A Behavioral View of Core-Periphery Dynamics in Social Networks
Nitin R. J oglekar
Boston University School of Management
595 Commonwealth Avenue, Boston MA 02215
Phone: 617 353 4290 Fax: 617 353 4098
joglekar@ bu.edu
Revision: 18 March 2005
A Behavioral View of Core-Periphery Dynamics in Social Networks
Abstract
We model the dynamics associated with evolution of the core and the periphery of a social-
network. The model is based on an existing behavioral theory of the inter-firm (Baum and
Ingram 2002). The formalization allows us to refine this existing theory through the introduction
of a target setting process. Allied analysis documents the efficacy of exploration and exploitation
policies within the core and across the periphery of a social network. Our results show that the
competitive advantage accrued through exploration and exploitation is crucially affected by the
behavioral biases, imitation and the target setting associated with the evolution of key constructs
such as core and periphery embeddedness.
(Behavioral Theory, Core-Periphery Dynamics, Exploration, Exploitation, Social Networks)
1. Introduction
The interest in studying social networks has been rising in diverse organizational settings
(Borgatti and Foster 2003). Within this context, core and peripheral embeddedness have been
shown to be key constructs that govern network evolution (Gulati and Gargiulo 1999). The term
core refers to the topography at the center of a network, whereas periphery refers to the edges of
such a network. Embeddedness is defined as a stock of social relations or organizational ties that
shapes economic action in ways that some economic schemes overlook (Granovetter 1985). For
example, Powell et al. (2005) observe embeddedness in terms of formal and informal exchanges
of R&D know-how across an emerging network of firms in the biotech industry. Scientists in this
industry trade information with like-minded scientists and experts outside their firms, even in the
absence of formal economic ties.
Managing trade-offs underlying the core-periphery evolution is a central theme in social
network research. We view this theme through the lens of behavioral theory (Cyert and March
1963). An example of such trade-off is the behavioral choice: exploration of the network, instead
of exploitation, is the preferred approach for organizational learning (March 1991) -- exploration
builds more embeddedness into the periphery than into the core. Exploitation reverses this bias.
Linkages of these choices into the network evolution process are complex. For instance, some
organizational scientists have argued that social networks evolve in a nonlinear manner owing to
a paradox of embeddedness (Uzzi 1997), i.e. the marginal gains from increasing embeddedness
are positive up to a threshold. Increasing embeddedness beyond this threshold provides
diminishing returns. Others have argued that there is a saturation level associated with the
evolution of embeddedness (Baum and Ingram 2002). These arguments raise many managerially
relevant questions: what might be the antecedents and consequences of embeddedness thresholds
and the saturation phenomena? Is exploration a desirable strategy for network growth, as
opposed to exploitation, when embeddedness lies below the above-mentioned threshold? And if
so, should a firm explore the core or the periphery of a social network?
While network studies have been using a variety of methodologies, ranging from
ethnography (Uzzi 1997) to system dynamics modeling (Rahmandad and Sterman 2004), much
of recent social network research has relied on empirical studies. Most of these empirical
approaches have not been able to explore above-mentioned questions due to data limitations. It is
difficult to find datasets that address scenarios where the network evolution spans the
embeddedness threshold or where embeddedness approaches a saturation level. Hence, most
studies cannot take on systematic exploration of allied behavioral choices (e.g. institutional and
firm decision rules associated with social network emergence, target setting processes and
cognition delays). On the other hand, this literature offers rich descriptions, careful statistical
analysis, and theory driven insights for selected phases of the social network evolution.
Modeling can stitch together a theory that spans all the phases of evolution and overcome
some of the limitations of empirical research. We formalize a qualitative description of a
network evolution theory put forth by Baum and Ingram (2002). System dynamics modeling is
our method of choice because of its ties to the behavioral research tradition (Sterman 1989,
Sastry 1997, Reppening 2002), and because non-linearity (Uzzi 1996) and feedback effects are
inherent within descriptions of social network emergence (Gulati and Gargiulo 1999). This
formalization allows us to connect March’s view of exploration/exploitation and the competition
for primacy (1991) with theories about the evolution of networks: the paradox of embeddedness
(Uzzi 1997), process evolution hypotheses (Baum and Ingram 2002) and Powell et al’s view of
co-evolution (2005) between a focal firm and an institution. The term institution refers to an
environment within which the social network can evolve. We explore, and in some instances
refine, previously postulated relationships among constructs such as embeddedness,
interdependence and positional advantage. These constructs are defined in §2 and §3.
