBSs and the ability of groups to
retrieve external information is related to the stability of information
origin. When the information origin is stable (announcements), the information
flow paths originate in the same node. If that information is perceived to be
relevant (as assumed for this study), the actors directly connected to the
origin will learn and develop a preference towards choosing it as their
source. Other actors who are only indirectly connected to the origin (i.e. via
other contacts) are likely to develop a preference for the actors among their
contacts that are the most directly connected to the origin (i.e. through the
lowest number of ties), given they are more likely to consistently receive and
share such information earlier than other contacts. Then, at each information
exchange along the path, actors are likely to collect from the contacts that
are the most directly connected with the information origin. As such, learning
is expected to generate shorter information flow paths from the origin of
information to the group that needs such information compared to the case in
which actors collect information randomly and do not develop preferences.

Conversely, if information has an unstable origin (shocks) the source of
information changes, and, thus, agents cannot learn which sources continually
provide relevant information. The actors therefore will benefit less from
developing information collection preferences. These considerations lead to
the following proposition:

Proposition 2 (Stability of information origin and learning): Learning leads
to more effective inter-group information exchange if and only if relevant
information is consistently generated by the same actors. If relevant
information becomes available from continually changing and uncertain sources
(unstable origin) learning has no effect in terms of improving inter-group
information exchange.

###  4.3 The effect of environmental turbulence

Environmental turbulence is the frequency of environmental change (Duncan,
1972). Specifically, turbulence in this study is defined as the frequency of
occurrence of events (i.e., shocks, and announcements) representing changes in
the environment. In order to detect and adapt to such changes, actors need to
find information regarding these events. As such, the higher the level of
turbulence the higher the volume of external information that agents need to
manage and find. However, actors have a limited capacity to process
information (Simon, 1955). In the case of disasters, the volume and speed of
information can be so prominent that actors reach the limit of their cognitive
capabilities and become overloaded with information, which impairs their
ability to retrieve and exchange the information needed (Van de Walle et al.,
2016; Comes, 2016). As such, the authors of this study posit that, for higher
levels of turbulence, the performance of the system decreases. Performance is
measured as the amount of information concerning environment-altering events
that is collected or received by the groups that need such information.

The number of actors that can explore the external environment was shown to
play a crucial role in helping groups to detect environmental change (Hazy et
al., 2003). In their study, the actors able to explore the external
environment are those with inter-group ties. An increased number of inter-
group ties entails a greater number of IBSs candidates who can emerge as IBSs
and contribute to detect information concerning events marking environmental
change. This is particularly relevant for high levels of turbulence, in which
the high volume of information needs to be distributed among a higher number
of IBSs to reduce the risk of information overload and enhance system’s
performance.

Additionally, LN is expected to increase the number of IBSs and improve their
performance compared to random collection for high levels of turbulence.
Considering that IBSs tend to process and exchange a high volume of
information across different groups, they are likely to become overloaded with
information. When the available IBSs are no longer able to provide relevant
information because of information load, the actors requiring information from
them will adapt their information sources through LN to find other actors able
to provide the information they need. This may lead the actors to develop
preferences towards IBSs candidates that are not yet as overloaded and that
thus can support the exchange of information. As such, the adaptability
introduced by learning is anticipated to enable actors to collectively
distribute the volume of information across a higher number of IBSs, and thus
improving overall system’s performance compared to the case of RC. This
performance increase is dependent on the agents’ capacity to select from
various IBS candidates resulting from a high number of inter-group ties,
leading to the following proposition.

Proposition 3 (Interplay of turbulence, inter-group ties redundancy, and
learning): A higher number of ties among groups results in a higher number of
emergent IBSs, enhancing a group’s ability to retrieve external information
even in highly turbulent environments. This enhanced ability to retrieve
external information is particularly pronounced when actors rely on learning
to adjust their information collection preferences.

##  5 Model Design

Agent-based modeling (ABM) is the modeling paradigm of choice as it enables
researchers to explore the collective consequences of individual behavior
(Epstein and Axtell, 1996).

An ABM was developed based on the methodology and ABM proposed in (Nespeca et
al., 2023) and modified to include the learning mechanism found for the
Jakarta case study in (Nespeca et al., 2020). The goal of the model is to
assess the validity of the method for measuring the emergence of IBSs and to
study the mechanisms that influence the emergence of IBSs. A graphical
overview of the results of this ABM is shown in Figure 2. Further, a
conceptual diagram of the entities, states, and tasks included in the model is
shown in Figure 3. Entities represent essential features of the model with
their properties, states, and tasks as presented in the legend of Figure 3.

Figure 2: Graphical overview of the Agent-Based Model (ABM) developed for this
study. The model involves two distinct groups, namely professional responders
(on the left, in black) and communities (on the right, in blue) that exchange
information. The grey lines represent the formal and informal ties used for
information exchange. The ties that cross the border between professional
responders and communities are the inter-group ties. Figure 3:  Graphical
description of entities, their properties, states, and tasks in the developed
ABM. The actors and environment are agents in the ABM given they carry out
tasks.

Two main groups of agents are considered in the ABM, namely communities and
professional response organizations or simply professionals (including
governmental and non-governmental organizations). The system’s performance is
measured in terms of the percentage of external information needed by each of
these two groups that is found by at least one of the actors belonging to the
group. Each group has direct access to the information that the other group
needs. Therefore, sharing information across group borders is vital.
Specifically, communities have direct access to information about shocks,
which represent the information needed by professionals. Conversely,
professionals can send announcements, which represent the external information
needed by communities. The exchange of information among the two groups is
enabled through the emergence of IBSs.

Information exchange within and across the two groups takes place via networks
of informal and formal ties or contacts (Cf. Figure 2). Informal ties are
obtained through preferential attachment algorithms based on (Barabási and
Albert, 1999). Formal ties representing hierarchical structures are introduced
within the professional response organizations according to three levels,
namely strategic, tactical, and operational. Within such networks, IBS
candidates (i.e., those that can potentially emerge as IBSs) are those that
have at least one connection with an actor belonging to a group different from
their own (cf. the ties connecting Professional Responders and Communities in
Figure 2).

