Firm Prominence through Sociotechnical Capital: A Social ... - MISRC

Competition in the Absence of Standards in Enterprise Software Industries: A
Social Network Perspective
Ramnath K. Chellappa 1
{ram@marshall.usc.edu}
Tel: (213) 740 3920
Nilesh Saraf 2
{nsaraf@marshall.usc.edu}
Tel: (213) 740 7283
ebizlab
BRI 401, 3670 Trousdale Parkway
Department of IOM
Marshall School of Business
University of Southern California
Los Angeles, CA 90089
Fax: 213-740-7313
September 2002
(Please do not quote without permission. Comments will be appreciated)
Acknowledgement
Research supported in part by the Center for Telecommunications Management, USC. The authors are high
indebted to the following people for their valuable comments: Paul Adler, Sriram Dasu, Omar ElSawy, Dan
Levinthal, Ann Majchrzak, Mahesh Nagarajan, Barrie Nault and Dan O'Leary.
Any error is solely the responsibility of the authors.
1
Ramnath K. Chellappa is an Assistant Professor of Information Systems and co-director of ebizlab at the Marshall
School of Business, University of Southern California.
2
Nilesh Saraf is a Ph.D. Candidate in Information Systems at the Marshall School of Business, University of
Southern California.

Competition in the Absence of Standards in Enterprise Software Industries: A
Social Network Perspective
Abstract
Whether developed by a firm (de-facto) or set by a committee (de-jure), interface standards are
an important element of competition in software industries. While adopting the right set of
technology standards for their products is crucial for firms in the enterprise software industry, the
absence of a single set of open standards or leading standards from a dominant firm makes this
choice difficult for firms. Despite the absence of standards seamless interaction between
products of different firms is a requisite for organizational end-users. Therefore, firms maintain
alliances to render their products technical compatible. While prior research identifies primarily
access to user bases as the network externality benefits arising from technical compatibility, we
argue that in addition alliances also enhance social compatibility. We view this dimension of
compatibility as the market’s perception of compatibility resulting from reputation transfer and
knowledge spillovers through alliances. We also argue that benefits from such compatibility are
transmitted through both direct and indirect partners in the alliance network. We use the social
network perspective to understand how resources are transferred in this alliance network and
aggregate these resources into a construct that we call Sociotechnical capital. We then propose
that in the absence of uniform industry-wide leading standards the relative prominence of a firm
in this network is a valid surrogate for market power and is correlated with its performance. To
address the limitations of extant social network measures we develop an alternative theoretically
grounded metric for firm prominence that is based on the Sociotechnical resource transfer. An
analysis of 65 enterprise system firms empirically supports our proposition. Our study offers
insights into the behavior of firms in the enterprise systems software industry.
Keywords: Technology standards, software industry, enterprise resource planning (ERP),
software architecture, partnerships, social network theory, standards competition
2

1. Introduction
"Standards wars (are) battles for market dominance between incompatible technologies
(and) are a fixture of the information age"
-Carl Shapiro and Hal Varian, Information Rules
In the information technology industry an enterprise systems software (ESS) firm’s choice of
interface standards for its products significantly influences competition in its market. This is
because from the perspective of organizations that use information technology (IT) standards
play an important role in the building of IT infrastructure supporting their business processes
(Keen 1991). IT infrastructure at user organizations consists mostly of software components
manufactured by ESS vendor firms such as SAP, I2, JDEdwards, PeopleSoft, etc. (Davenport
1998). Given that these components need to work with each other an ESS vendor has the
alternative to either develop all the components by itself (i.e., the entire system); or to make a
few components that can be easily integrated with complementary components from other ESS
firms. When there are no uniform industry-wide interface standards an ESS vendor has to
incorporate into his own components one or more complementary vendor’s proprietary
standards. Thus, ESS vendors have to make strategic choices in their selection of standards. The
primary goal of this paper is to identify an alternative metric to represent the relative market
power of ESS firms in this industry characterized by: 1) no uniform industry-wide open
standards 2) multiple vendors offering one or more competing or complementary components 3)
integration across components of different vendors being very important for organizational end-
users. Past research suggests that in the absence of uniform industry-wide open standards the
leading set of standards is controlled by the firm(s) with the most market power. As more
functionality is added to enterprise software, for ESS vendors the selection of the right set of
standards becomes important and influences their survival 3.
There is little research in information systems (IS) that offers understanding about competition
and how market power is derived in a standards-driven industry. The primary focus has been on
the benefits of adopting uniform standards within an organization - also known as a corporate IT
standard (Gordon 1993). Here an organization frames policies to ensure enterprise-wide
3 “… market selection and incremental innovations induce each firm to converge towards the dominant standard and
less adaptive firms are pushed out of the market,” Antonelli, C. (1994). "Localized technological change and the
evolution of standards as economic institutions." Information Economics and Policy 6: 195-216..
3

compatibility of its systems and processes. Benefits of adopting such a corporate IT standard
include improved coordination (Malone 1987), enhanced connectivity from data integration
(Wybo and Goodhue 1995), reduction in IT maintenance costs and local IT responsiveness
(Kayworth and Sambamurthy 2000) among others. Standardization of IT in organizations is also
found to be related to performance of firms (Chatfield and Yetton 2000) and supply chains
(Yang and Papazoglou 2000). However, other than one recent article on competition in the
Japanese PC market (West and Dedrick 2000) research in IS has largely ignored the competition
between ESS manufacturers whose products incorporate standards required by organizational
users. While such competition has been addressed to some extent by economics literature the
impact of organizational user perceptions of compatibility (i.e., corporate IT standards
requirement) on competitive behavior of IT manufacturers has not been explored at all. Our
research attempts to bridge this gap through an analysis of competition in the enterprise software
industry.
In order that organizational users derive the benefits of corporate IT standards it is essential that
components of one ESS vendor works well with multiple other ESS vendors’ components. As
against in the past, currently an organization's enterprise system is often a collection of software
components manufactured by a multitude of vendors (Davenport 1998). For example, a payroll
system that was programmed in COBOL and housed in a mainframe may now consist of
components ranging from Oracle databases, Web servers by Apache, browsers from Netscape
and an application component from an Enterprise Resource Application (ERP) vendor like SAP.
In this industry while there exist standards for low level communication such as at the transport
level and object stages there do not exist a uniform set of high level compatibility rules to enable
a plug-n-play type of operation (Yang and Papazoglou 2000). Thus, to ensure interoperability
among their complementary components ESS vendors may adopt each other’s standards even if
they maybe offering competing components. This is typically accomplished through explicit
alliances between firms such as those involving licensing, product development and release
agreements (David and Greenstein 1990) through which an ESS firm’s technology propagates.
There are also adapters or consultants in this industry who benefit by the lack of common
technological standards (Farrell and Saloner 1992) and are influential in the social interaction
processes. Such social interactions (examples: joint conferences, trade shows, and training
sessions) not only result in knowledge exchange between ESS vendors but also enhance
4

