An Ising-based dynamic model to study the effect of social interactions on firm absorptive capacity

Author’s Accepted Manuscript An Ising-based dynamic model to study the effect of social interactions on firm absorptive capacity Ilaria Giannoccaro, Giuseppe Carbone

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S0925-5273(17)30140-8 http://dx.doi.org/10.1016/j.ijpe.2017.05.003 PROECO6708

To appear in: Intern. Journal of Production Economics Received date: 22 April 2016 Revised date: 5 May 2017 Accepted date: 7 May 2017 Cite this article as: Ilaria Giannoccaro and Giuseppe Carbone, An Ising-based dynamic model to study the effect of social interactions on firm absorptive c a p a c i t y , Intern. Journal of Production Economics, http://dx.doi.org/10.1016/j.ijpe.2017.05.003 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

An Ising-based dynamic model to study the effect of social interactions on firm absorptive capacity

Ilaria Giannoccaro*, Giuseppe Carbone

Department of Mechanics, Mathematics, and Management, Politecnico di Bari, Viale Japigia 182, Bari, Italy

[email protected] [email protected]

*

Corresponding author.

Abstract We present a dynamic model of firm absorptive capacity, which is consistent with a processoriented conceptualization and based on the teaching-learning approach, to investigate the effect of social interactions among the firm members on the firm absorptive capacity. In particular, two main learning processes are considered: the explorative and the transformative learning. To develop the model, the Ising approach, which is a very well established framework to study the dynamics of social interactions, is employed. Furthermore, a simulation analysis is carried out to investigate the effect of two patterns and four levels of social interactions on the firm absorptive capacity. Results show that block-diagonal patterns, where interactions occur inside groups and not between groups (such as in modular organizations), lead to higher absorptive capacity, compared to hierarchical patterns (e.g., those exhibited by centralized organizations). We also show that the relationship between the level of social interactions and the firm absorptive capacity follows an inverted-U shape in the block-diagonal patterns, while the absorptive capacity decreases as the level of interactions

1

rises, in the hierarchical patterns. Finally, we find that the social network also plays a moderating role on the relationship between the complementary knowledge and the firm absorptive capacity.

Keywords: Absorptive capacity, learning processes, social interactions, social networks, complementary knowledge, Ising-based model, simulation.

1.

Introduction

The absorptive capacity is a critical factor for firm competitive advantage. The first conceptualization of the construct traces back to Cohen and Levinthal (1990), who define the absorptive capacity as the firm ability to identify, assimilate, and exploit new knowledge from the environment. More recently, the construct has been re-conceptualized adopting a processoriented perspective. In this respect, the absorptive capacity is viewed as a dynamic capability, which follows from three different learning processes: 1) the explorative learning, 2) the transformative learning, and 3) the exploitative learning (Lane et al. 2006). The basics of this re-conceptualization consist in recognizing the dynamic nature of the absorptive capacity, which develops cumulatively over time and is path dependent, and in stressing that the absorptive capacity cannot be disentangled from the systems, processes, and structures of the organization (Sun and Anderson 2008). For this reason, this approach is particularly valuable to understand the internal drivers of the absorptive capacity and, in particular, to analyze the role of social capabilities, an issue that is not adequately addressed in the literature (Hotho et al. 2012). Previous studies on the determinants of the absorptive capacity have analyzed both external and internal factors, such as the features of the external knowledge, the complementarity between the prior knowledge and the new knowledge, the firm organizational structure, the firm combinative, coordination, and social capabilities (Cohen and Levinthal 1990, Van den 2

Bosch et al. 1999, Jansen et al. 2005, Lane et al. 2006, Zahra and George 2002). However, despite the use of a process-oriented approach, there is a lack of studies on the role played by the social interactions occurring among firm members on the development of firm absorptive capacity, with few notable exceptions (Zahra and George 2002, Reagans and McEvely 2003, Jansen et al. 2005, Hotho et al. 2012). Since the social interaction is the basic mechanism for knowledge transfer among the individuals, it plays a critical role in affecting the firm absorptive capacity. Despite some studies recognize this point as being important, they focus on the knowledge transfer among firms. For example, Tsai (2002) finds that the level of social interactions among the organizational units of a firm favors the knowledge transfer. He also shows that the network position of the organizational unit and, in particular, its centrality is a critical aspect to acquire new knowledge (Tsai, 2001). Dhanaraj et al. (2004) show that tie strength, trust, and shared values enhance the knowledge transfer between the foreign parent and the international joint ventures. In a similar way, we argue that the network of the social interactions involving the firm members during the learning processes influences knowledge transfer among them and, consequently, the firm absorptive capacity. Learning is indeed a social process: groups of individuals collectively learn and influence the way the new knowledge is assimilated inside the firm (Sun and Anderson 2008). In this respect, the influence of the social pattern and the level of social interactions on the firm absorptive capacity remains unclear. The pattern of social interactions identifies “who interact with whom”. For example, individuals can be arranged in small isolated groups, where social interactions only occur among the members of the group and not between the groups. Alternatively, social interactions may follow a hierarchical pattern, where only a few members have a high number of social interactions (hubs), whilst most of them have only a small number of connections with the other members of the network. Since the social pattern 3

affects the knowledge transfer (Uzzi 1997, Hansen 1999, 2002), it follows that the social pattern should also influence the firm absorptive capacity. However, to the best of our knowledge, this aspect of the problem has not been yet analyzed in the scientific literature. Social interactions among firm members differ in the extent to which the members interact one with each other. Zahra and George (2002) show that the density of social interactions affects the firm absorptive capacity. Similarly, Hotho et al. (2012) highlight the importance of the strength of social relationships in enhancing the learning and knowledge transfer. We are also interested in investigating how the number of social interactions, activated by the firm members, influences the learning processes, thereby affecting the firm absorptive capacity. To accomplish our research aims, we develop a dynamic model of the firm absorptive capacity, which reproduces the explorative and the transformative learning, leaving out the exploitative learning. We adopt a teaching-learning process approach (Lane and Lubantik 1998), where each single learning process is conceptualized in terms of learning pairs involving social interactions. The explorative learning is associated with the teacher (external knowledge source) - student (firm member) learning pair and the transformative learning is associated with the student (firm member) - student (firm member) learning pair. In each learning pair, the knowledge transfer is favored by the social interaction between the agents involved. Two social networks are thus defined: 1) the network made up of the social links between the external knowledge source (teacher) and the firm members (students) and 2) the network consisting of the social interactions among the firm members (students). We selected the Ising approach as the basic framework wherein our model could be developed. This choice lays on several reasons. The Ising methodology has been successfully employed in social science, economics, and management science, to model the complex dynamics of opinion formation inside groups, by considering that each individual opinion is affected by the opinion of his/her neighbors (Bordogna and Albano 2007a, 2007b, Zhou and Sornette 2007, Stauffer 2008, Sornette 2014, Carbone and Giannoccaro 2015). The Ising 4

framework has been also applied to model the teaching-learning process and study the efficacy of the knowledge transfer from the teacher to the students (Bordogna and Albano 2001). In the latter case, students (likewise magnetic spins) change their level of knowledge (direction) as the result of the social interactions with the teacher and the other students in the classroom. In all applications, the basic patterns of the system behavior are driven by the interactions among the agents and described by the laws of statistical physics (Braha and BarYam 2007, Oh and Jeon 2011). The main reason for applying statistical physics to the domain of human interactions relies on social influence theory (Bordogna and Albano 2007, Oh and Jeon 2011). This theory argues that social influence is the process by which individuals make real changes to their feelings and behaviors, as a result of the interaction with the others. The Ising approach is, thus, very suitable in our case, as the main theoretical assumption of the present study is that the fundamental dynamics of the firm absorptive capacity reside in the learning processes accomplished by individuals through social interactions. Furthermore, the Ising approach is very well suited also to reproduce the main building blocks of

the

absorptive

capacity,

according

to

the

aforementioned

process-oriented

conceptualization. This approach is able to capture the complex dynamics of firm absorptive capacity and study it as an emergent, non-linear, path-dependent, and bottom-up process, thus permitting to shed light on the micro-level origin of the absorptive capacity, which, as noticed in the scientific literature (Hotho et al. 2012), is a crucial point to be further investigated and clarified . The Ising-based model of the firm absorptive capacity is employed to carry out a simulation analysis, aimed at investigating the influence of the interaction pattern and level of interaction on the firm absorptive capacity, the latter being measured in terms of the average level of firm members’ knowledge.