The following paragraphs discuss the key features introduced in the model to
measure the emergence of IBSs and explore each of the propositions.

Measuring the emergence of IBSs: emergent IBSs are those that consistently
provide new and external information to a group thus playing a key role in
fostering information exchange across the groups (cf. Section ”Measuring the
emergence of informational boundary spanners”). To apply such a definition, it
is crucial to measure each agent’s contribution to information sharing across
groups. This measurement is facilitated by the introduction of the ’number of
informational boundary-spanning Function Executions’ or FEs, where an actor
agent increases its FE count each time it provides new and external
information to any group that requires it. The number of FEs accumulated by
agents are then used to study which of the IBS candidates emerge as IBSs.

Understanding emergence: the first proposition focuses on studying the
emergence and effectiveness of IBSs by comparing random information collection
(RC) with learning (LN). RC and LN are characterized by different information
collection preferences. Such preferences are modeled as non-uniform
distributions in the probability that agents have to collect from each of
their contacts, denoting that some of the agents’ contacts are preferred
compared to others. For RC, the information collection probabilities assigned
by an agent to its contacts are equally divided among all contacts, indicating
that the agent has no preferences (uniform distribution). For LN, each agent
develops and adjusts its information collection preferences over time
(possibly leading to a non-uniform distribution). Specifically, a
reinforcement learning algorithm is used to adjust preferences over time for
each agent based on the relevance of the information provided by each of the
agent’s contacts from the beginning of the simulation up to the current time
step. The adopted reinforcement learning algorithm is Q-learning (see Appendix
A).

The second proposition considers the interplay of learning and uncertainty. To
test the impact of stability in information origin, announcements (with a
stable information origin) and shocks (with an unstable information origin)
are introduced in the model. The degree of uncertainty is determined by the
parameters shocks per day and announcements per day. For instance, if shocks
per day is set to 0 and announcements per day is set to a value greater than
0, environmental uncertainty is considered to be low, as only stable-origin
announcements are considered.

The third proposition focuses on studying the combined effect of learning,
turbulence, and number of inter-group ties on the emergence and performance of
IBSs. Varying levels of turbulence are captured by the different frequencies
in the number of shocks and announcements (parameters shocks per day and
announcements per day) considered. The number of ties across communities and
professional responders are specified by the parameter number of inter-group
ties. The inter-group ties are introduced in the model with a preferential
attachment algorithm modified to choose pairs of agents belonging to different
groups with a likelihood that depends on their current degree (i.e. number of
ties). Bounded rationality is captured by limiting the amount of information
that actors can process, share, and collect to 3 pieces of information within
each simulation step (set the ’info. processing limit’ parameter in the
model).

Regarding the temporal and spatial scales considered in this model, the time
step of simulation is 10 minutes, while the duration of the simulation is 4
days. Spatial scale is considered at an abstract level in this model as the
actors exchange information through networks. As such, a specific spatial
scale is not assigned in this case.

##  6 Methods

This section describes the way the model parameters were set and the
experiments that were run to test the propositions.

####  6.0.1 Model Parametrization

Three parameters were constant for all experiments namely: duration of a
simulation, the learning rate, and the information processing limit. The
duration of each simulation was set to 4 days to simulate information exchange
in the early stages of disaster response, a phase in which volatility is
especially pronounced and rapid inter-group information exchange and
coordination are particularly crucial (Kreiss et al., 2010; Bode and
Macdonald, 2017). The learning rate was set to a relatively low value (assumed
to be 0.1) as the time step in the simulation is small (10 minutes) compared
to the chosen duration of the simulation, requiring a smaller learning rate to
compensate for the high frequency with which information exchange preferences
are updated (up to every 10 minutes). Finally, the information processing
limit was set to a value of 3, representing humans’ limited ability to process
information per unit of time (in this case every 10 minutes) (Simon, 1955).

####  6.0.2 Experimental design

In total, four batches of experiments were designed to study (a) the method
for measuring the emergence of IBSs and (b) each of the 3 propositions as
shown in Table 1. Experiment 0 focuses on testing the approach for capturing
and measuring the emergence of IBSs. The simulations are run for varying
numbers of inter-group ties. Experiment 1 focuses on simulating the impact of
the two different information collection mechanisms to study Proposition 1.
Next, Experiment 2 studies Proposition 2 and thus investigates the interplay
between learning and varying levels of uncertainty (stability in information
origin) by combining different levels of shocks per day and announcements per
day. Finally, Experiment 3 explores Proposition 3 and thus focuses on the
interplay between varying levels of environmental turbulence (established with
the parameters shocks per day and announcements per day), learning (LN VS RC),
and the number of inter-group ties (established with the homonym parameter).
These experiments are run through the service provided by the Delft High
Performance Computing Centre (DHPC).

Parameters |  Experiment 0
(method):
Measuring emergent IBSs |  Experiment 1
(Proposition 1):
Comparing LN and RC |  Experiment 2
(Proposition 2):
Effect of Environ. Uncertainty |  Experiment 3
(Proposition 3):
Effect of Environ. Turbulence
---|---|---|---|---
Info. Collection Mechanism |  RC |  LN, RC |  LN, RC |  LN, RC
shocks per day |  10 |  10 |  0, 10, 20 |  1∗, 5∗, 10∗, 15∗, 20∗
announcements per day |  10 |  10 |  0, 10, 20 |  1∗, 5∗, 10∗, 15∗, 20∗
number of inter-group ties |  1, 2, 5, 10, 20, 30 |  20 |  20 |  1, 2, 5, 10, 20, 30
duration of the simulation (days) |  4 |  4 |  4 |  4
learning rate |  N.A. |  0.1 |  0.1 |  0.1
info. processing limit |  3 |  3 |  3 |  3
number of repetitions |  80 |  40 |  40 |  20
total simulations |  120 |  80 |  720 |  1200
Table 1: Parameters setting for the simulation experiments aimed at testing
each of the propositions. The experiments were full factorial with the
exception of the values marked with an asterix ’∗’. The use of ∗ for
experiment 3 indicates that for each simulation in the experiment an equal
value of shocks per day and announcements per day is considered (e.g. 10
shocks per day and 10 announcements per day) rather then their full factorial
combination. LN = LearNing, RC = Random Collection.