Along with theory refinements, our model offers opportunities for policy analysis. The
model structure and outputs are seen to be consistent with Uzzi’s (1996) empirical findings on
the paradox of embeddedness and Baum and Ingram’s (2002) process evolution hypotheses. This
has built confidence in our belief about the validity of the underlying model structure. The
second half of this paper demonstrates how the model can be applied for policy analyses in order
to verify and extend existing empirical findings. We simulate a variety of exploration and
exploitation policies for growing the network core or the periphery, or both. These simulations
provide insights for accruing positional advantage (defined in §3.3) under a wide range of
behavioral conditions: when the institution values core more than periphery, when the firm has a
bias for growing its dyadic relations in the core instead of the periphery, when the institution is
seen to set up embeddedness targets in an endogenous manner and so on. Our results show that
the competitive advantage accrued through exploration and exploitation is crucially affected by
the behavioral biases, imitation and the target setting associated with the evolution of constructs
such as core and periphery embeddedness.
The rest of the paper is organized as follows. In §2, we discuss the behavioral theory of
the inter-firm and identify dynamic hypotheses. §3 and §4 cover model specification and
validation respectively. We lay out policy analysis results in §5 and conclude in §6.
2. Behavioral Theory for Network Evolution
Goal setting, expectations and choice are central tenets of the behavioral theory of the firm
(Simon 1959, Cyert and March 1963). This theory addresses decision-making processes. The
unit of analysis of the theory is a firm or a node within a social network. Firm’s behavioral
choices involve picking a goal and getting close to this goal in a satisfying manner. Cyert and
March have argued that, “we can analyze the process of decision making in a modem firm in
terms of the variables that affect organizational goals, the variables that affect organizational
expectations and the variables that affect organizational choice.” In this theory, choices and
search are closely intertwined: search mechanisms (e.g. exploration or exploitation) are often
motivated, simple minded and biased by behavioral choices.
Translating the concepts underlying a nodal theory of the firm into an inter-firm or
network-based theory is not a trivial exercise. Recent advances in organizational science have
explored many underlying concepts with “links” or “dyads of firms” as their unit of analysis (see
Borgatti and Foster 2003 for a review). Key constructs and their interrelations are described in
the next section.
2.1 Key Constructs and Interrelations
Organization science literature has identified core and peripheral embeddedness as key dyadic
constructs that govern the emergence of networks. Numerous studies have added to our
understanding of how these constructs might be measured and what their antecedent and
consequences might be. Some researchers have observed core embeddedness in structural terms
by measuring the extent to which dyads shared common partners. Peripheral embeddedness has
been viewed in terms of structural differentiation by measuring the standard deviation of the
normalized prominence (Gulati and Gargiulo 1999). Others have added cognitive dimensions
such as shared beliefs and mental models to these measurements (Baum et al. 2003).
Interorganizational Network Organization
Imitation Mental Model
Relational
Embeddedness
Positional
Embeddedness
Interdependence -
in the face of Fim Clique
Transaction Costs tus
Cliques averwork
‘Clique
Performance
Organizations)
Figure 1: Postulated Relationships between C onstructs (Baum and Ingram 2002)
Third-Party
Embeddeness
Several other constructs have been observed to be significantly associated with the evolution of
embeddedness. These constructs are often related to network performance such as growth in
network size (Gulati and Gargiulo 1999) and status (Baum and Ingram, 2002). Interdependence
is a construct that measures formal information exchanges across a dyad. Raising embeddedness
can lower interdependence in the face of transaction costs (Williamson 1975). Interdependence
has also been shown to rise as a consequence of increased coordination requirement when the
network size grows.
Based on a review of social network theory and empirical findings, Baum and Ingram
(2002) postulate that these key constructs relate to one another in the manner shown in Figure 1.
Their approach is a conceptual - it does not focus on whether some of these relationships are
causal or correlated and a goal setting process has not been captured explicitly in their argument.
We will draw upon their work while specifying the constitutive relationships in §3.
2.2. Dynamic Hypotheses
The term dynamic hypothesis refers to the nature of changes in the strengths of key constructs, as
these constructs evolve based on their interplay with other constructs. Baum and Ingram use the
structure in Figure 1 to postulate the modes of evolution for embeddedness, interdependence and
network performance as shown in Figure 2. They separate structural and cognitive elements of
embeddedness in their figure. We have eliminated some details from their hypotheses for ease of
presentation.