compatibility perceptions of the organizational user. These perceptions are important for
corporate IT requirements and influence organizational users’ selection of ESS vendors. Thus,
while propagation of technology through alliances contributes to a firm’s dominance along the
supply-side, favorable compatibility perceptions of end-users are demand-side drivers of
dominance (Stewart 1996). In this scenario prominent ESS firms can better influence adoption of
their standards (Kotabe, Sahay et al.), influence consultants and integrators and leverage better
their effort in social promotions to improve firm performance.
In this paper we first provide an alternative theoretical framework to address certain limitations
of economic models towards understanding the sources of market power for ESS vendors. Using
the social network perspective we develop a model of resource transfer for industries where
interface technology standards play an important role. We propose that in addition to benefits
from technological compatibility ESS firms also derive social benefits such as reputation and
knowledge spillovers through alliances. The firms attain a favorable structural position due to
their access to resources. First we aggregate these resources into a construct called
“Sociotechnical capital” and then propose that the market power of a firm, termed as a firm’s
relative prominence, can be measured through its structural position in the network. To develop
an empirically tractable metric for such a structural position we improve upon an existing
prominence measures by incorporating flow of benefits from both direct and indirect partners.
By analyzing data on 65 ESS firms and their alliances we verify that our metric is correlated with
firm performance.
The paper is organized as follows: In the following section we present our research questions and
briefly discuss extant literature in the context of the ESS industry. In section 3, we develop a
model of resource transfer in alliance networks and describe the construct of Sociotechnical
capital. In section 4 we develop the modified measure of firm prominence and examine its
applicability in a study of 65 ESS firms. Section 5 concludes with the implications of this work
for future research in information systems as well as for scholars in the field of strategy and
management.
2. Frameworks to study competition in standards-driven IT industries
It is predominantly literature in economics that has addressed firm competition where standards
are involved (Saloner 1990; Axelrod, Mitchell et al. 1995). Examples are the early VCR
5

industry where VHS emerged as the winning standard and: the operating systems markets where
multiple separate standards such as Unix, Windows, MacOS, etc. still exist. The main element in
these models is the accumulation of externality benefits either by adopting a common standard or
by constructing adapters to enable compatibility. Along these lines Katz and Shapiro (1985)
have argued that firms with small user bases have strong incentives to make their products
compatible with those of players will larger user bases. Even in multi-component markets or in
competition between multiple firms of equal size compatibility is still the desired outcome
(Economides 1989). All these models conclude that it is beneficial to adopt the leading standard
in terms of user bases. However, it is believed that where there are no explicit standards present
for adoption the applicability of these models is limited (Economides 1989, p1180). However, it
has been observed that using economic models such as conventional game-theoretic analysis to
empirically study complex alliance compositions is "especially difficult because payoffs for each
firm depend upon the choices made by all other firms (Axelrod, Mitchell et al. 1995, p. 1497). "
Further, these models imply that that i) externality benefits of adopting standards (measured as
increase in user bases or market share) maybe the only benefits to an ESS vendor through an
alliance and ii) these benefits accrue only due to a direct linkage across vendors.
Though it is suggested that formation of implicit and explicit alliances maybe required for
development and sponsoring of standards (Saloner 1990), little empirical research actually exists
that can be applied to the context of ESS industry. To gain market power individual firms must
be incentivized by coalitions to join them (Axelrod, Mitchell et al. 1995). The authors (Axelrod,
Mitchell et al. 1995) observe earlier that purely analytical models cannot consider complex
alliance compositions since individual firm payoff functions depend on simultaneous choices of
all other firms and as a result define the utility of firm joining an alliance in pair wise relations.
Hence the authors propose modifications for empirical tractability and assume that firms are
either close or distant rivals. However such strong assumptions may not be suitable to study our
industry context as firms compete in multiple component markets and they may complement
each other in one segment while competing in another. More importantly it does not elaborate
on the nature of benefits maybe transferred between the ESS firms and fails to take into account
benefits from their indirectly connected partners.
To devise a surrogate measure of market power we suggest that the understanding offered by the
economics literature has to be combined with the insights from literature on alliance networks. In
6

the absence of uniform industry-wide open standards we note that ESS firms form alliances that
allow them to absorb other’s standards and propagate their own. Thus these alliances are formed
not only for the purpose of deriving network benefits from access to larger user bases but also for
enhancing learning and knowledge transfer (Hagedoorn and Duysters 1999, p.9). This becomes
especially important in constantly evolving technologies such as enterprise software where, to be
successful, ESS vendors invest in aligning their products along dominant technological designs
(Suarez and Utterback 1995). When ESS vendors form alliances they acquire competencies
through exchange of knowledge bases and align their information processing structures with one
or more alliance partners. Therefore, it becomes important for ESS firms to identify other ESS
firms having higher market power. Towards this end we introduce social network theory as a
framework to study competition among firms in the ESS industry and to devise a measure for
market power of ESS vendors. Just as one approach to analyzing firm behavior in markets is
through economic paradigms more recently theories from social sciences such as economic
sociology (Kogut, Walker et al. 1995) and actor network theory (Monteiro 2000) also are able to
represent complex social, economic and technical perspectives (Chellappa and Saraf 2000;
Fomin and Keil 2000).
2.1. Using social network theory to study competition in enterprise software industry
The goal of this sub-section is to familiarize the reader with basic concepts in social network
theory to be able to understand the development of constructs in the later section that are specific
to the ESS industry. Social network theory has typically been used to study set of individuals
with links between them representing specific social ties including interaction ties (Contractor,
Seibold et al. 1996), friendship ties (Zeggelink, Stokman et al. 1996), and marital ties (Padgett
and Ansell 1993). Research in organizational behavior, human communication and computer-
mediated communication has also adapted this approach to study networks of members within an
organization (Barley 1990). Most of this early work in social networks focused on within-firm
issues where the actors typically represent employees and the relationship linkages were
enclosed in boundaries of the particular organization. During the last decade the social network
metaphor proposed earlier by Tichy et al. (1979) has been considerably extended to analyze
market level behavior where linkages in the network represent various types of relationships
between firms (Ahuja 2000). For example, such networks have been used to study pricing
7