##  7 Results

This section illustrates the results of the experiments shown in Table 1.

###  7.1 Experiment 0: Measuring the emergence of informational boundary
spanners

Figure 4 illustrates the distribution of the number of instances where agents
with inter-group ties (IBS candidates) effectively contribute new and relevant
external information to the groups that need it, earning them informational
boundary spanning Function Executions (FEs).

Figure 4: Frequency of occurrence of # FEs (number of informational boundary-
spanning Function Executions) obtained by the IBS candidates, and the
threshold used to capture the emergent IBSs.

The distribution reveals that several IBS candidates attain relatively few
FEs, while only a few candidates achieve a high number of FEs. This finding
illustrates that a few IBS candidates contribute to a great extent to inter-
group information exchange by providing new and relevant information to the
groups who need it, while many other candidates do not contribute
significantly. The candidates that contribute significantly to inter-group
information exchange qualify as emergent IBSs. One approach to identify these
candidates is to assume that those that achieve a number of FEs above a given
threshold contribute effectively also at the inter-group level and thus
qualify as emergent IBSs (cf. the red vertical line in Figure 4). Such
threshold or thresholds should be high enough to avoid capturing those IBS
candidates that obtain only a few FEs (and as such do not considerably improve
inter-group information exchange), but also not too high to avoid not
capturing agents that may not have the highest FEs but still contribute
significantly to inter-group information exchange. However, it is unclear how
to select a threshold that satisfies these conditions.

To investigate the effects of the choice of this threshold, Experiment 0
focuses on studying the implications of adopting different thresholds, namely
the 1st, 10th, 20th, 30th, 40th, 50th, 60th, 70th, 80th, and 90th percentiles
in the frequency distribution shown in Figure 4. For each of these thresholds,
the number of IBSs emerged is plotted against their effectiveness at the
inter-group level, measured as the % of external information needed found by
the groups. Figure 5 illustrates the results for selected thresholds (i.e. the
1st, 30th, 60th, 90th percentiles) to enhance clarity of representation. These
results show that for all considered thresholds a higher number of emergent
IBSs corresponds to a higher performance. Further, the number of emergent IBSs
grows considerably when increasing the threshold. This figure, however, does
not consider the number of IBS candidates available, which represents the
maximum number of IBS that can emerge. As such, a more in depth analysis is
required that considers not only the threshold adopted, but also the number of
IBS candidates available.

Figure 5: Relationship between the number of IBSs that emerged and the % of
external information found by the groups who need it for different values of
the threshold set as a percentile in the distribution of FEs from Figure 4.
Figure 6: Number of IBSs that emerged for each of the thresholds considered in
Figure B and for different numbers of Inter-group Ties (# IGTs).

To analyze emerging IBSs across varying numbers of IBS candidates and
threshold settings, it is key to consider that the number of IBSs candidates
depends on the number of Inter-Group Ties (# IGTs) available among groups.
Precisely, the number of IBS candidates is twice # IGTs given that each
connection ties two agents who can both emerge as IBSs. As such, the analysis
depicted in Figure 5 is expanded to consider not only different thresholds (in
this case all of those between the 1st and 90th percentiles), but also
different # IGTs. Figures 6.A to 6.J depict the results. A comparison of these
figures reveals that, at low thresholds, as depicted in Figures 6.A to C,
nearly all IBS candidates transition into emergent IBSs. For instance, with 10
inter-group ties (meaning 20 IBS candidates), the emerging number of IBSs tend
to be around 20, underscoring the high conversion rate of IBS candidates into
actual IBSs (cf. Figure 6.A, B, and C). Furthermore, the simulation results
cluster in specific areas of the plot when holding the number of inter-group
ties constant. This clustering suggests minimal variability in both the number
of emerging IBSs and the overall system performance. Such lacking variability
shows the little sensitivity in capturing emergent IBSs provided by low
thresholds. Conversely, for high thresholds such as the 90th percentile
(Figure 6.D), there is significant variability in the number of emergent IBSs,
yet the percentage of external information remains relatively constant, as
shown by the horizontal lines. This shows that the emergent IBSs captured with
high thresholds do not contribute significantly to effective inter-group
information exchange. Thresholds between these extremes, like those between
the 30th and 80th percentiles (Figures 6.D to 6.I), show variability in the
number of IBSs emerged. Further, for an increase in the #IBSs, the % of
external information found also increases, showing how the additional emergent
IBSs captured positively contribute to fostering inter-group information
exchange. One exception to such an increase is observed for the 80th
percentile and 20 IGTs when the number of emergent IBSs found is 3. This is
most likely an outlier given that the plot does not show a confidence interval
around the value.

These findings illustrate that the method proposed in this paper captures the
number of emergent IBSs that significantly contribute to providing new and
external information to groups, thereby supporting effective inter-group
information exchange.

However, for this method to be effective, thresholds need to be carefully
chosen according to two criteria. First, adequate thresholds are not too low,
thus presenting sensitivity to the emergence of varying numbers of IBSs across
different simulations. Second, such thresholds are not too high, meaning that
when the number of IBSs captured through the threshold increases, also their
effectiveness in fostering inter-group information exchange increases.

These two criteria are sufficient to find multiple adequate thresholds rather
than a single one (in this case those between the 30th and 80th percentiles),
leaving an open question as to whether adopting different adequate thresholds
will provide different results when studying the emergence of IBSs. As such,
rather than simply choosing one of the adequate thresholds, it is key to use
multiple thresholds and assess the consistency of the findings obtained. The
remaining experiments (1 to 3) are analyzed with six thresholds, namely the
30th, 40th, 50th, 60th, 70th, and 80th percentiles. For brevity, the following
sections show the results for the 60th percentile. However, a comparison of
the IBSs emergence results obtained with the six percentiles chosen are
presented in Appendix B.