_ |“ Interdependence
_oc
: = —= = Fim Level
a Embeddedness
: —— «= = Network Level
Embeddedness
—-" " Network
Performance
7
—_ —_——
Time
Figure 2: Postulated Evolution of Process Strength (Based on Baum and Ingram 2002)
These modes of evolution suggest that while embeddedness exhibits growth and saturation, the
network size continues to rise. The rise in embeddedness is accompanied by a reduction in the
interdependence. Subsequent increase in the network size raises interdependence. Baum and
Ingram also suggest that for search processes to he effective, a focal firm within a network ought
to organize their search policies in the manner shown in Table 1. They have tested their
hypotheses for exploration and exploitation by conducting empirical studies in the Canadian
banking industry (Baum et al. 2003).
Table 1: A Satisfycing Organizational Search Policy
Behavior Mode
Exploration Exploitation
Embeddedness_ | Firm Level Weak ties Strong ties
Network Level | Structural holes | Closure
The policy in Table 1 does not account for the institution’ s bias (e.g. core versus periphery) for
assessing competitive advantage. We introduce the idea of positional advantage in §3 and later
discuss the efficacy of a family of policies, based on Table 1, in accruing such an advantage.
2.3 Refinements
The process of building a formal model has allowed us to verify, and in some instances refine,
the relationships between key constructs.
The most important refinement offered by our approach is the introduction of a target
embeddedness construct explicitly into the theory. While Uzzi (1997) has pointed to a paradox of
embeddedness, explicit attention to goal setting has been lacking in the theory of inter-firm
literature. Drawing upon the basic tenets of the behavioral theory, we add embeddedness target
to the list of key constructs. This allows us to explain the S-shaped growth of embeddedness
shown in Figure 2 with a parsimonious formulation (Sterman 2000). We set up our model
sequentially: we begin with exogenous target embeddedness and later make it endogenous. The
empirical evidence on how embeddedness targets evolve is scant. We assume that one
mechanism that will contribute to the target setting process is interdependence in the face of
transaction costs. This assumption is motivated by a boundedly rational view of transaction
costs.’ We exclude other constructs, e.g. trust, that could contribute to target setting to keep the
formulation parsimonious.
Another refinement involves the segregation of causal versus correlated relations between
constructs. Existing theories do not specify whether connections between various embeddedness
constructs are have causal links. Based on evidence of co-evolution of firms and institutions
(Powell et al 2005), we treat all the embeddedness stocks as correlated, although there may be
time delays between their evolution due to imitation and/or formation of expectations. A side
benefit of this effort is the construction of a system dynamic structure for co-evolution of
networks and a focal firm’s links within an institution.
We also make explicit causation assumptions about other constructs (e.g. status and
network size). These assumptions are discussed in §3. Recall that the goal of our policy analysis
effort is to assess the efficacy of the policies for exploitation (and exploration) of the network
core and periphery. We have made modeling choices that allow us to set up policy analysis ina
structured manner. For instance, decision rules for assignment of embeddedness are set up as
exogenous variables, so that they can be varied systematically during policy analysis.
3. Model Specification
For ease of description, our model specification has been divided into three sectors that address
the diffusion of overall embeddedness, the assignment of individual embeddedness stocks, and
' The parameters used for the endogenous specification have been selected arbitrarily. We have tested our model for
all possible values of these parameters and the results of our subsequent analyses are robust over the entire range.
We call for empirical measurements of such a specification in future research.
the computation of positional advantage based on these individual stocks, respectively. We begin
by specifying constituent relations in each sector. We then identify feedback relations that
integrate these sectors to set up the base case model. We end this description by specifying
additional relationships, that make certain control constructs endogenous, and extend the
boundaries of the base case model.
3.1 Embeddedness Diffusion
In the base case, we assume that there exists a level of embeddedness, termed as embeddedness
target (ET), which is set to be the goal for each firm within an institutional context. We also
assume that initial embeddedness is set at a level below the target. The diffusion of
embeddedness from the initial condition to the target level is governed by two mechanisms.
Embeddedness attracts embeddedness. And, the growth in embeddedness is also driven by the
gap between ET and the existing embeddedness stock. These mechanisms are shown as feedback
loops in Figure 3. The interplay between these mechanisms yields a S-shaped diffusion curve
(Sterman, 2000).