strategies of investment banks (Podolny 1993), power relations between corporations and
investment banks (Baker 1990) and niche overlap in a patent citation network of firms in the
semiconductor industry (Podolny, Stuart et al. 1996).
In our research, we view the ESS industry as a network of firms with each link between them
representing an alliance through which resources flow between firms. Research in this field has
also developed a variety of network measures with purpose of describing and capturing network
level phenomenon. Of particular interest to us is the measure of relative status (prominence) of a
firm compared to others in its network. This measure can be used to represent the dominance of
the different ESS firms relative to each other. This is consistent with the observations that
“industrial structures can be represented as a set of positions that are arranged hierarchically
according to the prominence of their occupants (Stuart, Hoang et al. 1999, p.318).” In the status-
based models of market competition prominence plays an important role in influencing
organizational performance of a firm as well as that of its affiliates (Ahuja 2000; Burt 2000;
Stuart 2000). According to this literature the status of an actor is influenced by its firm specific
attributes such as past demonstrations of quality, technological pioneering or higher market
share. In addition, in many industry contexts status of firm can also be increased through
linkages with prominent firms. These linkages provide the alliances partners with access to
knowledge, technological capabilities, newer markets, production know-how, R&D joint
ventures, etc. (Liebeskind, Oliver et al. 1996; Walker, Kogut et al. 1997). The prominent a firm
is, the better it can leverage its own position through benefits such as lower transaction costs and
risks (Podolny 1993), preferential treatment from suppliers and higher returns from quality - and
therefore price (Benjamin and Podolny 1999). Other findings are that that higher prominence
increases the chances of survival of a firm in the semiconductor industry (Podolny, Stuart et al.
1996) and that that firms with low status benefited in their market capitalization and time to IPO
due to their partnerships with high status firms (Stuart, Hoang et al. 1999).
The network process through which an ESS vendor achieves prominence varies considerably
across industry contexts in terms of a supply-side or a demand-side rationale. Prior literature has
mostly focused on only a supply-side rationale (Stewart 1996). For example, in the high-
technology semiconductor industry (Podolny, Stuart et al. 1996) or in the biotechnology industry
(Shan, Walker et al. 1994), research and development partnerships between firms are significant
in increasing prominence. Similarly, in the IT industry firms may achieve higher prominence
8

when they cross-license technologies and interface standards of prominent vendors. We suggest
that in addition to the above supply-side reasoning of why firms achieve prominence, the
demand-side factors, i.e., those that matter from the organizational user's (customer’s)
perspective, also need to be considered. These factors include market’s perceptions of
compatibility influenced by trade-shows, product compatibility announcements and certification
by consultants. The perception of compatibility has a role similar to that of brand in consumer
goods markets. We suggest that in the ESS industry, both supply-side and demand-side
reasoning needs to be considered to understand how firms achieve higher prominence.
3. A model of relative prominence in the enterprise software industry
Since our primary goal is to establish that relative prominence in the alliance network as a valid
measure of market power, we proceed in two steps. First, we propose that the alliance network is
indeed a non-trivial network, that is, the occurrence of the number of alliances is not
significantly low compared to other alliance studies in the high-technology industries. In
particular, we also apply the theory of network formation in economics literature (Bala and
Goyal 2000) to better understand the structure of the network 4. Second, we shall devise a rational
choice model of network prominence in the ESS industry by theoretically justifying four key
assumptions regarding the characteristics of and benefits from alliances among ESS firms. In this
discussion rigorously grounded to context, we also explain the nature of competition and how
market power accrues to ESS firms.
We consider a model of alliances where a focal ESS firm is a source of benefits that other firms
in the network can access by maintaining an alliance with the focal firm. We propose that while a
focal firm derives benefit from alliances it also benefits from indirect linkages. Further, we also
model benefits from all actors in the network of partners as attenuated before they reach any
focal firm. This model of alliance network formation has parallels with the recent Bala and
Goyal’s (Bala and Goyal 2000) model of social and economic networks. Bala and Goyal (Bala
and Goyal 2000) refer to the attenuated benefits as decay or delay associated with indirect links.
They observe, “in the case of two-way flow of benefits, networks with a single star and linked
stars are strict Nash.” (p. 1186) Note that Bala and Goyal’s model is aimed towards identifying
4 In our results section we present a partial empirical evidence for this proposition.
9