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Results provide important contributions to the literature. First, we complement previous studies adopting a process-oriented conceptualization by recognizing that social interactions among firm members are an important driver of firm absorptive capacity. Secondly, we find that the absorptive capacity is higher when social interactions occur only inside isolated groups and not between groups, compared to social patterns where interactions occur following a hierarchical pattern. Furthermore, we show that, depending on the specific pattern of interactions, the level of social interactions may influence the firm absorptive capacity. We also find that the network of the social interactions plays a moderating effect on the relationship between the complementary knowledge and the absorptive capacity. The paper is organized as follows. First, we present the theoretical background of the paper: we briefly review the concept of the absorptive capacity and its main determinants. Then, we describe the dynamic model of the firm absorptive capacity based on the Ising methodology. Afterwards, we present the simulation analysis carried out to answer our research questions and we discuss the simulation results. We end with conclusions and limitations of the study.

2.

Theoretical background

2.1 The concept of absorptive capacity The absorptive capacity is an elusive concept. Despite the great deal of research in the field (Lane et al. 2006 counts 900 peer-reviewed papers on the topic), a clear definition is still lacking. Cohen and Levintal (1990) in their seminal paper define the absorptive capacity as the collective firm ability to identify, assimilate, and exploit knowledge from the environment. Lane and Lubantik (1998) introduce the concept of learning dyad, distinguishing between the firm and the external knowledge source. Dyer and Singh (1998) emphasize the relational aspect of the absorptive capacity. Zahra and George (2002) reconceptualize the absorptive capacity in terms of organizational routines and organizational 6

processes, to produce a dynamic organizational capability. This dynamic conceptualization recognizes the multiple levels of learning and the path-dependent nature of absorptive capacity. Zahra and George (2002) also distinguish between potential and realized absorptive capacity. The former refers to firm’s capacity to identify and acquire external knowledge. The latter, instead, refers to the capacity to transform and exploit the knowledge for commercial purposes. Lane et al. (2006) identify the learning processes associated with the absorptive capacity. In particular, three sequential processes are defined: 1) the explorative learning, by which a potentially valuable new external knowledge is recognized and understood, 2) the transformative learning, by which the new knowledge is assimilated, and 3) the exploitative learning, by which the assimilated knowledge is used to create new knowledge. Lewin et al. (2011) make a further distinction between the internal and external dimensions of the absorptive capacity, consistent with a routine-based approach. They note that the literature has emphasized more the role of exploration of knowledge in the external environment, while almost neglecting the role of internal exploration of knowledge (new knowledge creation) and its assimilation. In this paper, we adopt the process-based conceptualization by Lane et al. (2006), which is more coherent with our research aim, i.e., to study the effect of social interactions among firm members on the firm absorptive capacity. This in fact requires considering the firm absorptive capacity as a dynamic construct, which evolves over time driven by the social interactions underlining the learning processes. Furthermore, we focus only on two learning processes: 1) the exploratory learning by which new knowledge is assimilated from the external environment and 2) the transformative learning by which the firm members assimilate the external knowledge. In fact, since our level of analysis regards individuals and social interactions among them, we only consider the learning processes occurring at individual and group levels, leaving out the exploitative learning that takes place at firm level (Sun and 7

Anderson 2010). Note that this choice is consistent with the ambidexterity nature of organizational learning, being it captured by the transformative learning, as observed by Lane et al. (2006).

2.2 The determinants of absorptive capacity The studies on the firm absorptive capacity identify a variety of factors that influence it. These determinants are linked with the specific conceptualization adopted. The static conceptualization of the absorptive leads to emphasize the role of those factors that are external to the firm, such as the characteristics of the environment and the knowledge features. The process-oriented conceptualization highlights the role of internal variables, such as the firm organizational structure, its strategy, the mental model of the individuals, and the social context. Cohen and Levinthal (1990) focus on the knowledge source and the prior knowledge. To foster the development of the absorptive capacity, the prior knowledge should be complementary to the new knowledge (Lane and Lubatkin 1998). This means that the new knowledge should be related to, but significantly different from, firm’s existing knowledge base. Zahra and George (2002) analyze the effect of the exposure to the external knowledge: the greater the exposure to complementary external knowledge, the higher the absorptive capacity. Past experience is also shown to influence the locus for search of new knowledge (Zahra and George, 2002). Activation triggers such as crises, radical innovations, and changes in the industry moderate the relationship between the knowledge source and the development of absorptive capacity. Lane et al. (2006) emphasize the role of the characteristics of knowledge, distinguishing between tacit and explicit. As to the internal factors, some studies have analyzed how the mental models and the cognitive schemes of the individuals affect the creativity of the process of search, 8

assimilation, and exploitation of new knowledge, thereby influencing the absorptive capacity (Hotho et al., 2012). The effect of the organizational form on the development of the absorptive capacity is studied by Van den Bosch et al. (1999), who compares functional, divisional, and matrix forms. Jansen et al. (2005) and Gebauer et al. (2012) highlight the important role of the combinative capability. They find that coordination capability, such as cross-functional interfaces, jobrotation practices, training, lateral communication systems, and system capability (e.g. directions, manuals, procedures used to integrated external knowledge) enhance the absorptive capacity. Despite the increasing number of studies adopting the process-oriented conceptualization, a very limited number of studies has analyzed the role of the social capabilities and, in particular, of the social interactions among the firm members on the development of firm absorptive capacity. Since the social interaction is the basic mechanism by which learning occurs, we argue that it plays a critical role in influencing the firm absorptive capacity. Zahra and George (2002) show that social capability, such as the density of social interactions, influences the realized absorptive capacity. Reagans and McEvely (2003) investigate the effect of network structure on knowledge transfer. They also show that strong ties, social cohesion, and network range favor the ease of knowledge transfer. Hotho et al. (2012) find that the difference in the firm capacity to absorb and apply new knowledge can be explained in terms of difference in social interaction features, such as social cohesion, the extent (or scale) of interaction and the diversity (or scope) of interacting firm members. In this study, we analyze the effect of social interactions in deeper detail.

3.

The teaching and learning process model of firm absorptive capacity

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Applying the teaching-learning process approach to the study of the firm absorptive capacity is not new. Lane and Lubantik (1998) proposed a model of absorptive capacity, where the firm is seen as a student and the external firm is seen as a teacher. Our approach however differs from this one in two respects: 1) we consider a diverse unit of analysis shifting from the firm to the firm member and 2) we distinguish two types of learning pairs, i.e., the teacher–student and the student-student pairs. The teacher stands for the external knowledge source, e.g., a firm, a research center, or a university. The student stands for the firm member. The teacher-student learning pairs are involved in the explorative learning; the student-student learning pairs are involved in the transformative learning. The learning occurs by means of the social interactions established by the learning actors. Thus, a social network is defined, where nodes are the knowledge source and the firm members and the links are the social interactions, for each learning process. We describe these social networks in the next. 3.1 The social networks In our model we consider that the firm is made up of N members (nodes) (Figure 1). They discover and recognize a new knowledge from an external knowledge source (external node), through social interactions they set up with the external knowledge source (red links). These social interactions concern the teacher-student learning pairs. The firm members also interact one with each other (blue links). By means of these social interactions, the new knowledge is assimilated inside the firm. These social interactions involve the student-student learning pairs. Thus, two social networks can be distinguished: 1) the red one corresponding the explorative learning and 2) the blue one corresponding to the transformative learning. Both the social networks can be characterized by means of network attributes. In particular, we characterize them by using the pattern and the level of interactions. The pattern describes “who interacts with whom” and is related to the distribution of links across the network. Different patterns are distinguished in the literature, such as the random (Erdos and Renyi, 1959), the small-world (Watts 1999, Uzzi and Spiro 2005), the scale-free (Barabasi and 10

Albert 1999, Barabasi and Bonabeau 2003), and the block-diagonal patterns (Siggelkow and Rivkin 2007). The level of interactions consists in the average number of links of each node and is related to the network density. The higher the level of interactions, the higher the density. How do the pattern and level of social interactions affect the learning processes, thereby influencing the firm absorptive capacity? To answer this question, we develop a dynamic model, based on the Ising approach, which reproduces the learning processes.