Embeddedness
Attracts Embeddeness
+
dE/dt
+
But the growth has a
aceiling
Time to =
adjust - .
embeddedness ____y»_ Fractional Embeddedness Target
increase rate Gap + embeddedness
“UC
Figure 3: Embeddedness Diffusion Mechanisms
10
The speed of diffusion is controlled by the Time to Adjust Embeddedness (T 4). If E(t) is the
overall embeddedness at a firm within the institution, then:
dE/dt =(E/Taz)*(ET-E\VE ae (1)
3.2 Decision Rules for Assigning Embeddedness
The growth rate (dE/dt) for overall embeddedness for any one firm within an institution is
derived in §3.1. We assign this growth rate to two pairs of stocks. Each pair features core
embeddedness and peripheral embeddedness. While making this assignment, we draw upon the
work of Powell et al (2005) to posit that these two pairs of embeddedness stocks co-evolve over
the time duration of interest.
The first pair consists of the firm core embeddedness (Fer) and firm peripheral
embeddedness (Fpg). The firm is identified as an agent within an institution that can make
assignment decisions in self-interest. These decisions may either be identical be different from
the decisions made by another firm in the surrounding institution.
@c-- Core Tie
Strength
b-- Institutional Network Core
Decision Rul | Embeddedness SS
a ee Agee ag
ar natwoae Network Peripheral] er Link
Correction for a | Embeddedness
Firm's Risk
Aversion
6 p-- Peripheral Tie P.- Relative A ttractiveness of
Strength Periphery in the institution
Enbecdedhess
EAL DACeOoss
Firm
‘Attractiveness
Decision Rule
6c-- Core Tie
Strength
Figure 4: Decision Structure for Growing Two Pairs of Embeddedness Stocks
11
The second pair consists of institutional core embeddedness (Icg) and institutional peripheral
embeddedness (Ipz). This pair tracks the embeddedness associated with an “average” firm within
the institution. Without a loss of generality, we will assume that the institutional decisions lag the
firm decisions by a fixed time constant, termed as imitation delay (T)), as shown in Figure 4.
Let ‘a’ (s.t. 0 < a< 1) represent a non-dimensional decision parameter that captures the firm’s
assignment mule and ‘pb’ (s.t. 0 < b < 1) represent another non-dimensional parameter that
captures the institution’ s assignment rule on average. Setting up either ‘a’ or ‘b’ above 0.5
indicates a bias in favor of growing the core embeddedness and vice versa. Then,
dFce/dt = a *0,* dE/dt
d Fre /dt =(1-a) * @)* dE/dt
and
dIcz(tTp/dt = b *r* 0,* dE/dt
d Ipg (t-Ty)//dt =(1-b) * r* 6, * dE/ dt
8b)
Here, r (> 0) is a correction for the risk averseness of the firm. The default value for ris set to
1.1, implying that the institution will reach a level 10% above ET for the firm. 0, (s.t. 0< 0, < 1)
and 6, (s.t. O< @p < 1) capture the strength of ties within the core and the periphery respectively.
We assume that the initial stocks For (0), Fr (0), Icz (0), and Ipz (0) are known. We stipulate that
0 <Fee (0) <Icg (0) <ET and 0 <Fpg (0) <Ipg (0) <ET. These stipulations restrict the follow on
analyses to situations where the firm starts out with lower embeddedness than the institution.
We measure the attractiveness of the firm or the institution by combining respective core
and peripheral embeddedness. We follow Uzzi’s (1996) results to set up this specification: core
embeddedness makes a linear contribution to attractiveness, but peripheral embeddedness makes
a linear and a quadratic contribution. This specification ensures a convex attractiveness function,
and allows the model to address both the under and the over embedded regimes.
12
Let p (= 0) be the parameter that defines the relative attractiveness of core and periphery
and let q (> 0) be the multiplier on the quadratic terms. F, and Ia, the firm and institutional
attractiveness constructs are specified as:
F,(t)
Ia(t)
For(t/ET} +p * { Fps(t/ET - q* ae / ET)’} we
Ice(t)/(*ET)} +p * {Ipe(t)/(*ET) - q * (Ipe(t)/(* ET))’} ....
=f
= ti
To mirror the proportions in Uzzi’s data, the default values of p and q are set to be 1 and 0.5.