###  7.2 Experiment 1: Learning VS Random Collection

Proposition 1 is composed of two parts. The first part indicates that when
actors learn and adjust the information collection preferences based on the
quality of information provided by their contacts (LeaRning mechanism or LN)
this leads to the emergence of more IBSs compared to the case in which actors
collect information randomly (Random Collection mechanism or RC). The second
element of the proposition states that when actors learn (LN), this leads to
the emergence of IBSs that are more effective in fostering inter-group
information exchange compared to random collection (RC). In the following
these two parts are assessed against the results of experiment 1.

Figure 7 shows the results of experiment 1 including the emergence of IBSs
(left) and their performance (right) respectively for the information
collection mechanisms LN and RC.

Figure 7: Results of Experiment 1: Effect of the information collection
mechanisms Random Collection (RC) and LearNing (LN) on the # IBSs emerged
(left) and the % of external information found by the groups that need it
(right). The white dots represent the averages.  Figure 8: Results of
Experiment 2: Interplay between the information collection mechanisms Random
Collection (RC) and LearNing (LN), and varying environmental uncertainty. The
effect of such an interplay is assessed for (a) the emergence of Informational
Boundary Spanners (IBSs) (upper row) and on (b) the effectiveness of such IBSs
in enabling groups to retrieve external and relevant information (lower row).
The varying environmental uncertainty is characterized by stable (20
announcements per day - left column), mixed stable and unstable (10
announcements per day and 10 shocks per day - middle column), and unstable (20
shocks per day - right column) origins of external information.The white dots
represent the averages.

First, Figure 7 (left) illustrates how, compared to RC, LN results in an
average increase of about three emergent IBSs. The 5th, 25th, 75th, and 95th
percentiles and the median are also shifted towards higher values in the case
of LN compared to RC. The interquartile range of the number of IBSs emerged is
larger for LN than in the case of RC, showing that learning also increases the
variability of the results. However, the 5th percentile is closer to the
median in the case of LN compared to RC, illustrating how, despite its higher
variability, the distribution is skewed towards higher values of # IBSs
emerging in the case of LN compared to RC. These results supports the first
part of Proposition 1 by showing that the number of IBSs emerged tends to
increase with LN compared to RC.

Second, according to Figure 7 (right) the effectiveness of IBSs measured as
the percentage of external information retrieved by each group increases
roughly by 7.5% on average with LN compared to RC. The 5th, 25th, 75th, and
95th percentiles, and the median shift towards higher values in the case of LN
compared to RC. Additionally, the interquartile range for LN is considerably
reduced compared to RC, illustrating how, in combination with the higher
median, the retrieval of external information is more likely to be higher in
the case of LN compared to the case of RC. These results support the second
part of proposition 1 by showing that when agents learn (LN) the IBSs that
emerge are able to find and provide higher percentages of the external
information needed by groups compared to the case in which information is
collected randomly (RC). In sum, both parts of Proposition 1 are supported by
the results.

###  7.3 Experiment 2: The effect of environmental uncertainty (stability of
information origin)

Figure 8 shows the results of Experiment 2 regarding the emergence of IBSs
(upper row) and their performance (lower row) for both LN and RC. These
results include different combinations of frequencies in shocks and
announcements, namely 20 announcements per day (left column), 10 shocks per
day and 10 announcements per day (middle column), and 20 shocks per day (right
column). In all three cases the number of events (shock, announcements, or
combinations of them) amount to a total of 20 for each day of simulation to
ensure comparability among them.

The results show that, in the case of announcements (Cf. left column of Figure
8), LN increases the # IBSs emerged (by roughly 7 IBSs) and their performance
(by around 15%) compared to RC.

When announcements and shocks are combined, as illustrated in the middle
column of Figure 8, LN leads to an average emergence of 2 additional IBSs and
a performance increase of 7% over RC. However, these gains are modest when
compared to scenarios solely involving announcements. For announcements only
(see left column of Figure 8), there was a notable rise of 7 emergent IBSs and
a 15% performance improvement.

Next, in the case of shocks (Cf. right column of Figure 8), the number of IBSs
that emerge and their performance does not change significantly with LN or RC.

These findings support Proposition 2 by showing that the effect of learning
depends on stability of the information origin. If the information origin is
stable (announcements), then learning leads to an increase in the number of
IBSs and in their effectiveness in improving inter-group information exchange.
Conversely, if the source of information is unstable (shocks), learning has
little effect.

###  7.4 Experiment 3: The effect of environmental turbulence

This experiment focused on the emergence of IBSs and their effectiveness under
different levels of turbulence and numbers of Inter-group Ties (# IGTs). The
level of turbulence consists of the frequency of disruptive events (shocks and
announcements) occurring every day of simulation and generating external
information needs for the groups (measured as external information needed per
day). In other words, the turbulence level is set as the sum of shocks per day
and announcements per day. An equal number of shocks and announcements per day
is considered in all experiments. As such, a Turbulence level of ten
corresponds to five announcements per day plus five shocks per day. The
results are shown in Figure 9.

Figure 9: Results of experiment 3: Effect of increasing environmental
turbulence on the number of Informational Boundary Spanners (IBSs) emerged
(left) and their collective performance in exchanging external relevant
information across groups (right) for different numbers of Inter-group Ties (#
IGTs) between communities and professionals, and for the two information
collection mechanisms LN (LearNing) and RC (Random Collection).

Figure 9 on the left shows that for higher turbulence a higher number of IBSs
emerges. The number of IBSs that emerge grows with the # IGTs, and it does not
change significantly with the information collection mechanism considered (LN
or RC).

Figure 9 on the right shows that for higher levels of turbulence (and
corresponding increasing information needs), the share of the external
information that is retrieved decreases. However, a higher number of inter-
group ties increases the performance of the system at all levels of
turbulence. Further, such performance increases with LN compared to RC for
high levels of environmental turbulence (10 or more events per day) if the
number of inter-group ties is also high (20 or more IGTs).

In sum, these findings support proposition 3 for two reasons. First,
independently from the information collection mechanism, more inter-group ties
are associated with the emergence of more IBSs that more effectively convey
information across groups. Second, for high numbers of IGTs and levels of
environmental turbulence, the performance of the IBSs emerged increases with
LN compared to RC.