3.2 The main contextual variables Three main contextual variables influence the efficacy of teacher-student and student-student interactions in terms of learning outcome: the use of information technology systems, the level of complementary knowledge, and the social cohesion. We describe them in details in the next. Information Technology Systems The study of absorptive capacity, focusing on learning processes favored by social interactions, needs to take into proper consideration the role played by modern information technologies (ITs) and, in particular, IT knowledge systems. They in fact enable the processes of inter- and intra-knowledge sharing. Firm members improve their computational and communication abilities by using IT systems, thus enhancing the efficacy of learning processes and, in turn, the firm absorptive capacity (Malhotra et al. 2005, Roberts et al. 2012). Roberts et al. (2012) classify IT systems in three groups based on the IT capabilities they support, i.e., outside-in, scanning, and inside-out capabilities. They show that outside-in IT systems, such as web-platforms, utilized to collect and share knowledge, facilitate the identification of a new source of external knowledge. Spanning systems, such as enterprise resource planning and knowledge management systems, give support to individuals in storing, archiving and retrieving knowledge, thereby improving their ability to assimilate and 11

transform the external knowledge. Finally, inside-out ITs enhance the application of external knowledge in new products and processes. Since in modern organizations the use of IT systems cannot be ignored, we consider that individuals involved in both teacher-student and student-student social networks make use of IT knowledge systems, so that the efficacy of explorative and transformative learning is enhanced. Complementary knowledge Complementary knowledge refers to a new external knowledge that is related to, but significantly different from, firm’s existing knowledge base (Lofstrom 2000, Tanriverdi and Venkatraman

2005). Hitt et al. (2001) highlight the non-overlapping feature of

complementary knowledge. Fang (2011) focuses on the level of redundancy. The main feature of complementary knowledge is a low level of redundancy accompanied by a good level of similarity. The key issue is that complementary knowledge increases the efficacy of explorative learning. A certain level of similarity is needed to absorb the external knowledge. Individuals should have a basic understanding of the new knowledge to evaluate the importance of the knowledge itself and activate learning (Lane and Lubatkin 1998). Furthermore, individuals find it easier to absorb new knowledge belonging to the same expertise, than new knowledge outside of their area of expertise (Reagans and McEvily 2003). At the same time, too high redundancy limits knowledge transfer because there is no opportunity to learn. On the contrary, large diversity makes learning ineffective, because it prevents the mutual understanding from occurring and enhance misconception and misinterpretation (Noteboom et al. 2007). Based on the above, we include complementary knowledge in our model as a contextual variable influencing the efficacy of the explorative learning. Social cohesion

12

Cohesion in social relationships is crucial in promoting knowledge transfer among individuals. Cohesion influences the willingness of a firm member to share knowledge with a colleague. The higher the cohesion promoted by cooperative norms, trust behaviors, and reputation norms, the higher the propensity of individuals to collaborate and interact one with each other. This situation reduces the conflict and the competition, enhancing the efficacy of the learning. Conversely, when social cohesion is low, firm members are less prone to transfer knowledge, and their behavior becomes more random (Reagans and McEvily 2003). Thus, we include, in our model, the social cohesion as a contextual variable influencing the efficacy of transformative learning. Figure 2 summarizes the main variables and relationships among them.

4. The Ising-based model of the firm absorptive capacity The Ising model describes how a group of individual agents tends to point in a common direction (behavior). It is originally developed in physics, but counts a large number of applications in social science (Borgogna and Albano 2007a, Castellano et al. 2009). In particular, it has been employed to model the social behaviors of economic agents in financial markets (Zhou and Sornette 2007, Sornette 2014), to analyze social opinion formation process (Borgogna and Albano 2001, 2007b), to study herding dynamics in open source software communities (Oh and Jeon 2007), and to reproduce and analyze the mechanisms of decision making in human groups (Carbone and Giannoccaro 2015). In all these cases, the way in which those systems evolve is described using tools and concepts from statistical physics. In its original formulation, the Ising model is applied to study the phase transition of a collection of magnetic spins from a chaotic (paramagnetic state) to an ordered (ferromagnetic) state, the latter being characterized by all spins taking the same direction (+1 or -1). For more details, see Appendix 1.

13

In order to model the teaching-learning process among the firm members and between the firm members and the external knowledge source, we adopt an approach belonging to the class of generalized Ising models that resembles the one proposed by Borgogna and Albano (2001). Here, a classroom of students (spins) learn new knowledge from an external knowledge source, i.e. the teacher. It is also allowed that the students can learn one from each other, when they work in group. Individuals are arranged in small groups where they fully interact one with each other. The knowledge is transferred by means of the social interactions. Each individual is exposed to a cognitive impact resulting from the interactions with the teacher (CITS) and the other students (CISS). In the sequel, we describe how this teaching-learning approach is applied to model how the firm absorptive capacity evolves. In particular, we consider the external knowledge source as the teacher that possesses the new knowledge the firm members (students) should learn. This new external knowledge is recognized by the firm members through the social interactions they establish with the external knowledge source (explorative learning). This new knowledge is assimilated by the firm members by means of the social interactions occurring among them (transformative learning). The learning processes are modelled by means of cognitive impacts received by the individuals. Thus, similarly to Borgogna and Albano’s model, each firm member receives two types of cognitive impacts: one exerted by the teacher and the other applied by the other firm members.

4.1 The cognitive impact on the firm member The total cognitive impact

on the individual j is made up of two components: 1) the

cognitive impact of the teacher (CITS) and 2) the cognitive impact of the other student (CISS). The Teacher-Student learning pair (explorative learning) The cognitive impact that the teacher T has on the individual j at the time t, defined as follows: 14

is

[

where

is the teacher knowledge (

time , and

]

,

(2)

is the knowledge of the individual

at

is the degree of exposure to the external knowledge by the individual j. As

mentioned in the Theoretical Background Section, the exposure to external knowledge is shown to affect the transfer of external knowledge (Cohen and Levinthal 1990, Zahra and George 2002, Fosfuri and Tribò 2008). In this respect the appropriability regimes plays an important role. If the protection regime is strong, firms tend to patent extensively, thereby contributing to generate comprehensive and accessible exposure to high quality and codified external knowledge source. This, in turn, increases the knowledge transfer. Conversely, under a regime of weak property rights protection, firms are prone to protect their innovation by decreasing the amount and the quality of information disclosed to other firms, thereby reducing the knowledge exposure. In such a case, secrecy is recognized as the most preferred mode to protect against imitation (Escribano and Fosfuri 2009). Based on this theoretical argumentations, we set EjT = ET for all firm members j, with ET assuming a high (low) value in case of a regime of strong (weak) protection. We set

. Notice that

is minimal for

, as it corresponds to the impact

between two individuals having the same (maximal) knowledge. In this case, is maximal for case

and

.

, due to the largest difference in the knowledge. In this

.

The Student-Student learning pair (transformative learning) The cognitive impact that the other students exert on the individual j, follows: 15

, is defined as

∑ {{

[

]

[

]}

}

(3)

where N is the number of firm members. The first term is referred to the mutual persuasiveness and the second term to the mutual support (Bordogna and Albano 2001, 2003). Both of them are critical features affecting social influence (cognitive impact) in groups. The mutual persuasiveness is important when the group involves charismatic individuals, who persuade the others to follow their opinion. The mutual support, consisting in the extent to which individuals involved in a social network help and support one with each other, is a critical feature in collaborative social networks (Hoegl and Gemuenden 2001). We consider that mutual support is expected to be larger when the interacting individuals have similar knowledge ( opposite case (

). Mutual persuasiveness plays a more relevant role in the

). Similarly to Bordogna and Albano (2003), the persuasiveness

(support) of individual i on the individual j is so defined:

(4)

(5)

where

and

are intrinsic individual factors and depend on the strength of psychological

coupling, affinity of social status, education, and personal skills. The term

means

that both the persuasiveness and support between the individuals could be either reinforced or weakened by taking the knowledge of the teacher as a reference level (Bordogna and Albano, 2001). The term

accounts for fact that an individual with knowledge lower 16

than the average (

) has a limited possibility to produce an increase of knowledge,

compared to an individual with knowledge higher the average the individual with knowledge higher than the average (

. In the opposite case,

) has great possibility to cause

an increase of knowledge.