With p=1, attractiveness is unbiased in terms of core and peripheral embeddedness. If p <1,
attractiveness favors the core and vice versa.
3.3 Positional Advantage
March (1991) argues for inclusion of centrality and variance constructs while assessing the
firm’s position within a competition for primacy. Our definition of PA, a positional advantage
construct, follows March’s formulation for advantage within a competition for primacy:
PA(t) =Fa(t) / {Fa(t)+ N(t) * Ia(t) } wena (6)
Here, N(t) is the size of the network at time t. This sector of the model is shown as a causal loop
diagram in Figure 5.
Time to
Adjust Status
+_. Change in Status
Network __ se OED
Attractiveness
Per Link = Rise of network status and
Sg. size are mutually reinforcing ae
Firm ree a —
Attractiveness —— ary Nea Network Size Network Status
+ Time to
Adjust Size
Network
Embeddedness Sse SS _
Change in Network Size
Figure 5: Evolution of Positional Advantage
13
We have drawn upon the work of Baum and Ingram (2002) and Baum et al (2003) to assess N(t)
and allied status and interdependence constructs: S(t) and D(t).
Network Size:= N(t) =C1 * S(t) * { Co*Ice(t) + C3 Ipp(t)} / Tan...
Network Status:= S(t) =Ca* N(t) * { C5«Ice(t) +Cox Ipe(t)} / Tas .
Interdépendance:= D(t) =1- Ai * { C7«Ice(t) +Cg« Ipp(t)} + Ao» N(t) oo (9)
C; (> 0) for i=1,8 are scaling parameters set to be unity without loss of generality. T,y (> 0) is
the time to grow the network. Tas (> 0) is the average cognition time needed to establish network
status. A; and A2 are positive fractions. The specification for interdependence in the face of
transaction cost mirrors Baum and Ingram (2002)’s argument that interdependence reduces while
embeddedness is building up. However, as the network size grows, the coordination burden
increases and overcomes the reduction in interdependence due to the presence of embedded
relationships.
3.4 Overall Model
Equations (1) through (8) are integrated to build the overall model. The structure of the overall
model is shown in Figure 6. Feedbacks have been shown with dotted lines.
Information
Interdependence
a~Fim's
Decien Rul
j Firm Core and Peripheral Fim
yuears passe ree = eee Embeddedness Attractiveness
a i :
Co-Evolution p- Relative Finn's Positional ’
pecs, <4---------- <t—_ Network Size
ot with Imitation Delays ABrpeveness of Advantage
‘Network Core and Peripheral Network ;
MG patswncweny
Embeddedness Density resin —— \
Oe ee Network Status|
Decision Rule
Figure 6: The Overall Model Structure
(Some constructs and polarity on the arrows omitted for ease of depiction)
14
Construct E(t) is linked with the outcome parameters in the assignment sector as follows:
E(t) = Fee (t) +p (t) or E(t) = {Ice (t) +Ice (yr sceennscosnveeees (LO)
Before setting up the base case, decision parameters ‘a’ and ‘b’ and the strength of ties 0, and 0)
are kept as independent variables. These parameters are varied systematically to explore the
response of the model over their entire range of validity. In the base case, these decision
parameters have been set to be equal (i.e. a =b). In analyses that follow the base case, target
embeddedness (ET) is set up as an endogenous parameter as follows:
ET(t) =Co * max{1- D(t)}, Vt= t>0 tester eee eee (LL)
Cg is a scaling parameter. The specification in (11) relates the target embeddedness with the
evolution of the interdependence construct. We justify this specification based on transaction
costs associated with information interdependence. When the interdependence falls, due to a rise
in embeddedness, institutions are willing to raise the desired level of embeddedness. The desire
for increased embeddedness is curbed when information interdependence rises due to increases
in the network coordination costs.
4. Validation
Owing to a lack of empirical data for one to one comparison, we cannot calibrate the model
performance against time series for each of construct of interest. Instead, we have selected a
complete and reasonable range of input parameters and explored the evolution of the full model
in a systematic manner. The goals of this exploration are to ensure that model performs
consistently, internally and externally, against the theoretical underpinnings (e.g. paradox of
embeddedness) and the dynamic hypotheses (a.k.a. the empirically observed changes in
embeddedness parameters, network size, and interdependence over the entire life cycle of
evolution).