the most stable alliance network structure, and their findings indicate that if all actors are rational
then eventually the networks will be empty or if connected, they will rapidly converge to a limit
network, i.e., a star or a linked star.
The findings of Bala and Goyal can be interpreted to conclude that three alternative structures of
a limit network in the ESS industry are possible. These are: a. eventually all standards will be
open and no firm will see a need to invest in alliances (empty) or b. there will be a de facto
leader and leading standard and firms will invest only in alliances with this leader (star) or c.
there will be several distinct leaders and leading standards linked to each other and firms will
invest in only one of them (linked star). In fact alternative c, agrees with the findings of
Axelrod, et al (Axelrod, Mitchell et al.) that where technology standards are involved, eventually
distinct coalitions will emerge such that the extent of rivalry within coalitions is minimum.
Proposition 1: The current alliance structure of the enterprise software industry is sub-optimal
(not strictly Nash), representative of a partially matured industry.
Proposition 1 states that it is not possible to clearly identify leaders as the industry structure and
standards have not converged to stability. We argue that understanding the source of market
power is important at this stage of the evolution of the ESS industry since convergence to
uniform industry-wide open standards is unlikely in the long term. Every firm behaves rationally
so as to maximize its returns from alliances. At any point in time the networks resulting from
these actions are intermediate stages converging towards the most stable formation, i.e., strict
Nash (Bala and Goyal 2000). This implies that all firms simultaneously re-evalute their alliance
decisions for their own profit maximization and eventually converge to a strict Nash when there
is no incentive to re-evaluate. We attempt to understand the enterprise software industry at such
an intermediate stage since we believe that this industry will be characterized by non-unified
standards in the longer terms. This conclusion is also supported by economics theory on
standards adoption where existence of adapters retards standards adoption (Farrell and Saloner
1992). As consultants and integrators are active entities in this industry, we propose that waiting
for standards to converge is unrealistic. Hence the relative prominence of an ESS firm in its
alliance network is a strong indicator of its market power. The rest of our paper is focused
towards devising a surrogate metric for market power of ESS vendors. First we formalize the
benefits and costs to each ESS firm in maintaining alliances using which we develop a new
metric for relative prominence of an ESS firm within a network.
10

3.1. Social and technical resources transferred between ESS firms
To understand more clearly how ESS vendors benefit from their alliance networks, we proceed
in the following two steps. First we discuss the nature of benefits to an ESS vendor from an
alliance with another vendor. Second, we discuss how these benefits flow through the alliance
network. The nature of benefits from an alliance arises from two facets of compatibility,
technical and social compatibility. Technical compatibility results from an alliance when the
partners align their product interface design at the data, application and business process level
(Yang and Papazoglou 2000). Economic models of standards competition primarily describe
benefits from technical compatibility as access to user bases of partners. Social compatibility is
the market’s perception of compatibility between the products of alliance partners. The
investments made by aligning vendors in joint promotions, conferences and pre-announcements
enhance this perception of compatibility. Thus this perception becomes specific to alliance dyad.
It is further enhanced as third party integrators and consultants develop integration tools to
enhance interoperability. In this way alliance benefits including transfer of reputation, third party
investments and access to consultants contribute to enhancing the organizational users’
perceptions of compatibility. Further, along these two dimensions, direct benefits are accrued
through direct and consciously forged alliances with partner firms and indirect benefits are
transferred due to recursive flow from partners of directly connected partners.
Consider a network of n ESS firms and a set of linkages among these representing alliances. We
assume that each firm has made a rational decision at a particular point in time in terms of the
choice of its alliances. Further, it has also invested in its relationships such that its net benefits
(less costs incurred in maintaining these) is maximized. We do not assume a dynamic network
where firms choose to expand their market and therefore strike newer linkages as also adopt
other asymmetric strategies. The alliance linkages can be associated with technical and social
compatibility with its partners and with a certain configuration of alliance linkages these firms
gain access to benefits directly and indirectly in this network (Figure 1 represents a subset of our
sample ESS vendors with alliances between them).
Technical benefits have been well documented in economics as well as some IS literature (Katz
and Shapiro 1985; Kauffman, McAndrews et al. 2000) as small firms having significant
incentives to make their products compatible with that of larger firms. This is due to the
11

expectation that user base of the larger firm is now accessible to the smaller firm due to
compatibility, i.e., larger the user base larger is the potential benefit. As discussed before,
demand-side drivers play an important role in emergence of market structure, and the perceptions
of compatibility by the organizational user is one such driver. Therefore, information transfer
through these non-technical (referred to as social) mechanisms such as joint advertising, trade
show, and user conferences contribute to user perceptions of compatibility. In an alliance social
compatibility between a pair of ESS vendors may be enhanced because such ties are transmitters
of reputation as also conduits of knowledge spillover. As third party investors and the industry
experts participate in diffusing knowledge the perception of compatibility is further enhanced as
organizations get embedded in networks or other kinds of super-ordinate relationships (Argote
2000, p.162). This knowledge transfer occurs through people-technology, people-task and task-
technology networks across the partners. Also, investment in alliances increases absorptive
capacity of the partners through which knowledge about product interface design can be
exchanged efficiently (Conner and Prahalad 1996).
In our context, to begin with, every firm by virtue of its own technology and past demonstrations
of quality, brings with it a certain amount of resources (including user bases, reputation, access
pool of consultants, etc.) to the network, that are now available as potential benefits to its
partners. Adler et al., (2000, p.6) observe that a network resource like Social capital is more
commonly complementary to other resources and further it is more akin to a collective good,
rather than a pure private or public good. Unlike a private good, these resources are shared, but
not to every body, as public goods are. These resources are available only to those partners who
have invested in relationships with the firm.
Assumption 1: The greater are the exogenous (non-network based) resources of the alliance
partners greater are the social and technical benefits derived by the focal ESS firms.
Formally we call this exogenous value as j( j > 0, ∀j)
e e and normalized for the whole
⎛ n ⎞
network⎜∑ej=
1⎟.
This value is intrinsic to each firm in the network. It is representative of
⎝ j=
1 ⎠
resources such as existing user base, consultants, integrators, implementers, etc., all who have
accumulated knowledge about integrating products of the focal ESS vendor. These resources are
12