4.2 The evolution of the firm member knowledge over time The knowledge of the individual j,

is defined as a dynamic variable evolving over time

due to the influence played by the total cognitive impact CIj acting on the individual j. The change in the level of knowledge is modelled by defining the quantum of knowledge, After a time interval

, the knowledge of the individual j changes according to the following

rule:



,

with probability

(6.1)



,

with probability

(6.2)

The probability

is so defined: ,

where

.

(7)

is the generalized Metropolis rate (Springer-Verlang and Heidelberg 1987) equal to:

(8)

17

The terms

and

are the levels of noise (i.e., the environmental temperature)

characterizing the social interactions. They model the contextual variables influencing the absorptive capacity, i.e., the adoption of IT systems, the level of complementary knowledge, and the level of social cohesion. As discussed in Section 3.2, the adoption of IT systems is argued to affect both the explorative and the transformative learning, while the complementarity of knowledge and the level of social cohesion positively influence the explorative and the transformative learning, respectively. High (low) values of the parameters β correspond to a high (low) likelihood of effective knowledge transfer among individuals. As to the level of social cohesion, it is worth to note that we will compare in the simulation analysis social networks differing in the level of social interactions (K), but characterized by the same level of social cohesion. However, social cohesion is affected by the extent of social interactions and, in particular, the higher the social interactions, the higher the social cohesion (Granovetter 1973). Therefore, in order to guarantee that the social networks, which will be compared to each other, have the same level of randomness associated with the social cohesion, the parameter

is set so as to satisfy the following rule:

(9)

where SC is the level of social cohesion inside the social network and K is the average number of social interactions per firm member. The system dynamics, i.e. the evolution of the level of knowledge of the firm members, are simulated as described by the following steps: 1. Compute the cognitive impacts CITS and CISS on the individual j; 2. Compute the probability

;

18

3. Generate a random number (rand), drawn at random from a uniform distribution [0, 1]. 4. If

, Then

; Otherwise,

.

5. Repeat steps 1-5 for all N individuals and for T times. For more details about model simulation, see Appendix 2.

5.

Simulation analysis

We perform a simulation analysis aimed at analyzing the effect of the social network structure (pattern and level of interactions) on the development of the firm absorptive capacity. The analysis is also used to identify the possible moderating effect of the social network on the relationship between the complementary knowledge

and the absorptive capacity.

We consider a firm with N=96 individuals interacting among each other. In this study we prefer to fix the social network associated with the explorative learning and to change only the features of the social network associated with the transformative learning. In particular, as to the explorative learning, we consider that all firm members interact with the external knowledge source (see Figure 3a-b). As to the transformative learning, the social network is assumed to be characterized by two types of interactions patterns: 1) the block-diagonal and 2) the hierarchical patterns. In the block-diagonal pattern (Figure 3a), the firm members are grouped so as to guarantee that, while the individuals belonging to each block (i.e., group) interact one with each other, no interaction occurs among the individuals belonging to different blocks. This social interaction pattern is shown, for example, by firms adopting a modular organization, characterized by firm members grouped in completely autonomous teams (Ethiraj and Levinthal 2004, Siggelkow and Rivkin 2007, Capaldo and Giannoccaro 2015a, 2015b). In the hierarchical pattern (Figure 3b), the node distribution connectivity

19

follows instead a power law1. This means that there are a few nodes (individuals) with a high number of interactions (called hubs) and many others with few connections (Barabasi and Albert 1999). This hub and spoke social pattern is displayed, for example, in centralized organizations, where there are a few central decision makers interacting with a high number of individuals, which, on the contrary, share only a few connections among each other. We also consider that the social network associated with the transformative learning can assume four increasing levels of interactions (K = 2, 3, 5, and 7). This means that each firm member has exactly K interactions with the other members in the block-diagonal pattern and on average K interactions in the hierarchical pattern. Summarizing, in total we simulate eight social interactions structures (2 patterns x 4 levels of interactions). We also replicate all simulations for increasing values of βTS. At the beginning of simulation, a prior knowledge is assigned at each firm member, drawn at random from a uniform distribution [-0.5, 0.5]. On average, the prior knowledge of the firm member in the organization is thus equal 0. Successively, the development of the knowledge of the individuals in the firm is simulated. We measure the average knowledge of the individuals at the end of the simulation period, as proxy of the firm absorptive capacity. Simulation parameters are set according to Bordogna and Albano (2001) and shown in Table 1. The simulation time is set to 200 steps, large enough to assure that simulations reach a stationary state (except in the case of one single hierarchical pattern that never reaches the stationary state). Each simulation is replicated 100 times. The results are averaged over the 100 replications. The model was coded using the software Mathematica by Wolfram 6.

Results

6.1 The effect of the social network on the firm absorptive capacity

1

We used the Barabasi-Albert preferential attachment model to generate the hierarchical network. The exponent  of the power law p(k) = k  is set equal to 3.

20

Results are shown in Table 2, where the average knowledge of the firm members at the end of simulation is reported for four levels of interactions and two networks structures, i.e., the block-diagonal and hierarchical patterns. First, we analyze the effect of social pattern on the average knowledge of the firm members. We compare the performance achieved in the case of block-diagonal and hierarchical patterns, given the level of interactions (K) and the complementary knowledge ( independent of K and

. Notice that,

the average level of knowledge is always higher in the block-

diagonal pattern than in the hierarchical one. We computed the performance differences obtained over the entire set of couples of values K and

(significance tested by means of a

t-test with α=0.1). The results show that block-diagonal pattern develops higher knowledge than the hierarchical one. In the hierarchical pattern, in fact, there are many members with a small number of interactions and few members with high levels of interactions. These individuals play a critical role in the learning process. They exert a cognitive influence on a large number of individuals in a way similar to the teacher. Because of this substantial influence, they contrast the effective assimilation of teacher’s knowledge, driving the transformative learning process on the wrong way by self-supporting one with each other. Thus, the resulting effect on the development of knowledge is negative. The block-diagonal pattern, instead, exhibit a different behavior. In such a case, no individual has the necessary high number of social interactions to play a central role in the learning process and inhibit the diffusion of teacher’s knowledge. As a result, in the block-diagonal pattern the average knowledge of the individual is higher than in the hierarchical pattern. As to the effect of the level of interactions, two different trends can be identified (see Figure 4). In the block-diagonal pattern, the average knowledge of the individuals first slightly increases as the level of interactions moves from K=2 to K=3 but, then, decreases as the level of interactions rises to K=5 and K=7, irrespective of

21

. On the contrary, in the hierarchical

pattern, the average knowledge of the individuals always diminishes as K grows, independently of

. These outcomes demonstrate that high levels of social interactions

among firm members are detrimental for firm absorptive capacity. In both social patterns, for high values of K, the teacher becomes less effective in influencing the learning process, because the high number of social connections, established among the firm members, determines a sort of lock-in effect to the assimilation of the external knowledge. The cognitive influence that the firm member receives by the teacher is, in fact, lower, than the cognitive influence she receives from the firm members having a high number of connections. As already mentioned, in such conditions the social interactions among the firm members drive the learning process in a way that inhibits the assimilation of the external knowledge. Thus, the higher the number of interactions, the more the transformative learning hampers the explorative learning, thereby decreasing the development of external knowledge within the firm. This negative effect is more pronounced in the hierarchical pattern compared to the blockdiagonal one, where individuals with a high number of connections are identified. For example, the average number of social links of the most connected member increases from 35.0 for K=2 to 41.2 for K=3, to 51.2 for K=5, to 56.0 for K=6, and 59.6 for K=7. Therefore, in the hierarchical pattern even for low values of K, we find that, as K rises, the average level of knowledge of the firm members decreases. Conversely, in the block-diagonal pattern for low level of interactions (K=2), the increase of K is beneficial. In such a case, in fact, because of the low average number of social interactions, the cognitive impact exerted by the teacher is certainly higher than the cognitive impact provided by the other firm members. However, as soon as K increases, the influence of the teacher lowers, the transformative learning contrasts the explorative learning, and the level of knowledge of the individuals is on the average reduced.