15
Following standard practice in the system dynamics literature, we have set up a series of
tests to explore the structure and the evolution of constructs in each sector. The term structure
refers to the constituent relationships specified in the previous sections. These tests set up
selected constructs, such as decision parameters ‘a’ and ‘b’ as exogenous parameters. Tests have
been conducted over the entire span of the feasible values for each parameter (e.g. 0< a< 1), and
for all reasonable combinations (e.g. changing 0< a< 1 and 0<b<1). In this section, we present
a subset of test results. The rest of the validation results are available upon request. The output
parameter for these tests is the value of the average positional advantage (A PA) over the entire
duration of evolution. Results have been grouped under two headings: paradox of embeddedness
and evolution of process parameters.
4.1 Paradox of Embeddedness
0.11
rosttonat O-2
Advantage
0.09
0.08
Firm's 08 4 Network
Assignment Assignment
Bias (a) Bias (b)
Figure 7: Response to Variation in the Decision Bias
Figure 7 shows the model response surface as a function of decision parameters ‘a’ and ‘b’.
Recall that higher value of ‘a’ (a > 0.5) represent the firm’s bias towards building core
embeddedness and lower values (a <0.5) are biased towards building the periphery. Similarly
16
higher values of ‘b’ indicate the institution’ s bias towards building the core. The saddle shaped
response surface confirms that the model can reproduce the paradox of embeddedness postulated
by Uzzi (1996): setting ‘a’ (or ‘b’) to extremes will yield the lowest (or highest) positional
advantage. Note that our outcome variable (Average Positional Advantage, APA) is not the same
as the outcome variable used by Uzzi (Probability of Failure, POF). The functional form of APA
and USF are analytically analogous, however POF accounts for the network effect implicitly by
comparing the firm’ s performance against a constant value for the network attractiveness.
We have repeated (but not shown) our analyses using Uzzi’s input parameters with both
POF and APA as the outcome variables. Results are materially similar. Since we are interested in
isolating APA and network size effects during policy analyses, rather than compare the survival
probability, we have used APA as an outcome parameter in the rest of this paper.
Average Positional
0.094
0 0.2 0.4 0.6 0.8 1
= = = Low Risk Aversion: Assignment Bias (b)
Midium Risk Aversion
— _= High Risk Aversion
Figure 8: Effect of Changing Risk Aversion
Figure 8 shows that when the focal firm’s risk aversion rises, its average positional advantage is
reduced. Uzzi (1996) has reported similar results while using a POF formulation. We have also
explored the model response beyond replication of Uzzi’s results. For instance, we have varied
17
the relative attractiveness of periphery (i.e. parameter p in Equation 5). Figure 9 illustrates that
the APA for low values of network assignment bias will be diminished and when periphery (p)
becomes more attractive.
0.12
0.11 | “x
Average x
Positional N
Advantage 0.1 we
0.09
Attractiveness
Bias
0.5
Assignment Bias (b)
Figure 9: Effect of Varying Attractiveness Bias (p)
APA for high values of assignment bias (b) will increase with this increase in attractiveness.
4.2 Evolution of Embeddedness
In Figure 10, we illustrate evolution of key constructs assuming that the embedded target is set
up as an exogenous parameter. These results mirror Baum and Ingram’s dynamic hypotheses
(described in §2.2), except that the interdependence curve in our results has two points of
inflection.
We have repeated these results by making ET, the embeddedness target, endogenous
within the model (as per specification in Equation 11). Figure 11 verifies that the dynamic
hypotheses, i.e. the manner in which embeddedness, interdependence and network size evolve,
remain materially similar, even with this change in the model structure.
We confirm (but do not show) that the above-mentioned dynamic hypotheses remain
robust for entire feasible range of test parameters. This has increased our confidence that the
18
model is suitable for setting up further policy analyses. Before discussing policy analysis, we
direct reader’ s attention to the transient nature of positional advantage in Figure 12.
Interdependence
Fim
Embeddedness
Network
Embeddedness
Network Size
Target
Embeddedness
Lr
x4
2.7
se.