useful to alliance partners. Our above assumption is in line with the observation made by Portes 5.
In the absence of any network or relationship with other firms a firm’s benefit is only based on
its own resources, i.e.,b f ( ) . e =
∑
i j
j j
However these alliances not only need initial investment but they also incur a maintenance cost
(Adler and Kwon 2000). We assume that these costs incurred by a focal ESS vendor increase are
increasing in the prominence of its partners. Given that prominent firms are considered to be
selective in their partnerships (Benjamin and Podolny 1999) the cost of maintaining an alliance
can be considered to be dependent on a firm's prominence. In the ESS industry firms that wish
to make their components compatible with another firm's components incur a cost either in the
form of licensing fees or self-constructed adapters. Therefore, in order to be selected as an
alliance partner a firm may have to invest in upgrading its product quality and developing
additional capabilities that are complementary and useful to partners. In other words the cost of
creating/maintaining technical and social compatibility depends on firm status.
Assumption 2: Higher the relative prominence of the focal ESS firm higher is the technological
and social cost required by alliance partners to maintain a relationship with the focal firm.
For a focal firm i let the relative prominence of its alliance partners be and let be the c
aggregate cost incurred in forming alliances with these selected vendors. Formally we can state
assumption 2 as c ∝ s , ∀i
↔ j = 1.
s j
i
Since a firm’s status is lowered if the affiliate has a low quality product (Stuart, Hoang et al.
1999), they strive to maintain their reputation and to signal quality when forming alliances. This
may involve social signaling through hiring of a high profile CIO, engaging a branded, expensive
advertisement firm, partnering with specific adapters, etc. Often these costs are directed at the
type of firm they wish to partner with. In order to exploit and sustain the opportunities afforded
by relationships with partner firms organizations also have to invest in continuous learning
mechanisms (Metcalfe and Miles 1994) where learning is then dependent on the prominence of
partners. Not only may a prominent firm, charge higher licensing fees but it may also require its
partner firms to invest in jointly sponsoring user conventions, trade shows, etc. Thus, these costs
5 He clearly distinguishes between resources themselves from the ability to obtain them by virtue of membership in
different social structures. Portes, A., "Social capital: Its origins and applications in modern sociology," Annual
Review of Sociology, 24, (1998), 1-24.
13

not only include the cost of making product interfaces compatible but also aimed at maintaining
relationships at a non-technical sense to enhance market’s perceptions of compatibility with
alliance partners.
A unique element of multi component markets is that while firms have to cooperate in some
complementary component markets to leverage externality benefits, they have to compete with
the same firm in other markets. Therefore, firm relationships or alliances have to be
representative of such co-opetition. We could argue that firms that have more of the same
components and less of complementary requirements would choose to form a weak relationship.
Thus, we could describe a generic term, "strength of the aggregate relationship” as a measure of
the extent to which firms are interdependent due to their competition, cooperation requirements.
The degree of such interdependency between firms can reflect the level to which learning
mechanisms are customized, information-processing structures (Galbraith 1973) are aligned and
absorptive capacities are developed (Cohen and Levinthal 1990). One such measure in our
context could simply be multi-market contact as two firms are unlikely to have a high degree of
interdependency if they have a high multi-market contact (Axelrod, Mitchell et al. 1995). Thus
if a firm chooses to have a very close relationship such as not just mere licensing of technology,
but co-development of products as well, then it would naturally have to invest heavily in both
technical as well organizational mechanism alignments. Consequently due to a strong
relationship, flow of benefits would be better facilitated.
Assumption 3: An ESS firm’s required investment and corresponding benefits from a
partnership, is dependent upon its desired strength of the relationship.
If rij is representative of the focal firm i ’s strength of relationship with adjacent firms j , and if
rjk , ∀i ↔ k =2
is the strength of relationship between firms that one and two path lengths away,
then combining assumptions 1 and 2, we can write the sum total benefits to a firm as
∑ ∑∑ ∑∑∑
b = r e + r r e + r r r e + ... ∀i ≠ j, k,
l
i ij j ij jk k ij jk kl l
j j k j k l
i ↔ j = 1, i↔ k = 2, i↔ l = 3,...
Similarly, combining assumptions 2 and 3, the cost of a focal firm in investing in relationships
with its adjacent firms is
14
∑
c = r s , ∀i≠ j, i ↔ j
i ij j
j
= 1
(1.1)
(1.2)

By selecting alliance partners firms directly incur the costs of maintaining these relationships.
However, organizational users not only construct their IT systems using components from
alliance partners but they also purchase and implement components from unconnected vendors.
This implies that if a third firm is compatible with a direct partner of a focal firm, then the third
firm's components are likely to more compatible with the focal firm as compared to a completely
unconnected firm. Thus product bundling across different component makers can further
enhance technical benefits to an indirect affiliate of one of the participants in the product
bundling strategy.
Indirect ties
Direct ties
Benefits
• Access to user bases
• Potential to be bundled with
other components
Benefits
• Access to user bases due to
technical compatability (Katz
and Shapiro 1985; Matutes and
Regibeau 1988; Economides
1989)
• Increases likelihood of
bandwagon effect (Katz and
Shapiro 1985)
• Increased likelihood of
collaborative component design
(Henderson and Clark 1990)
Costs
• Licensing fees (Kotabe, Sahay et
al. 1996)
• Constructing and maintaining
adapters (Farrell and Saloner
1992)
Benefits
• Knowledge spillovers and
information transfer (Holm,
Eriksson et al. 1999; Ahuja
2000)
• Acquisition of ideas and
practices (Burt 2000)
Benefits
• Transfer of reputation (Podolny
1993)
• Knowledge spillovers and
information transfer (Ahuja
2000; Argote and Ingram 2000)
• Acquisition of ideas and
practices (Burt 1987)
• Stimulating third party
investments (Metcalfe and
Miles 1994)
Costs
• Installing learning mechanisms
(Metcalfe and Miles 1994)
• Aligning information
processing structures (Galbraith
1973)
• Increasing absorptive capacity
(Conner and Prahalad 1996)
Technical dimension Social dimension
Table 1: Sociotechnical Resource Transfer Matrix
The assumption that benefits can flow through multiple network linkages has also been a main
element in network models of firm behavior and competition in strategy literature. Similar to
direct ties indirect ties also are conduits of knowledge spillovers and technical breakthroughs
(Ahuja 2000). It is also argued that new ideas and practices also permeate through the network
of ties (Burt 2000) and these effects from indirect ties are mediated by the intermediate
15