22

In Table 3 we compute the performance difference between the block-diagonal and the hierarchical patterns for any level of social interactions (K). On the average, the improvement in the performance obtained by the block-diagonal pattern compared to the hierarchical one increases with K, taking the values 2.82%, 6.17%, 8.42%, and 8.61% for K= 2, 3, 5, and 7, respectively. As already observed, this result is a consequence of the contrasting effect of the transformative learning that hampers the assimilation of teacher’s knowledge when K is high, and, hence, is more pronounced in the hierarchical pattern. Thus, the higher is the level of social interactions, the more valuable is the block-diagonal pattern in terms of knowledge development, compared to the hierarchical case. These findings suggest that the blockdiagonal pattern is a useful strategy to contrast the negative effect of transformative learning when the level of social interactions is high.

6.2 The moderating effect of the social network on relationship between the complementary knowledge and the firm absorptive capacity. We analyze results for increasing level of βTS ranging from 4 to 10. As expected, the average knowledge of the firm members increases as the level of complementarity of knowledge grows. This is actually an internal confirmation of the validity of our model, which is, in fact, able to produce results consistent with the theoretical argumentations. Table 4 shows the performance improvement caused by a βTS increment of one single unit. Notably the performance improvement decreases as βTS is increased. For example, in the case of the block-diagonal pattern, the improvement of the average knowledge of the individuals is 3.52%, 2.81%, 2,29%, and 2.14%, as βTS is increased from βTS =4 to βTS =5, from to βTS=5 to βTS=6, from βTS=6 to βTS=7, and from βTS=7 to βTS=8, respectively. Therefore, increasing the level of knowledge complementarity makes the benefit for the firm absorptive capacity diminish.

23

Results in Table 5 also show that the performance improvement associated with increasing values of βTS is higher for the block-diagonal pattern, compared to the hierarchical pattern, irrespective of K. For example, on the average, for K=2 the increase in performance (last row) is 2.31% and 1.37% for the block-diagonal and hierarchical patterns respectively. This means that the pattern of social interactions plays a moderating effect on the relationship between the complementary knowledge and the firm absorptive capacity. In particular, in the blockdiagonal pattern, increasing the complementarity of knowledge has a higher effect on the development of the firm members’ knowledge, compared to the hierarchical pattern. As βTS rises, the efficacy of the explorative learning increases, because of the higher likelihood that the new external knowledge is recognized and understood. This is more beneficial in the block-diagonal pattern compared to the hierarchical case, as in the hierarchical pattern the lock-in effect limits the assimilation of the external knowledge. Thus, enhancing the efficacy of the external knowledge transfer becomes, in such case, less profitable. Furthermore, we note that, in the case of a block-diagonal pattern, the increase in the average knowledge of the firm members, due to βTS , is not influenced by the level of interactions K, whereas it grows with K when the social network shows a hierarchical pattern. To exemplify, the increase of the average knowledge of the individuals moves from 1.37%, to 2.04%, to 2.14%, and to 2.18%, as K is increased from 2 to 7. Recalling that in the hierarchical pattern, the higher the number of interactions, the higher the number of connections of the central individuals and, hence, their influence, makes it clear that. These central members act in a way that hampers the assimilation of the external knowledge, thus guiding the learning process along a wrong way. In such a case, increasing the transferability of the external knowledge is beneficial in terms of the efficacy of the transformative learning process, because it improves the level of knowledge of the central individuals, who, in turn, become able to better drive the learning process.

24

7.

Validation

The model is validated applying multiple criteria. The micro-face criteria (Rund and Rust 2011) is satisfied because the model behaviors, both at the level of the agents (i.e., firm members) and at the level of processes (i.e., learning processes), are defined coherently with the literature (see Section 2.1 and Section 3). Furthermore, the model satisfies the macro-face validation criterion (Rund and Rust 2011), because it reproduces the expected behaviors coherently with the theories adopted. In particular, as expected, the complementary knowledge is positively associated with the average level of knowledge of the individuals. The model also satisfies the empirical validation input criterion (Rund and Rust 2011). We used different strategies in this respect. To set the input parameters that remain fixed across all simulations (i.e.,

,

σ, T), we chose the same values adopted by Bordogna and

Albano (2001), as shown in Table 1. As to the parameters

and

that differ across the

simulations, the values used by Bordogna and Albano (2001) were chosen as baseline values. Then,

was increased, ranging from 4 to 10, so as to analyze the effect of increasing

complementarity of knowledge.

was modified according to eq. (9), ranging from 0.6 to 2,

as the level of social interactions decreases. Considering that empirical data about the structures of real social networks are lacking, we chose patterns that, more than others (e.g. random pattern), could be representative of realworld networks. We chose the block-diagonal and the hierarchical social patterns (Barabasi and Albert 1999; Barabasi and Bonabeau 2003, Ethiraj and Levinthal 2004, Rivkin and Siggelkow 2007, Capaldo and Giannoccaro 2015a, 2015b, Giannoccaro 2015). We also performed sensitivity analyses aimed at testing the robustness of results to a particular set of inputs not included in Bordogna and Albano’s study, i.e., the value of ET (appropriability regime) and βT (adoption of IT systems). We chose the case of the block25

diagonal pattern with K=2 as baseline. First, we decreased ET, all the other parameters being fixed. The same we did for βT. As expected, decreasing ET (βT) the average level of individual knowledge decreases. In particular, moving from ET = 1 to ET=0.5, the average level of knowledge is decreased to 0.447 (s.d.=0.014). Similarly, decreasing β T from 1 to 0.5 reduces the individual level of knowledge to 0.549 (s.d.= 0.013). The main trends of results are also confirmed (see Tables 6 and 7 in Appendix 3). In particular, we found that the relationship between the level of interactions and the average knowledge of the firm members follows an inverted-U relationship in the case of a block-diagonal pattern, while it is a continuously decreasing function in the case of a hierarchical pattern. Furthermore, the block-diagonal pattern outperforms the hierarchical one, irrespective of K and βTS. We also perform an additional sensitivity analysis to test the robustness of the results for diverse firm sizes (N=48 and N=192). Results confirm previous outcomes (see Tables 8 and 9 in Appendix 3). Finally, we compared the proposed model against Bordogna and Albano’s one. We run our model using the same parameters as those used by Bordogna and Albano (2001) ( ,

,

,

,

, and

. Since in Bordogna

and Albano’s model, students are grouped in small team with size equal to three, we chose the case of block-diagonal pattern and set K=2. Furthermore, since this test corresponds to Bordogna and Albano’s case of heterogeneous groups, we used those results as benchmark. We run two simulations: 1) our model with just two sources of cognitive impacts (teacher and student) and 2) our model modified, because we included an additional contribution to the cognitive impact due to the learning from the book (βBS = ∞), as in the model by Bordogna and Albano. Same (similar) results are achieved in the second (first) case, confirming the validity of our model (see Figure 5). 8.