0 5 10 15 20 2 30 35 40 45
5055 60 65 70 75 80 85 90 95 100
Time (M
Figure 10: Evolution of Process Strength with Exogenous Target Embeddedness
Interdependence
Firm
Embeddedness
Network
Embeddedness
Network Size
Target
Embeddedness
0 5 10 15 20 2 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100
Time (Month)
Figure 11: Evolution of Process Strength with Endogenous Target Embeddedness
Within the setup for our base case, positional advantage attains a maximum value early during
the network evolution, however this advantage atrophies due to imitation and co-evolution
(Powell et al. 2005) within the institution, while the network size attains a maximum at the end
of our period of assessment. Hence, for the purpose of policy analysis, we include the following
four constructs as outcome variables of interest: maximum positional advantage (MPA), the time
19
at which MPA occurs (T-MPA), the average positional advantage (A PA), and the maximum size
of the network (N-max) accessed at the end of simulation. The first two variables characterize
the positional advantage in the short run and the last two terms measure the advantage over the
entire time period of observation.
be
Firm's Positional Pci °
Advantage a
o
ye
Pa
Network o
Siz ~ 8 a
7
« -
0 10 20 30 40 50 60 70 80 90 100
Time (Month)
Figure 12: Evolution of Positional Advantage and Network Size
5. Policy Analysis
Recall from the literature discussion that the primary goal for policy analysis is to assess the
efficacy of the strategies for exploration (and exploitation) of the core and the periphery. For
ease of discussion, we label the input parameter as follows: we either set a =b =0.75 ora =b =
0.25. The higher value represents a bias towards assigning ties to the core, and the lower value
represents a bias towards assigning ties to the periphery. It is clear that both policies will build
links into the core and the periphery. However an assignment bias towards the core is likely to
yield a connected network and an assignment bias towards the periphery is likely to yield
structural holes (Burt1992). We set the strength of tie parameter either at 1.0 or at 0.5. The
higher value indicates a strong tie and the lower value represents a weak tie. We also set the
20
value of ‘p’ to be either 1.5 or 0.5. The higher setting represents a bias towards the periphery
while computing the positional advantage, and a lower value represents a bias towards the core.
While naming these policies, we presume that when the institution values the periphery
more than the core (i.e. p =1.5), the focal firm and the institution are more likely to explore than
exploit the core of a network. Hence we label these policies EPR#1 through EPR#8. On the
other hand, when the institution values the core more than the periphery, the focal firm may wish
to exploit the core, and the policies are labeled as EPT #1 through EPT #8. This allows us to test
a total of sixteen policies as shown in Table 2. The following four constructs, defined in §4.3, are
used to measure the performance: MAP, T-MPA, APA and N-Max. The last two columns rank
the outputs based MPA and APA, respectively.
Table 2:Performance of Exploration and Exploitation Alternatives
INPUT Output
Embedded- Strength Strength Instination Maximum pine at Average |Sizeof {Rank |Rank
ness 4 lof Tiesin |Biasin eee which we
Assignment of Ties in the Valuing Positional MPA Positional |Network |for [for
A the Core a Advantage Advantage |Accessed |MPA |APA
Policy {Bias Periphery |Advantage Occurs
Id # aandb 6c op p MPA T-MPA APA N-Max
EPR#1| Connected | Strong | Strong | Periphery 0.582 22.4 0.1034 340 1 9
EPR#2| Connected | Weak | Strong | Periphery 0.528 26.3 0.1081 306 5 1
EPR#3| Connected | Strong | Weak | Periphery 0.350 43.3 0.1055 175 9 6
EPR#4| Connected | Weak Weak | Periphery 0.256 62.6 0.1076 40 13 2
EPR# Hole Strong | Strong | Periphery 0.554 23.1 0.0961 340 4 14
EPR#6 Hole Weak | Strong | Periphery 0.350 43.3 0.1055 175 11 7
EPR#7 Hole Strong Weak _| Periphery 0.481 27.6 0.0942 306 8 16
EPR#8 Hole Weak Weak | Periphery 0.233 64.6 0.0948 40 16 15
EXT#1| Connected | Strong Weak Core 0.519 26.7 0.1064 306 6 3
EXT#2| Connected | Strong | Strong Core 0.576 22.6 0.1028 340 2 10
EXT#3| Connected | Weak | Strong Core 0.350 43.3 0.1057 175 12 5
EXT#4| Connected | Weak | Weak Core 0.250 63.2 0.1045 40 14 8
EXT# Hole Strong Weak Core 0.350 43.3 0.1057 175 10 4
EXT#6 Hole Strong | Strong Core 0.563 22.8 0.0980 340 3 13
EXT#7 Hole Weak Weak Core 0.241 63.9 0.0990 40 15 11
EXT# Hole Weak | Strong Core 0.498 27.0 0.0982 306 7 12
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The outcome parameters confirm that in general, strong ties result in higher positional
advantage (e.g. policies EPR#1 and EXT #2) and weak ties yield a lower positional advantage
and slow the diffusion process down (e.g. EPR#8 and EXT #7). Weak ties in combination with
strong ties, either at the core or at the periphery, can yield high levels of positional advantage
(e.g. EPR #2 and EXT #1). The top three policies for MPA show high levels of network growth
(N-max), however only two of the top three APA policies come with large N-max. These
rankings also show that in some instances (EPR#) and (EXT#6), the maximum positional
advantage (MPA) may not yield a high value for average positional advantage. In effect, these
instances identify myopic search strategies (Levinthal and March 1993).