##  8 Discussion

This section discusses the implications of the findings, and suggests
directions for future research.

###  8.1 Measuring emergent IBSs

This study introduced a method for measuring the emergence of IBSs. Compared
to previous work that measures the emergence of informational boundary
spanning at the level of a group or groups (Ancona and Caldwell, 1992; Hansen,
1999; Cummings, 2004; Zagorecki et al., 2009; Marrone, 2010; Van Osch et al.,
2016), the method introduced here directly measures the individual agents that
emerge as IBSs. Emergence of IBSs can thus be tracked in greater detail, and
the heterogeneous characteristics of those that emerge as IBSs can be observed
at the micro level. Further, the interplay between the individual, group, and
inter-group levels and its impact on the emergence of effective IBSs can be
studied through this method. These aspects are crucial to inform the design of
effective information management strategies that foster the emergence of IBSs,
enhance inter-group information exchange, and support coordination and
collective intelligence (Levina and Vaast, 2005).

To qualify as IBSs, the IBSs candidates need to fulfill a minimum ”number of
informational boundary spanning Function Executions” or FEs (i.e. a minimum
threshold) that enables them to significantly improve information exchange
among groups. To ensure the correctness of this method, thresholds must be
carefully selected based on two criteria: they should not be too low to
maintain sensitivity to varying occurrences of IBSs in different simulations,
and not too high to ensure that as more IBSs are detected, their collective
ability to enhance inter-group information exchange also increases. Here,
inter-group information exchange is measured as the percentage of the total
external information needed found by the groups.

Experiment 0 showed that this method enables to measure emergent IBSs by
individuating those actors that effectively contribute to inter-group
information exchange. Further, multiple adequate thresholds were found to
satisfy the two criteria mentioned above. To clarify whether adopting
different adequate thresholds lead to different results when studying the
emergence of IBSs, the results of Experiments 1 to 3 were analyzed and
compared with six adequate thresholds: the 30th, 40th, 50th, 60th, 70th, and
80th percentiles of the FE distribution for IBS candidates. The results of
this comparison in Appendix B show that adopting different adequate thresholds
does not change the conclusions of the experiments as Propositions 1 to 3
remain supported by the findings independently of the thresholds considered.
However, Appendix B also shows that it is still essential to consider a wide
range of adequate thresholds when studying the emergence of IBSs.
Specifically, a discrepancy was found in Experiment 2 in the results observed
with the minimum and maximum thresholds (respectively, the 30th and 80th
percentiles). These results were considered as outliers and thus discarded
given their extreme value, inconsistency in the effects found, and the fact
that the majority of the other thresholds indicated consistent results (cf.
Appendix B). This process illustrates the importance of considering multiple
thresholds and carefully analyzing any discrepancies that may arise. Such an
analysis allows one to determine whether discrepancies indicate
inconsistencies in the findings that require reconsideration or modification
of the conclusions, or if they simply represent outliers resulting from the
adoption of extreme thresholds (i.e., too low or too high).

In sum, this method enables the study of the emergence of IBSs. To ensure the
method’s correctness, it is first crucial to select thresholds that are
neither too low nor too high, thereby effectively capturing emergent IBSs that
contribute to inter-group information exchange. Second, a wide range of
adequate thresholds should be considered to test consistency across results on
the emergence of IBSs and to assess whether any discrepancies are outliers or
if the conclusions need to be reconsidered and modified in light of such
discrepancies.

###  8.2 Understanding emergent IBSs

First, this paper introduces a novel agent-based modeling (ABM) framework that
enables to study the emergence of IBSs in volatile environments. This ABM
simulates inter-group information exchange and outputs the number of times IBS
candidates fulfill the informational boundary spanning function at the micro
level, as well as their overall effectiveness. This provides the basis to
identify those that emerge as IBSs through the proposed method and to
systematically test mechanisms for their emergence in volatile conditions.
Compared to previous ABM frameworks introduced to study inter-group
information exchange and boundary spanning in volatile conditions (Hazy et
al., 2003; Zagorecki et al., 2009), this framework measures the emergence of
IBSs rather than imposing a predefined number of IBSs a priori (Hazy et al.,
2003), and captures this emergence at the micro or individual level rather
than solely at the macro level (Zagorecki et al., 2009).

Second, this study furthers the understanding of learning for the emergence of
IBSs. Learning entails that each agent develops information collection
preferences over time based on the past quality of information provided by the
agent’s contacts. This mechanism was compared to the case in which actors
collect information randomly. As posited in Proposition 1 and supported by the
results of Experiment 1, learning leads to the emergence of more IBSs as
compared to random information collection, and these IBSs contribute to more
effective inter-group information exchange. Learning therefore is a micro-
macro mechanism as learning at the micro level leads to the emergence of IBSs
and effective inter-group information exchange at the macro level. This
finding confirms the results of the study by Levina and Vaast (2005) and
extends it to volatile environments by showing that effective boundary
spanners emerge through a process resulting from the decentralized
interactions among actors belonging to different groups. It also adds to the
work by Marrone (2010) by showing how micro level antecedents such as learning
and the availability of connections with other groups can lead to macro level
outcomes through an emergent process.

Third, this study highlights the necessity to consider environmental
volatility, i.e. the uncertainty and turbulence of the environment, for
studying the emergence of IBSs. As posited in Proposition 2 and corroborated
by the findings from Experiment 2, the effect of learning on the emergence and
efficiency of IBSs is contingent on environmental uncertainty and specifically
on the stability of the information source or origin. If the information
origin is stable, as in the case of announcements, the number of IBSs and
their performance in enhancing inter-group information exchange increases when
the agents adopt learning. In contrast, an unstable information source, as in
the case of shocks, renders learning ineffective. This difference can be
explained by the differences of information origin and network structures:
while announcements are constantly originating from the same location of the
network, shocks originate from random locations in the disaster-affected area
of the model. Under learning, announcements propagate through the network
following increasingly strong preferential channels. In contrast, the way
shocks propagate continually changes depending on where the shock occurred and
which nodes/actors in the network find this information and share it with
others. These results explain why learning has little effect on shocks or more
generally information of unstable origin: when information can come from ever-
changing locations of the network, developing information collection
preferences for the contacts that provided the most relevant information in
the past has the same effect as collecting information randomly given that
none of the agents tends to consistently provide relevant information due to
the instability of the information origin.