Discussion, Conclusions, Limitations 26

In this paper we provided a dynamic model of the firm absorptive capacity based on a process-oriented conceptualization and a teaching-learning process approach. Two main learning pairs were identified: 1) the teacher-student and 2) the student-student pairs. The social interactions among the firm members were conceived as the basic mechanism by means of which the learning processes develop. The influence of the pattern and level of the social interactions on the firm absorptive capacity were investigated. In doing so, our research complements the studies on the micro-origins of firm absorptive capacity (Jansen et al. 2005, Regans and McEvily 2005, Hotho et al. 2012), by contributing to analyze how individual behavior and social interactions translates into firm absorptive capacity. From a methodological point of view, our study responds to the call by D’Souza and Kurlkarni (2015), who, recognizing that recent developments on the topic have been primarily theoretical, advocate to use other approaches to triangulate results, and build a rigorous theory. In particular, we built a model adopting a methodology, belonging to the general class of Ising models, which is very suited to reproduce complex system dynamics driven by interactions among single agents at a micro-system level. So doing, we added fresh insights on the relationship between social network structures and firm absorptive capacity. Our study also capitalized on the interpretive potential of the Ising approach, extending its applications to a new field of management studies, while so far have mainly concerned social science and finance (Zhou and Sornette 2007, Sornette 2014). Our results also extend previous findings of the absorptive capacity literature, which recognizes social features as important drivers of firm absorptive capacity. While these studies have analyzed the positive effect of the scope and range of social interactions, tie strength, and social cohesion (Zahra and George 2002, Jansen et al. 2005, Reagan and McEviliy 2003, Todorova and Durisin 2007, Hotho et al. 2012), we analyzed the effect of the pattern and level of social interactions on the firm absorptive capacity. In particular, we found that the block-diagonal pattern, where social interactions occur inside groups and not between 27

groups (like in modular organizations), is associated with higher absorptive capacity compared to the hierarchical pattern, the latter being, instead, characterized by a hub and spoke structure, shown, for example, in centralized organizations. Our study identified the root cause of this finding in the existence of highly central individuals with many social connections, who assume a driving position of the learning process, which, in turn, by means of self-supporting mechanisms, is led in the wrong direction, concurrently limiting the transfer and assimilation of the external knowledge. This is an original contribution of our study. In contrast to previous findings by Hotho et al. (2012) who found that the level of interactions is positively associated with the firm absorptive capacity, we showed that the level of social interactions influences firm absorptive capacity depending on the type of interaction pattern. In the block-diagonal pattern, the relationship between the level of social interactions and the absorptive capacity follows an inverted-U trend. As long as the level of interactions among firm members remains low, the explorative learning is effective and firm members result able to assimilate the external knowledge. In such a case, an increase of the number of interactions determines an improvement of the level of knowledge because it favors the transfer of the external knowledge within the firm. However, when the number of social interactions becomes too high, those firm members who have a high number of connections tend to drive the learning process. Then, the transformative learning contrasts the effective assimilation of the external knowledge, thus reducing the learning outcome. This also explains why in the hierarchical pattern, increasing the level of interactions decreases the absorptive capacity. In fact, in those patterns characterized by the existence of central individuals, the number of connections of the central individuals grows more as the level of interactions is increased, thereby reinforcing the negative effect played by these individuals on the assimilation of the external knowledge (explorative learning). Furthermore, since this effect is more critical in

28

the hierarchical pattern, the block-diagonal pattern outperforms the hierarchical one, independent of the level of social interactions. Our study also investigated the moderating effects played by the pattern of social interactions and the level of social interactions on the relationship between the complementary knowledge and the absorptive capacity. In particular, whilst previous studies highlighted the positive relationship between the complementary knowledge and the firm absorptive capacity (Lane and Lubantik 1998, Regans and McEvily 2003), we showed that the positive effect of the complementary knowledge on the firm absorptive capacity is more pronounced in the blockdiagonal compared to the hierarchical pattern. In the latter case, the enhancement of the external knowledge transfer due to the increasing complementarity is counter-balanced by the lock-in effect favored by the existence of highly central individuals. This is a further innovative contribution of our study. We also found that in the hierarchical pattern the level of interactions moderates the relationship between the complementary knowledge and the firm absorptive capacity. The higher the level of interactions among the individuals, the higher the positive effect of the complementary knowledge on the absorptive capacity. Our findings also contribute to the organizational learning literature. In line with Lazier and Friedman (2007), we found that the social network structure affects the trade-off between exploration (explorative learning) and exploitation (transformative learning). In particular, we confirm that increasing levels of social interactions positively influence knowledge diffusion, but can be detrimental for the exploration of new knowledge (Lazier and Friedman 2007). Furthermore, we add that the same negative effect on the exploration of new knowledge is achieved in social patterns characterized by the existence of highly central individuals (such as the hierarchical one), who can drive the learning processes along wrong directions. The results of our study provided interesting implications for the improvement of firm absorptive capacity. In particular, we recommend modular interaction patterns among the firm 29

members, rather than centralized ones. We also suggest to keep low the level of interactions among individuals so as to avoid lock-in effect that can hamper the assimilation of the new external knowledge, especially if there are highly central individuals. Based on these results, and aiming at improving the firm absorptive capacity, we suggest that the social interactions be organized in small autonomous groups. In such a case, investing to enhance the complementarity of knowledge is a further valuable strategy to improve the firm absorptive capacity. Our study presents also some limits. It considers only two types of interaction patterns. Some other options such as the random and the small-world patterns are also possible and could be analyzed in further research. The study only focuses on two learning processes, i.e. the explorative and the transformative learning, neglecting the exploitative learning. Further developments of the model will move along these unexplored lines, so as to include this learning process. Moreover, future research will be directed to empirically test the main findings of this study.

Appendix 1. The Ising model The Ising model was originally developed in physics to study the behavior of ferromagnetic systems, described in terms of spins. Spins are binary variables, which may take only two values: “up” and “down”. The basic idea of the Ising model is very simple: each spin interacts with neighboring spins through the mutual interaction energy. When two spins point “up” or “down”, the mutual energy is lowered; whenever they point in different directions, the energy is heightened. Since systems, whatever they are, tend to lower the total energy, a driving force arises, which pushes spins to point in the same direction, by counteracting the effect of temperature, which tends to make spins fluctuate randomly. The conceptual simplicity of the Ising model has made it a very well accepted tool to describe system dynamics in different contexts, such as finance (Zhou and Sornette 2007, Sornette 2014), social science (Bordogna 30

and Albano 2007a, 2007b), organization science (Oh and Jeon 2007, Carbone and Giannoccaro 2015). Figure 2 shows a schematic of an Ising model on a 2D square lattice. Each spin has, at the beginning, a random direction and the state of the system is chaotic. The system then evolves over time and reaches an order stationary regime.

+1 -1

Fig A1. The Ising model.

The dynamics is governed by a specific rule. Each spin may change its direction. This is influenced by the directions of the neighboring spins, thus leading to a certain level of interaction energy (E). This energy is positive (negative) if the spin and the majority of the neighbors have a different (same) direction. Each spin changes its direction, according to a transition probability p, which is a function of the energy and the temperature T. In order to solve the dynamics of the system of spins, the transition probability p should be computed. Different choices, leading to statistically identical behaviors, are possible. One possibility is to use the Glauber rate (Glauber 1963), where the transition probability p is chosen so as to obey the formula:

31

p

1 1  exp E 

(A1)

In Eq. (A1) E is the difference between the current energy level and the energy level that would be reached if the spin changes its direction. The temperature T=1/β measures the level of noise in the environment. The higher the temperature, the higher the probability to change the spin direction. Thus, an increase of temperature adds turbulence to the system behavior, thereby reducing the herding effect of the energy, and hindering the transition to an order state.