Thus, advantages accrued through exploration and exploitation policies are crucially
affected by behavioral biases (e.g. parameters ‘a’ and ‘p’ in the table), imitation and target
setting associated with the evolution of core and periphery embeddedness constructs.
6. Conclusion
We have formalized a behavior theory of network evolution using a system dynamics model.
The modeling process has yielded insights about the internal consistencies within this theory
(e.g. firm’s risk averseness raises network embeddedness above the firm’s embeddedness) and
also allowed us to test new formulations (e.g. endogenous evolution of embeddedness targets).
Our model quantifies multiple outcome constructs: the maximum positional advantage, the
average positional advantage and the maximum network size. Policy analysis results for these
constructs illustrate that, consistent with Baum and Ingram’s view shown in Table 1, it is a good
idea to consider the strength of ties, and the degree of structural holes or connected nature of
networks, while coming up with exploration or exploitation choices. Our results also show that
22
aside from the focal firm’s assignment biases, the institution’ s bias in valuing the advantage is a
significant determinant of positional advantage.
These policy analysis results are preliminary and come with many limitations. Our
modeling view is aggregate because it ignores individual attachment details and uncertainty
addressed by an agent based model (Rahmandad and Sterman 2004). Hence, our results can only
indicate aggregate performance. Owing to modeling assumptions, our results can only be tested
over a selected range of parameters. For reasons of parsimony, we ignore many critical aspects
of behavioral choices, e.g. trust and mental models. Moreover, labels may confound our results:
exploration and exploitations are not mutually exclusive alternatives within our formulation.
Exploration comes with some exploitation and vice versa. A sophisticated firm may be interested
in altering its exploration and exploitation policies during different phases of network evolution.
We are in the process of extending the model boundary to relax some of these assumptions so
that we may test all the paradox of embedded hypotheses (Uzzi 1997). The model can then be
used to address more sophisticated exploration and exploitation policies.
Our approach builds a bridge between social network research and the system dynamics
methodology based on a behavioral theory of network evolution. The promise of this approach
lies not only in the formalism and precision that it can bring into organization science but also in
the theoretical justification it can provide for simulations of network evolution.
23
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Appendix: Model Parameters
Parameter | Equation #| Range |Base Case Units
a 2, Otol 0.5 Dimensionless
Ai 9 0.005 0.005 Dimensionless
Ad 9 0.0001 0.0001 | Dimensionless
b 3 Otol 0.5 Dimensionless
Ci-Cg 7,8,9 1 1 Dimensionless
Co 11 0.001-200| Not used | Dimensionless
ET land4 | 0.001-100 100 Dimensionless
For(t=0) | Implicitin2 | 0.0005 0.0005 | Dimensionless
Fpe(t=0) | Implicitin2 | 0.005 0.0005 | Dimensionless
Ice(t=0) _| Implicit in 3 0.5 0.5 Dimensionless
Ipgt=0) _| Implicit in 3 0.5 0.5 Dimensionless
N(t=0) Implicit in 7 1 1 Dimensionless
p 4 0.5-1.5 1 Dimensionless
q 5 0-2 0.5 Dimensionless
r 3, 6, 10 1-1.5 1.1 Dimensionless
S(t=0) Implicitin 8 | 0.001 0.001 Dimensionless
Tap 8 10-50 30 Month
Tag 1 2-4 2 Month
Tan 7 10-50 30 Month
Tr 3 2-4 3 Month
9c 2 0-1 1 Dimensionless
Op 2 0-1 1 Dimensionless
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