elationships (Holm, Eriksson et al. 1999, p.475). Thus, while firms do not incur any cost of
having an indirect connection, benefits do accrue indirectly. The indirect effect is consistent with
the notion of decay or delay that has been introduced in recent research on network formation
(Bala and Goyal 2000). Table 1 summarizes our understanding as stated in these four
assumptions.
Assumption 4: An ESS firm derives benefits from indirectly connected firms at no direct cost to
itself. These indirect benefits are mediated by the intermediate firms.
3.2. Socio-technical Capital as an aggregate resource construct
We define a firm's access to the net benefits (Table 1) from its network as the Sociotechnical
capital of a firm. This term is derived from an umbrella concept called "social capital" and is
broadly defined as "the sum of resources accruing to an individual or group by virtue of their
location in the network of their more or less durable social relations (Adler and Kwon 2000)."
Bourdieu and Wacquant's (1992) define social capital as “the aggregate of the actual or potential
resources which are linked to possession of a durable network of more or less institutionalized
relationship of mutual acquaintance or recognition.” While many definitions for social capital
exist in literature (see Adler and Kwon (2000) for a review) we primarily adopt the view that
Sociotechnical capital is a network resource, created in the alliance network of ESS firms, and
results in higher performance in standards immature markets. This resource is not a substitute for
intrinsic capability, exogenous to the network. Rather, as suggested by Portes (1998), it is a
complement to these exogenous abilities of the firm. Also, given that sociotechnical capital is not
"free" and requires a maintenance cost, the choice of alliance partners has to be a strategic
decision. Olson (1965) points out that alliances create collective benefits. Similarly, Coleman
(1988) and Adler et al. (2000) argue that social capital is a collective good, as against one that is
purely private to the creator or purely public to everyone. The sociotechnical capital of an ESS
vendor is a collective good that is available to everyone who invests in an alliance network.
Social capital has been operationalized mainly through network measures such as centrality,
betweeness, brokerage, prominence, etc (Burt 2000). As discussed in section 3.1 the relative
prominence of an ESS firm in its alliance network is an important determinant of the potential
access to network benefits and therefore an indicator of its market power. By virtue of its market
power an ESS vendor is able to enhance it performance. Thus we propose
16

Proposition 2: The relative prominence of an ESS firm due its access to social and technical
resources, from both directly and indirectly connected partners is correlated with its
performance.
4. Operationalization of relative firm prominence
We examined various prominence measures in social network literature, which could be used to
represent prominence as conceptualized in this article. Common measures for prominence are
centrality, power, status, proximity, and brokerage (Wasserman and Faust 1994), Bonacich
centrality (Bonacich 1987) and Knoke and Burt’s prominence (Knoke and Burt 1983). However,
existing prominence measures have limitations for this context. For example, while Freeman’s
degree-based measure considers only adjacent actors, his closeness-based centrality is measures
the aggregate path distance of a focal actor to all other actors. The betweenness centrality
measures how many times a particular actor lies on the shortest connecting path between all pairs
of actors. Though closeness-based and betweenness-based prominence measures capture the
network-wide influence of a focal actor, the moderating effect of intermediating actors’
prominence on the focal actor is not captured (Ibarra and Andrews 1993). Bonacich’s measure
(1987) overcomes both limitations, i.e., it considers not only adjacent actors but also indirectly
connected ones; and it also considers the intermediating influence of other actors. However
Bonacich does not provide a rational argument for the nature of the mediation (refer to (Braun
1997)) for a detailed discussion). Therefore to overcome the above limitations we extend the
rational choice model of status (Braun 1997). The critical assumptions of Braun are also
consistent with the recent model of network formation (Bala and Goyal 2000).
We consider a particular instance of a network where each ESS network has formed alliance
links with selected other vendors using a rational criterion. That is, every vendor seeks to
maximize its benefits in excess of costs. The profit maximization function of each firm is
[ b − c ], ∀ i
(1.3)
max i i
j
where b and are given by equation (1.1) and (1.2) respectively. If we assume that at any point
c
i i
in time the industry network is representative of collective rational decisions of all firms then we
can solve equation (1.3) to obtain an empirically measurable s , a focal firm’s relative
prominence in its network of alliances. This is given by:
i
17

n−1 p
∑∑zik n−1
p
∑∑zik ∑rkjsj p= 0 k p= 0 k j
si
= +
1+ n 1+
n
The derivation of the empirical metric is given in the appendix.
5. Empirical Study
We collected data from two independent sources from February to April 1999. Our first source
is an un-biased (not related to any vendor or end-user firm) industry group that employed a
consulting organization to collect revenue and other information for nearly a complete set of ESS
vendors. The consulting organization employed a survey instrument and the response rate was
nearly 100%. For our study we first considered all of the top 100 ESS firms (ranked by revenue)
made available to us. Our second source of data was press releases, corporate partnership
documents, personal telephone interviews and websites of ESS vendors. For each of the hundred
firms we collected information on the identity of its alliance partners who were also ESS
vendors. An alliance in our context refers to any formalized inter-organizational arrangement
that includes technology licensing to co-development of products. As per our coding scheme
whenever an ESS firm had an alliance with another vendors we assigned that as a ‘1’ in our
alliance matrix. This way we had a matrix of 1s (or 0s) signifying alliances (or an absence-of
one) among the top 100 firms.
From these 100 ESS vendors we selected 65 for our study. The criteria for selecting these 65
firms were i) each of these vendors should have at least one alliance with others in this group 6
and ii) all vendors should be as higher in the industry ranking as possible iii) the sample of firms
should form a completely connected network (that is, the all firms in the sample should belong to
the same component 7 of the 100-firm network). The first two criteria would also avoid the
possibility of a sparse network and capture the alliance behavior more accurately. The third
criterion was included because our measure of socio-technical capital was applicable and
comparable across actors that belong to the same component of the network. A similar sampling
6 A similar sampling criterion is also used by Chung et al. (2000) where they include investment banks in their
network sample depending on whether the bank was involved in an underwriting deal (p.8).
7 A component in a network is those set of actors that are reachable from all other actors. Wasserman, S. and K.
Faust (1994). Social Network Analysis. Cambridge, Cambridge University Press.
18
(1.4)