Appendix 2. Note on the Ising-based model of firm absorptive capacity Our Ising-based model of the firm absorptive capacitive is a generalized application of the original Ising model and resembles the application proposed by Bordogna and Albano (2001), who develop a model of the teaching and learning process in a classroom of students. In our model the firm members (students) corresponds to the magnetic spins and the individual level of knowledge corresponds to spin direction. However, similarly to Bordogna and Albano (2001), the level of knowledge rather than to be a binary random variable, likewise in the classical Ising approach, is a real random variable taking value in the interval [0,1]. As the direction of the spin is influenced by the neighboring spins, the individual level of knowledge is affected by the social interactions with the connected individuals, i.e. the teacher (knowledge source) and the other students (firm members). In particular, the change in the individual level of knowledge is driven by the cognitive impact exerted by both the teacher-student and student-student interactions. This change in the individual level of knowledge models the social learning processes underlying the absorptive capacity (i.e. 32

explorative and exploitative learning, respectively). Thus, the cognitive impact stands for the interaction energy acting on the magnetic spin. The change in the individual level of knowledge is defined by a transition probability p j depending on the cognitive impact and some contextual variables playing a similar role to the temperature in the classic Ising approach. We included three contextual variables, which, likewise the temperature, introduce noise in the social relationships, thereby contrasting the efficacy of learning: the adoption of IT systems, the complementarity of knowledge, and the level of social cohesion. More specifically, following Bordogna and Albano (2001), and in the same spirit of Eq. (A1), a generalized rule for the transition probability is used (see eqs 7-8). We now briefly exemplify how simulation is carried out with a numerical example. We consider a firm having 6 members arranged in a block-diagonal and hierarchical structures (Figures A2a-b). Each member is assigned with an initial level of knowledge (σi) drawn at random from a uniform distribution [-0.5; 0.5] (Table A1). The “quantum” of knowledge is σ = 0.1 and the knowledge of teacher is σT=1. The values of initial mutual support ( mutual persuasiveness (

and

are drawn at random from an uniform distribution [0,1] and are

given in Tables A2 and A3. ET is set equal to 1.

33

External source

3

2

1

External source

4

5

2

6

3

4

5

6

1

b) Hierarchical pattern

a) Block-diagonal pattern

Fig A2. Two exemplar cases.

Table A1. The initial level of knowledge of firm members.

σ0

1

2

3

4

5

6

0.0429

-0.2897

-0.2730

-0.2256

0.2565

0.0426

Table A2. The initial mutual persuasiveness values between firm members. 1

2

3

4

5

6

1

0.0000

0.1382

0.0173

0.2931

0.9953

0.3145

2

0.3027

0.0000

0.1929

0.5879

0.6214

0.1249

3

0.9990

0.0270

0.0000

0.5715

0.1152

0.1348

4

0.1352

0.5295

0.1579

0.0000

0.1369

0.8134

5

0.7914

0.1811

0.0299

0.1627

0.0000

0.9655

6

0.9644

0.2040

0.1897

0.5168

0.1037

0.0000

Table A3. The initial mutual support values between firm members.

34

1

2

3

4

5

6

1

0.0000

0.5677

0.8768

0.8018

0.2886

0.4945

2

0.4405

0.0000

0.3918

0.7575

0.9231

0.0063

3

0.8016

0.7733

0.0000

0.9609

0.7083

0.5650

4

0.8410

0.4609

0.9753

0.0000

0.6960

0.3929

5

0.5413

0.4062

0.1734

0.7053

0.0000

0.8576

6

0.7733

0.4460

0.2875

0.2143

0.0936

0.0000

Given the data above, the values of the cognitive impact of the teacher (CITS) and the cognitive impact of the connected students (CISS) can be computed by using eqs (2) and (3) (see Table A4). Table A4. The cognitive impacts of the teacher and connected students on the firm members. 1

2

3

4

5

6

0.8571

1.1880

1.1729

1.1256

0.6435

0.8574

C

0.0471

-0.0007

-0.0151

-0.0515

-0.0730

0.0035

CSS, hierarchical

-0.0240

-0.0594

-0.0151

0.0053

-0.1640

-0.0519

TS

CI

SS, block diagonal

The simulation follows this procedure. We set βIT=1, βTS=4, βSS=2. First, we compute the probability

using eq. (7) (see first two rows in Table A5). Then, we generate a random

number (rand), drawn at random from a uniform distribution [0, 1]. The change of knowledge by the “quantum” of knowledge σ is made by satisfying the following rule: If Then

; Otherwise,

,

(see last three raws in

Table A5). Table A5. Transition probability and update level of knowledge of the firm members. 35

rand

0.9713

0.9915

0.9906

0.9879

0.9189

0.9688

0.9671

0.9904

0.9906

0.9892

0.9043

0.9653

0.9690

0.4298

0.4392

0.6214

0.9144

0.7157

0.1429

-0.1897

-0.1730

-0.1256

0.3565

0.1426

-0.0571

-0.1897

-0.1729

-0.1256

0.1565

0.1426

Appendix 3. Results of the sensitivity analyses

Table A6. Results for ET=0.5. Block-diagonal βTS =4 βTS =5 βTS =6 βTS =7 βTS =8 βTS =9 βTS =10

Hierarchical

K=2

K=3

K=5

K=7

K=2

K=3

K=5

K=7

0.447

0.447

0.442

0.432

1.633*

0.799*

0.415

0.393

(0.014)

(0.013)

(0.013)

(0.012)

(0.762)

(0.488)

0.019

(0.013)

0.478

0.481

0.474

0.467

1.089*

0.547

0.439

0.422

(0.014)

(0.013)

(0.013)

(0.010)

(0.644)

(0.199)

0.017

(0.014)

0.506

0.507

0.501

0.491

0.731*

0.521*

0.466

0.448

(0.012)

(0.013)

(0.010)

(0.013)

(0.440)

(0.123)

0.015

(0.012)

0.529

0.530

0.525

0.516

0.609*

0.508

0.486

0.468

(0.010)

(0.013)

(0.012)

(0.013)

(0.281)

(0.019)

0.014

(0.013)

0.549

0.550

0.544

0.536

0.609*

0.525

0.501

0.487

(0.011)

(0.011)

(0.012)

(0.011)

(0.267)

(0.014)

(0.014)

(0.011)

0.569

0.569

0.563

0.556

0.568

0.542

0.518

0.504

(0.012)

(0.013)

(0.010)

(0.011)

(0.082)

(0.013)

(0.013)

(0.012)

0.584

0.585

0.579

0.571

0.570

0.554

0.532

0.516

(0.012)

0.010

(0.011)

(0.011)

(0.015)

(0.016)

(0.011)

(0.011)

Standard deviation into brackets. * not stationary system.

36

Table A7. Results for βIT = 0.5. Block-diagonal βTS =4

βTS =5 βTS =6 βTS =7 βTS =8 βTS =9 βTS =10

Hierarchical

K=2

K=3

K=5

K=7

K=2

K=3

K=5

K=7

0.550

0.551

0.547

0.535

0.991*

0.693*

0.410

0.395

(0.015)

(0.015)

(0.014)

(0.014)

(0.842)

(0.352)

(0.017)

(0.015)

0.5838

0.584

0.576

0.572

0.989*

0.551*

0.439

0.423

(0.014)

(0.013)

(0.014)

(0.014)

(0.715)

(0.168)

(0.013)

(0.013)

0.612

0.612

0.608

0.598

0.833*

0.508*

0.465

0.447

(0.014)

(0.014)

(0.013)

(0.013)

(0.565)

(0.144)

(0.014)

(0.011)

0.635

0.637

0.632

0.621

0.627*

0.509

0.485

0.468

(0.013)

(0.013)

(0.012)

(0.011)

(0.308)

(0.014)

(0.012)

(0.013)

0.654

0.656

0.651

0.643

0.605*

0.526

0.503

0.486

(0.012)

(0.013)

(0.013)

(0.011)

(0.237)

(0.014)

(0.013)

(0.012)

0.674

0.676

0.669

0.661

0.562

0.542

0.517

0.503

(0.012)

(0.012)

(0.013)

(0.010)

(0.024)

(0.013)

(0.011)

(0.010)

0.688

0.691

0.685

0.678

0.577

0.555

0.533

0.517

(0.012)

(0.011)

(0.012)

(0.011)

(0.017)

(0.013)

(0.011)

(0.012)

Table A8. Results for N =192. Block-diagonal

βTS =4 βTS =5 βTS =6

Hierarchical

K=2

K=3

K=5

K=7

K=2

K=3

K=5

K=7

0.550

0.551

0.545

0.537

0.682*

0.537

0.508

0.494

(0.010)

(0.008)

(0.009)

(0.008)

(0.250)

(0.028)

(0.010)

(0.009)

0.584

0.587

0.579

0.570

0.602*

0.560

0.540

0.524

(0.009)

(0.008)

(0.008)

(0.008)

(0.104)

(0.010)

(0.008)

(0.009)

0.611

0.615

0.608

0.600

0.606

0.586

0.563

0.550

37

βTS =7 βTS =8 βTS =9 βTS =10

(0.007)

(0.007)

(0.007)

(0.007)

(0.036)

(0.009)

(0.008)

(0.008)

0.636

0.637

0.631

0.623

0.621

0.607

0.587

0.572

(0.007)

(0.008)

(0.006)

(0.011)

(0.010)

(0.009)

(0.009)

(0.008)

0.656

0.657

0.652

0.643

0.636

0.623

0.605

0.590

(0.007)

(0.007)

(0.007)

(0.010)

(0.011)

(0.009)

(0.007)

(0.007)

0.674

0.675

0.670

0.662

0.653

0.639

0.621

0.607

(0.007)

(0.007)

(0.008)

(0.009)

(0.011)

(0.009)

(0.008)

(0.007)

(0.689

0.692

0.686

0.676

0.666

0.652

0.636

0.623

(0.008)

(0.008)

(0.007)

(0.010)

(0.010)

(0.008)

(0.008)

(0.007)

Standard deviation into brackets. * not stationary system.