Proposition 3 is supported by the findings of Experiment 3 and suggests that
an increased presence of inter-group ties leads to the emergence of a higher
number of IBSs that, as a collective, can more effectively facilitate the
exchange of information between groups. This effect occurs even for high
turbulence and when considering the actors’ limited information processing and
sharing capability. Further, for high levels of inter-group ties and
environmental turbulence, learning leads to higher performance than in the
case of random information collection. Such an improvement is negligible for
low numbers of ties and becomes evident for 20 and 30 inter-group ties. This
pattern can be attributed to the agents’ collective capacity to discern
through learning the most effective IBS candidates for relaying external
information (e.g., those that are exposed to less information load) as they
change over time. Further, the fact that learning has an effect only for 20 or
more inter-group connections illustrates that a sufficiently extensive network
of inter-group ties is crucial for enabling agents to choose from various IBS
candidates through learning.

###  8.3 Implications for Collective Intelligence

This study contributes to the collective intelligence literature by
illustrating how a cognitive process at the individual level (i.e., learning
(Sternberg et al., 1982)) can support the collective selection of actors (the
IBSs) that effectively convey information across multiple groups to support
their coordination (Argote, 1982; Wittenbaum et al., 2002). This can be
considered to be collective intelligent behaviour given that the groups are
able to select actors that are more effective than others at carrying out
particular tasks or activities - in this case fostering inter-group
information exchange - thus possibly improving the system’s performance
(groups’ retrieval of the external information needed for decision making and
coordination) (Malone and Bernstein, 2022).

Further, this study illustrates that this collective intelligent behaviour is
contingent upon the characteristics of the environments in which groups
operate (Lawrence and Lorsch, 1967; Duncan, 1979) and specifically its
volatility (characterized by uncertainty and turbulence). When environmental
uncertainty is very high and, as such, information presents unstable
information origins, learning does not lead to a collectively intelligent
behaviour. This effect is reversed when at least some of the information has
as stable origin. Additionally, when the turbulence of the environment is very
high learning produces a collectively intelligent behaviour only for high
levels of inter-group connectivity.

###  8.4 Implications for Information Management

Understanding the learning mechanism and its interplay with environmental
uncertainty, environmental turbulence, and the number of inter-group ties
available can provide useful insights for the design of information management
strategies that foster inter-group information exchange and collective
intelligence in volatile environments. Two main indications for policy can be
drawn from this study respectively related environmental uncertainty and
turbulence.

Concerning environmental uncertainty and the associated stability of
information origin, this research shows that learning increases the number of
IBSs that emerge and the external information they retrieve only in the case
of stable origin. However, in this chaotic and unpredictable world marked by
increasing volatility, the environments in which groups operate are often
characterized by high levels of environmental uncertainty and thus information
with an unstable origin (shocks). As such, effective strategies for managing
this type of information are required to support effective information
exchange across groups that fosters collective intelligence in volatile
environments. If information with an unstable origin can be re-directed to
stable origins which consistently provide it to other actors, this will enable
the actors develop an information collection preference for this source
through learning and more effectively retrieve the external information
needed. Such a change in stability could be achieved by gathering shocks
through crowdsourcing and sharing them widely through a fixed node in the
information exchange network such as an online platform, website, or social
media account (thus establishing a stable information origin) (Holderness and
Turpin, 2015).

With regards to environmental turbulence, a higher number of inter-group ties
was consistently found to be a key element in fostering the emergence of IBSs,
especially at high levels of environmental turbulence and at any level of
environmental uncertainty. To enable the availability of such inter-group ties
it is key to build trusted relationships across groups that can be leveraged
when external information needs to be retrieved by the group from its
environment, also known as bridging social capital (Claridge, 2018). This
aligns with previous research indicating that bridging social capital supports
inter-group information exchange and resilience in volatile settings such as
disaster response (Hawkins and Maurer, 2010; Aldrich and Meyer, 2015; Tasic
and Amir, 2016) and supply chain operations (Pettit et al., 2010; Jia et al.,
2020; Gölgeci and Kuivalainen, 2020). Additionally, this study shows the
importance of the degree of bridging social capital (measured by the number of
trusted inter-group ties available) in facilitating effective information
exchange via emergent IBSs, even amidst high volatility and uncertainty. Thus,
policy interventions should prioritize establishing bridging social capital
through initiatives that build trusted connections among different groups,
such as between communities and professional responders (Norris et al., 2008;
Agger and Jensen, 2015).

###  8.5 Future research

This study focused on theory building by advancing propositions concerning the
emergence of IBSs that effectively convey information across groups in
volatile environments. These propositions are designed based on the
literature, empirically grounded in the case study of disaster response in
Jakarta, and systematically explored through an empirical ABM (Nespeca et al.,
2023). Despite this grounding, the propositions still result from exploratory
research on one case study. As such, generalising the propositions will
require further investigation and testing e.g. via additional case studies and
experiments. Future studies should extend beyond disasters (as in this
research), to include other volatile environments such as supply chains during
rapid market shifts.

Further, this study focused on the emergence of boundary spanners, and was
agnostic to the specific information technology that was used. At the same
time, evidence suggests that information technology can play a key role in
information sharing and the emergence of inter-group information exchange in
volatile environments (Tim et al., 2017) and also interplay with the emergence
of IBSs (Levina and Vaast, 2005; Van Osch and Steinfield, 2016). Such an
interplay, is still poorly understood in volatile environments and requires
further research.