criterion 8 is also used by Chung et al. (Chung, Singh et al. 2000, p. 8) where they include
investment banks in their network sample depending on whether the bank was involved in an
underwriting deal. This method is mainly used to avoid the possibility of sparse networks and to
capture the role of linkages (in our context, alliances). Accordingly, from this 100X100 we
eliminated 30 vendors who had no alliances with others in the top-100 list and hence were
isolates. A large percentage (>60%) of these isolates were small firms. As for the remaining 70
vendors we used the distance matrix procedure in UCINET IV (Borgatti, Everett et al. 1992) and
found that that five vendors had links among themselves but not with the rest of 65 firms. These
were also then eliminated.
The matrix of remaining 65 vendors had a total of 196 alliance linkages. For the purpose of this
research we assume that benefits flow two-way (Bala and Goyal 2000), i.e., it did not matter
which firm initiated the alliance. Figure 1 presents a selected subset of vendors and the alliances
among them. Our final 65 ESS firms offered components from a list of 15 different components
ranging from advanced planning and scheduling packages to business intelligence software.
Example Set of Enterprise System Software Component Market
Firms*
**
(number of participating firms *** )
SAP America, Oracle Corp., J.D. Edwards, Baan Advanced Planning and Scheduling (19)
Company, JBA International, System Software Customer Response Management (7)
Associates, i2 Technologies, PeopleSoft, Inc., E-Business (16)
Trilogy Software, Kronos Inc., EXE Technologies, Enterprise Resource Planning (23)
HK Systems, Intellution, Wonderware Corp., Product Data Management (10)
Aspect Development, McHugh Software Component Management (10)
International, SCT Corp., Cincom Systems, Inc., Groupware (10)
GE Fanuc Automation, ILOG, Inc., Manhattan Supply Chain Planning (23)
Associates, LIS Warehouse Systems, SynQuest, Forecasting & Demand Management (9)
Inc., USDATA Corp., Adexa, iBASEt, Camstar Supply Chain Execution (17)
Systems, Provia Software, ESI/Technologies, Transportation & Logistics (9)
PowerCerv Corp., Friedman Corp., ROI Systems, Warehouse Management (16)
Intrepa
Advanced Planning and Scheduling (19)
Customer Response Management (7)
E-Business (16)
* This is a sample of the set of top 65 enterprise system firms considered for this study
** The component categories are based on classification done by the data collection agency.
*** Numbers in parentheses indicate the number of vendors offering the software component.
Table 2: Enterprise system firms and component markets they compete in
8 Sampling for network analysis differs from those employed for survey analysis. As opposed to random selection
for survey analysis, network sampling needs to be based upon rules of inclusion for each network element - actors,
relations and also events in which actors participate. In a network study, the use of inappropriate rules to include
network elements can invalidate the study, whereas in survey analysis for individual level studies, similar drawbacks
can be often addressed by eliminating the specific data points Laumann, E. O., P. V. Marsden, et al. (1983). The
Boundary Specification Problem in Network Analysis. Applied Network Analysis. M. J. Minor. Beverly Hills, Sage:
18-34..
19

5.1. Discussion of structural elements of the alliance network
Our sampling ensured that the alliance among 65 ESS vendors form a fully connected network,
i.e, all vendors belong to the same component, where a component is defined as those set of
actors that are reachable from all other actors (Wasserman and Faust 1994). In figure 1 we
visually note that most of the potential ‘sponsor’ nodes are highly central 9 (Bala and Goyal
2000). This provides a visual clue that the network maybe compared to a ‘linked star’ limit
network as described earlier (Bala and Goyal 2000). We examine the density of alliance
linkages in the network of 65 firms. The theoretical limit of alliance network density is (i.e.
number of possible links) is
( )
n! n−1
!
= 2080 (Wasserman and Faust 1994). As against this, in
2
our network there are a total of 196 links that suggests a network density of approximately 9.4%
(196/2080). Prior literature on technology alliances (Hagedoorn and Duysters 1999) refers to
networks with 40% density as being highly dense, and hence by comparison our network with
less than 10% density is a lightly dense network. Some qualitative inferences can be drawn from
this observation. First, this implies that even though alliances may yield various network
benefits as described earlier firms have not formed alliances with every other firm. This implies
that ESS vendors have invested in selected alliances – an indication that they are involved in
rational decision-making. Second, some firms (e.g., SAP, i2, Manugistics, Baan & PeopleSoft
with more than 10 links each) have significantly higher number of linkages with direct links
between them suggesting that our network is closer to the theoretical limit network of a linked-
star (Bala and Goyal 2000). At the same time it is also apparent that the non-sponsor types are
not only connected to the sponsor, rather they have linkages between themselves as well. This
implies that it is not a strict Nash state of the industry and our current network is not a limit
network. A representative sample of linkages (given in Table 3) shows that the distribution of
linkages is highly skewed towards a few vendors.
Vendor Degree Centrality
Oracle 25
SAP 23
9 For clarity the entire set of 65 vendors is not depicted; however, in the complete network graph this observation
holds similarly. This figure was generated in UCINET VI with the node labels representing the firm.
20

i2 13
Baan, Manugistics , PeopleSoft 11
J.D. Edwards 10
Kronos, Vastera 8
Manhattan Associate 7
Optum, McHugh, SCT, Trilogy 6
Foxboro, SynQuest, Descartes, Camstar, LIS, Logility, Intellution, ILOG 5
EXE, SSA, JBA, Indus, iBASEt, OSDI, Adexa 4
Western Data, Provia, ABB, Symix, Wonderware, POMS, Aspen, Industri-Matematik,
STG, Gensym, Datastream
Table 3: Degree centrality of vendors ranked by their software revenue
5.2. Analysis and discussion of relative firm prominence in the alliance network
We computed the relative firm prominence of each firm given by equation 1.4 as also Braun’s
measure using Matlab. The alliance matrix was the input variable to the Matlab procedure. Since
we had assumed that in any alliance initiated by any firm the benefits flow both ways the input
the alliance matrix was first dichotomized. Further, both alliance partners were assumed to
equally incur costs when either licensing their product interfaces or involving in joint product
development. Then we transformed the matrix of relationships into a normalized column matrix.
For example, for all 23 partners who maintained alliances with a top focal vendor the strength of
relationship of each alliance partner with the focal vendor was normalized to 1/23 in the matrix.
The result matrix was asymmetric since each vendor had varying number alliance linkages. We
computed the measure of prominence (equation 1.4) and Braun’s measure using this transformed
matrix.
Other social network measures of centrality and prominence are already available in UCINET IV
(Borgatti, Everett et al. 1992). In Table 4 the correlation coefficients of the firm prominence
metrics with the performance are reported. While it is less meaningful to compare the Pearson
correlation coefficient of different prominence measures these are more useful as supplements to
the theoretical arguments presented earlier since most research on prominence and status utilizes
centrality measures incorporated in UCINET IV. We computed Bonacich’s power measure for
two different values of β (0.05 and 0.12) - the attenuation factor in Bonacich’s power measure
3
21