Table A9. Results for N =48. Block-diagonal

Hierarchical

N=48

K=2

K=3

K=5

K=7

K=2

K=3

K=5

K=7

βTS =4

0.551

0.553

0.547

0.537

0.551*

0.517

0.496

0.479

(0.014

(0.015)

(0.017)

(0.017)

(0.103)

(0.020

(0.016

(0.016)

0.585

0.585

0.582

0.573

0.566

0.548

0.524

0.509

(0.015)

(0.017)

(0.017)

(0.015)

(0.024)

(0.020)

(0.016)

(0.016)

0.611

0.612

0.609

0.560

0.589

0.574

0.551

0.539

(0.016)

(0.015)

(0.014)

(0.014)

(0.024)

(0.019)

(0.017)

(0.014)

0.637

0.639

0.631

0.622

0.611

0.590

0.574

0.559

(0.015)

(0.013)

(0.014)

(0.014)

(0.023)

(0.018)

(0.014)

(0.014)

0.656

0.657

0.652

0.645

0.624

0.610

0.590

0.580

(0.016)

(0.014)

(0.013)

(0.013)

(0.020)

(0.015)

(0.012)

(0.014)

0.672

0.676

0.670

0.660

0.641

0.627

0.606

0.596

(0.016)

(0.013)

(0.014)

(0.014)

(0.018)

(0.018)

(0.013)

(0.013)

0.689

0.690

0.686

0.676

0.658

0.642

0.625

0.613

(0.016)

(0.012)

(0.014)

(0.014)

(0.018)

(0.014)

(0.013)

(0.011)

βTS =5 βTS =6 βTS =7 βTS =8 βTS =9 βTS =10

Standard deviation into brackets. * not stationary system.

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External source

Teacher-student interaction Student-student interaction

Fig 1. The social networks associated with firm absorptive capacity.

43

Complementary knowledge

IT systems

Teacher-student interactions

Explorative learning outcome

Student-student interactions

Transformative learning outcome

Absorptive capacity

Social cohesion

Fig 2. The main variables and relationships in the teaching-learning process model of firm absorptive capacity.

External source

External source

a) Block-diagonal pattern

b) Hierarchical pattern

Fig 3. The social interactions patterns analyzed.

44

a) Block-diagonal pattern

b) Hierarchical pattern

Fig 4. The average knowledge of the firm members for increasing level of interactions (βTS=1÷10).

Fig 5. Results for the same set of values used by Bordogna and Albano (2001).

Table 1. Cognitive parameters and noise coefficients used in the simulation. Coeff.

Description

Value

45

Exposure of the individual j to complementary external knowledge Idiosyncratic level of persuasiveness of the individual on the individual i Idiosyncratic level of support of the individual on the individual i Adoption of IT systems Noise in the teacher-student relationship

÷40

Noise in the student-student relationship

for for for for

Quantum of knowledge T

T=1

External knowledge

Table 2. Average knowledge of the firm members. Block-diagonal

βTS =4 βTS =5 βTS =6 βTS =7 βTS =8 βTS =9 βTS =10 βTS =20

Hierarchical

K=2

K=3

K=5

K=7

K=2

K=3

K=5

K=7

0.549

0.553

0.546

0.537

0.578*

0.523

0.504

0.486

(0.011)

(0.011)

(0.011)

(0.012)

(0.195)

(0.012)

(0.012)

(0.012)

0.584

0.586

0.58

0.562

0.578

0.555

0.535

0.518

(0.011)

(0.011)

(0.012)

(0.010)

(0.037)

(0.015)

(0.012)

(0.010)

0.612

0.613

0.608

0.592

0.594

0.581

0.559

0.544

(0.012)

(0.012)

(0.011)

(0.011)

(0.015)

(0.014)

(0.010)

(0.010)

0.635

0.637

0.632

0.616

0.613

0.599

0.579

0.566

(0.011)

(0.010)

(0.011)

(0.010)

(0.016)

(0.012)

(0.010)

(0.011)

0.657

0.658

0.651

0.637

0.633

0.619

0.599

0.585

(0.011)

(0.010)

(0.009)

(0.008)

(0.013)

(0.013)

(0.012)

(0.010)

0.672

0.674

0.669

0.654

0.646

0.633

0.616

0.602

(0.011)

(0.010)

(0.009)

(0.009)

(0.013)

(0.010)

(0.010)

(0.010)

0.688

0.691

0.685

0.672

0.66

0.646

0.632

0.617

0.009

0.010

0.009

0.010

(0.014)

(0.012)

(0.009)

(0.009)

0.785

0.787

0.784

0.769

0.745

0.737

0.725

0.713

(0.008)

(0.008)

(0.008)

(0.008)

(0.011)

(0.009)

(0.008)

(0.009)

46

βTS =40

0.864

0.867

0.863

0.854

0.821

0.817

0.807

0.801

(0.007)

(0.007)

(0.007)

(0.008)

(0.009)

(0.008)

(0.007)

(0.008)

Standard deviation into brackets. * not stationary system.

Table 3. Performance difference between the block-diagonal and the hierarchical structures. (σbd – σsf)/ σsf

K=2

K=3

K=5

K=7

Average

βTS=4

-

5.65%

8.42%

10.41%

4.87%

βTS=5

1.14%

5.70%

8.48%

8.45%

5.94%

βTS=6

3.05%

5.40%

8.86%

8.65%

6.49%

βTS=7

3.56%

6.21%

9.31%

8.86%

6.99%

βTS=8

3.75%

6.33%

8.79%

8.85%

6.93%

βTS=9

4.07%

6.50%

8.54%

8.72%

6.96%

βTS=10

4.19%

7.02%

8.37%

8.93%

7.13%

βTS=20

5.36%

6.67%

8.15%

7.90%

7.02%

βTS=40

5.25%

6.03%

6.89%

6.69%

6.21%

Average

2.82%

6.17%

8.42%

8.61%

Table 4. Performance improvement as the complementarity of knowledge rises. Block-diagonal K=2

K=3

K=5

Hierarchical K=7

K=2

βTS from 4 to 5

3.52% 3.35% 3.42% 2.54%

-

βTS from 5 to 6

2.81% 2.64% 2.81% 2.93%

1.65% 2.67% 2.39% 2.60%

βTS from 6 to 7

2.29% 2.37% 2.40% 2.46%

1.91% 1.79% 1.97% 2.15%

βTS from 7 to 8

2.14% 2.15% 1.88% 2.06%

1.95% 1.95% 2.01% 1.90%

βTS from 8 to 9

1.56% 1.61% 1.77% 1.73%

1.31% 1.42% 1.76% 1.66%

47

K=3

K = 5 K=7

3.14% 3.12% 3.22%

βTS from 9 to 10

1.56% 1.71% 1.58% 1.79%

1.42% 1.29% 1.56% 1.53%

Average

2.31% 2.31% 2.31% 2.25%

1.37% 2.04% 2.14% 2.18%

48