Additionally, agents in this study exhibit non-strategic behavior in
information exchange, lacking consideration for long-term goals or personal
agendas (i.e., they are myopic, cf. Appendix A). However, previous research
indicates that strategic information exchange occurs, for example, to persuade
others to reciprocate with valuable information, to obfuscate or withhold
information, or to spread misinformation to advance personal or organizational
interests (Heavey et al., 2020; Comes et al., 2020; Nespeca et al., 2020).
This strategic sharing can alter recipients’ information collection
preferences and impact the flow of information, thereby influencing the
emergence of IBSs. Future research should investigate how strategic sharing,
combined with learning and adaptation in information exchange preferences,
affects the emergence of effective IBSs.

Next, this study assumes a constant information exchange network, however,
establishing new connections to retrieve relevant information external to a
group is often considered as one of the tasks carried out by boundary spanners
(Ancona and Caldwell, 1990, 1992; Marrone et al., 2007). As such, the network
can also change and develop over time. This is for example the case in the
context of international humanitarian response operations in which, due to the
high staff turnover, few connections across groups enabling inter-group
information exchange are available and new ones need to be established ad-hoc
during the humanitarian response (Altay and Labonte, 2014). Zagorecki et al.
(2009) studies the emergence of inter-group information exchange when enabling
actors to establish connections that decay over time when unused. Their study
finds that these networking activities lead to the emergence of actors that
convey information across groups. However, the focus of their research is
placed on the quantity of information rather than on its quality (e.g.,
relevance of the information exchanged), and it does not measure the emergence
of effective IBSs at the micro level. As such, further research is required to
study the impact of networking activities and contact decay on the emergence
of effective IBSs in volatile environments from the micro level perspective.

Finally, the adaptation of information exchange preferences over time can not
only lead to the emergence of IBSs that facilitate information exchange across
groups but also to the formation of information exchange bubbles that isolate
groups from others leading to fragmentation and a lack of collective
intelligence (Comes et al., 2020). In other cases, fragmentation in the form
of pre-defined functional division of routine tasks (or differentiation) among
different organizations and groups (e.g., police and fire fighters) can be
beneficial for operational efficiency and collective intelligence as it
enables to operate according to pre-established standards and procedures that
require less integration and information exchange (Lawrence and Lorsch, 1967).
Such fragmentation can, however, be lost in volatile contexts as actors and
their groups adapt their activities to a continually and unpredictably
changing environment (Wolbers et al., 2018; Nespeca et al., 2020). In such
situations, inter-group information exchange via IBSs is necessary to
reinstate this fragmentation and support collective intelligence (Wolbers et
al., 2018). Further research is required to study the interplay between the
emergence of IBSs on one hand and the formation of information bubbles,
fragmentation, and collective intelligence on the other.

##  9 Conclusions

In this increasingly chaotic and rapidly-changing world different groups
including governmental and non-governmental organizations, and communities
need to work together effectively while operating in volatile conditions
(characterized by high turbulence and uncertainty). To this end, the prompt
exchange of vital information concerning environmental change across groups is
crucial to support coordination and collective intelligence. This article
aimed to propose a method to measure the emergence of Informational Boundary
Spanners (IBSs) and their effectiveness in fostering inter-group information
exchange. Further, a novel Agent-Based Modeling (ABM) framework was introduced
to systematically study mechanisms that lead to the emergence of IBSs. The
proposed method and ABM are then used to create new insight into one specific
mechanisms that explain the emergence of IBSs in volatile environments: i.e,
learning.

Our results show that learning leads to the emergence of effective IBSs when
the information needed has a relatively stable origin (i.e. it is consistently
provided by the same node in the network). Further, a highly turbulent and
volatile environment can easily lead to informational overload. In this
situation, retrieving and sharing all relevant information needed becomes
challenging. This paper shows that the availability of several contacts (here
20 or more) that can share information across the groups is essential for
facilitating the emergence of more IBSs, which helps distribute the load of
inter-group information exchange and improves the effectiveness of such
exchange. Moreover, when the inter-group contacts are numerous (20 or more),
and the level of environmental turbulence is high (above 10 disruptive events
per day), the performance of IBSs in facilitating inter-group information
exchange is increased with learning.

Implications of this study include the possibility to use the proposed method
and ABM framework to investigate and understand mechanisms for the emergence
of informational boundary spanning through a combination of case study
research and agent-based simulation. Further, in promoting the emergence of
IBSs through learning, actors from different groups exhibit collectively
intelligent behavior by choosing agents that effectively facilitate
information exchange across groups. This collective intelligence is contingent
on the volatility of the environment and requires stable sources of
information and a high density of inter-group ties to be effective. Finally,
policy implications of this research consist of the need to (a) collect and
summarize information from unstable origins (e.g., via crowdsourcing) and
release such information from stable sources so that agents can learn where to
find the information they need and (b) build and maintain trusted connections
among groups to ensure collectively intelligent behaviour and effective inter-
group information exchange, and support coordination and collaboration even
for high levels of volatility.

Further research will focus on investigating the interplay between the
emergence of boundary spanning, learning, and the use of information
technology, strategic information exchange behaviour (e.g. spread of
misinformation, obfuscation, and persuasion to share back), and the formation
of information exchange bubbles and fragmentation.

##  10 Acknowledgements

The authors thank Dr. Vìtor V. Vasconcelos for his helpful suggestions.

##  11 Funding

This work was partly funded by the COMRADES project Grant agreement No 687847,
under the EU’s Horizon 2020 research and innovation programme.

##  12 Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the
research, authorship, and/or publication of this article.

Figure 10: Experiment 1: comparison of the number of emergent IBSs obtained
with different thresholds ranging from the 30th (first figure on the left) to
the 80th (last figure on the right) percentiles for the two information
collection mechanisms LN (LearNing) and RC (Random Collection).

## Appendix A: Learning Mechanism

To implement the learning mechanism introduced in the section ”Mechanisms for
the emergence of informational boundary spanners” and mentioned in Proposition
2 this study relies on a reinforcement learning algorithm. Specifically,
Q-learning (Watkins, 1989; Watkins and Dayan, 1992) was chosen given it
enables agents to develop information collection preferences over time through
a series of information collection activities, as introduced in Proposition 1.
The following formula is used to update the expected reward resulting from
collecting information from each of the agents’ contacts.

$Q(s_{t},a_{t})\leftarrow(1-\alpha)\cdot Q(s_{t},a_{t})+\alpha\cdot
R(s_{t+1},a)$ (1)

Where:

  * •

$Q(s_{t},a_{t})$ = expected reward for the action a (collecting information
from a particular contact) at a given observed state of the environment
(responding to a disaster). In practice, Q represents the extent to which the
agent expects that a particular contact will provide information that can
address its information needs.

  * •

$\alpha$ = learning rate determining the relative importance of the quality of
the new information provided by contacts compared to the quality of the
information provided so far by the contacts.

  * •

$R(s_{t+1},a)$ = actual reward obtained by the agent through carrying out the
information collection action $a$ given its information collection state $s$.
In this study, this reward is $1$ when the collected information addresses the
collecting agent’s information needs, and $0$ otherwise.

The agents are assumed to be myopic, meaning that they do not consider the
strategic pursuit of long-term high rewards. Rather, the agents simply
consider current rewards in their learning process. As such, the value of the
discount factor is equal to 0 (and thus not displayed in the equation above).

An agent’s information collection preferences are represented by the
probabilities of the agent choosing each of its contacts as its information
collection source. Such probabilities are computed for each contact as the
ratio of the Q value associated with the contact, divided by the sum of all Q
values associated with all of the agent’s contacts. As such, a higher Q value
(expected reward) compared to other contacts, entails that the agent will be
more likely to choose such contact among the others when collecting
information.

## Appendix B: studying emergent IBSs with different thresholds

Experiment 0 showed that multiple thresholds enable to individuate IBSs
candidates that significantly contribute to inter-group information exchange,
thus qualifying as emergent IBSs. Further analysis is needed to determine if
such different thresholds yield the same results in the study of IBSs
emergence. In this case, providing the same results means that the conclusions
regarding IBSs emergence remain the same, i.e. the propositions remain
supported by experimental results independently from the thresholds adopted.

In this appendix, the data from Experiments 1 to 3 is analyzed through six
different thresholds deemed adequate to capture emergent IBSs, namely the
30th, 40th, 60th, 70th, and 80th percentiles in the FEs distribution (cf.
Experiment 0 - Results Section). The following paragraphs compare the results
obtained with these thresholds for each experiment. The appendix considers
only the number of emergent IBSs and not their effectiveness in fostering
inter-group information exchange. This is because IBSs effectiveness is
independent from the threshold adopted.

Figure 10 shows the results of Experiment 1 and illustrates a comparison
between the influence of LN compared to RC on the emergence of IBSs when
adopting different thresholds. Despite quantitative variations, LN
consistently produces more IBSs than RC, thereby supporting Proposition 1
regardless of the threshold used.

Figure 11: Experiment 2: comparison of the number of emergent IBSs obtained
for LearNing (LN) and Random Collection (RC) with the 30th, 40th 50th, 60th,
70th, and 80th percentiles (each represented by one row) and different numbers
of stable and unstable information becoming relevant for the groups during
each day of simulation (captured in the three columns). While the composition
is different, the total number of daily relevant information remains constant
at 20 pieces of information per day.

Figure 11 presents the results of Experiment 2, comparing the number of
emergent IBSs observed with different thresholds for RC and LN when varying
the stability of the information origin. In the figure, each row represents
the results obtained with one threshold, while the columns represents varying
levels of stability, namely stable (only announcements), a combination of
unstable and stable (both announcements and shocks), and unstable (only
shocks) information. As can be observed by comparing the figures in each row
from the from left to right, an increasing number of shocks (unstable
information origin) compared to the number of announcements (stable
information origin) reduces the impact of learning on fostering the emergence
of more IBSs. This observation supports proposition 2 and holds across all
thresholds.

Further, with only unstable information (right column), learning minimally
impacts the number of emerged IBSs, with effects varying by threshold. From
the 40th to the 70th percentiles, LN has no significant influence on IBS
emergence. However, the lowest and highest thresholds (respectively the 30th
and 80th percentiles) produce different and conflicting results. Precisely,
with the 30th percentile, LN increases IBS emergence, but with the 80th
percentile, this effect reverses. In this case, these discordant results are
considered outliers and disregarded for two reasons. First, they lead to
opposite conclusions, likely because they are the most extreme among those
found to be adequate. Second, all of the other thresholds (four out of six)
consistently produced similar results, confirming that the discrepancies
observed with the 30th and 80th percentiles are due threshold selection rather
than experimental data. Consequently, results from the 30th and 80th
thresholds are excluded. The remaining findings from the 40th, 50th, 60th, and
70th percentiles consistently indicate that learning has no impact on the
emergence of IBSs with unstable information origins, supporting Proposition 2.

Figure 12: Experiment 3: comparison of the number of emergent IBSs obtained
with LearNing (LN) and Random Collection (RC) for the 30th, 40th, 50th, 60th,
70th, and 80th percentiles, different levels of Turbulence, and numbers of
Inter-Group Ties (# IGTs).

Finally, Figure 12 presents the results of experiment 3 and shows a comparison
in the number of emergent IBSs with LN and RC for varying levels of
environmental turbulence and inter-group ties. This figure illustrates that
for all thresholds the number of IBSs emerged grows with the number of inter-
group ties and the level of environmental turbulence. Further, the number of
IBSs emerged is not significantly affected by the information collection
mechanism adopted. These findings support proposition 3 and are evident
independently from the threshold adopted.

This appendix demonstrates that using various adequate thresholds, as
established in Experiment 0, leads to consistent conclusions across
Experiments 1 to 3, supporting Propositions 1, 2, and 3 regardless of the
threshold used. It highlights the importance of comparing and assessing the
consistency of findings across different thresholds when using the method to
study the emergence of IBSs. This is necessary as, in specific instances like
the 30th and 80th percentiles in Experiment 2, different thresholds may yield
conflicting results. Such discrepancies can lead to reconsider and revise
conclusions regarding the emergence of IBSs. In this case, the discordant
results with the 30th and 80th were considered outliers and disregarded given
their extreme values and inconsistent results with the majority of the other
thresholds. Therefore, the conclusions of Experiment 2 remained unchanged.

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