(1987). The maximum value of β we tested was 0.12 which is the theoretical maximum 10
specified by Bonacich. Other measures presented are Freeman’s closeness and betweenness
centrality. We also computed the correlations for sub-samples. We reasoned, as discussed earlier,
that maintaining alliances requires substantial investments, which small vendors (with smaller
resource base) may not be able to afford. By computing correlations for the top 30 and top 20
vendors we controlled for the differences in vendors’ resource bases. We found that the socio-
technical capital is more strongly correlated with performance indicating that for larger players
who are able to afford maintaining alliances – increasing socio-technical is a more effective
strategy.
Network Measure
Modified firm prominence
(equation ..)
N=65 *
Correlation
(Sig. Prob)
N=30 *
Correlation
(Sig. Prob)
N=20 *
Correlation
(Sig. Prob)
0.5517 (0.000) 0.774 (0.000) 0.767 (0.000)
Freeman's Closeness 0.212 (0.0899) 0.587 (0.001) 0.626 (0.0899)
Braun's Status Measure 0.5504 (0.000) 0.760 (0.000) 0.748 (0.000)
Freeman's Betweeness 0.5327 (0.000) 0.764 (0.000) 0.790 (0.000)
Bonacich's Power (beta=+0.05) 0.4902 (0.000) 0.753 (0.000) 0.755 (0.000)
Bonacich's Power (beta=+0.12) 0.4024 (0.0009) 0.717 (0.00) 0.729 (0.0009)
Outdegrees 0.3179 (0.0099) 0.646 (0.000) 0.699 (0.0099)
Table 4: Correlation of Network Prominence Measures with Revenue
While the modified measure of firm prominence has among the highest correlation with revenue,
closeness centrality is the least correlated. However, in general all measures of a firm’s relative
status or firm prominence by virtue of their alliances are significant thus lending support to
proposition 2. Interestingly, the correlation of Bonacich’s power measure with firm performance
decreases with increasing value of β, implying that while indirectly connected firms do
contribute to firm prominence, their relative influence is small. Similarly, Braun's measure is
also well correlated well with firm performance. The difference between our modified firm
prominence and that of Braun’s is that while we consider all indirectly connected actors, Braun
10 The maximum theoretical value is the reciprocal of the largest eigenvalue of the input matrix.
22

only considers the influence of adjacent ones and those that are two path lengths away.
Outdegrees, closeness and betweenness measures are presented as examples of common network
measures and it should be noted that these are measure of alliances only without any
consideration of intrinsic firm capabilities. It is to be noted that while closeness and betweenness
measures capture the network wide influence they do not satisfy all our conceptual requirements
of how relative prominence evolves in our industry. They are presented as a matter of academic
interest and may have more meaning in relation to other network constructs such as clustering,
and multi-mode exchanges that are beyond the scope of this paper.
6. Theoretical and managerial implications
A key practical implication of this research is that in multi-component industries with
complementary products, alliances are initiated not merely to provide technical compatibility,
but also to garner social resources. Firms benefit by complementing their intrinsic resources with
collective benefits from an alliance network, and are successful if they increase their relative
prominence in the network. This work also suggests that software product managers should not
only consider resources of their direct partners but also those of indirect partners in any decisions
regarding alliances.
6.1. Implications for IS research
The contribution of this paper to IS research is many fold. First, it is one of the first works to
study standards competition in IS literature. While standards have been studied from an intra-
organizational perspective in IS, a second important contribution of this work pertains to linking
the notion of corporate IT standards to standards based competition of the software firms
themselves. The need to incorporate such demand-side mechanisms into determining prominence
at the supply side has been called for in other fields as well (Stewart 1996). In the software
industry, the most important supply side mechanism that contributes to the prominence of a firm
is its choice of standards for technical compatibility. However, we point out that that an
organization's selection of its ESS vendors is based on its own corporate IT standards. Given
that corporate standards include other organizational considerations such as availability of
consultants, training programs, etc., we argue that ESS firms take these considerations into
account during the selection of their partners. We term these non-technical factors as creating
benefits in the social dimension and contributing to organizational user perceptions of
23

compatibility. This research then incorporates both the social and technical benefits in its
conceptualization of sociotechnical capital. A third contribution of this work is the introduction
of social network theory to understanding standards competition of software firms. The richness
of this framework in creating empirically tractable measures allows us to overcome the
limitations of some of economics based modeling as discussed in section 2.
Finally, the theories and model outlined in this work is rich enough to help examine realistically,
a variety of issues in any industry that is dependent on standards. For example, a longitudinal
study of a software industry using our model can provide insights into the standards formation
process itself. Even though we consider the transient stage of this industry, i.e., during the
absence of uniform standards, we could easily represent equilibrium or end stages such as pure
oligopolies or a technological monopoly by manipulating the level of the exogenous resources of
the software firm. This research can also be extended to understand competition even in the
presence of industry wide, open standards, as the social dimension becomes the only
differentiating basis for competition. For example, it may help to understand how software firms
use the resources in the social dimension such as reputation signaling from trade shows, joint
product announcements, etc., to derive competitive advantage. Our model can also be applied to
IS decisions in intra-organizational situations. For example, systems supporting organizational
units can be modeled as a network with linkages between them representing flow of resources
such as data on the technical side and expertise, process skills on the social end. While semantic
data integration and a common infrastructure platform (Wybo and Goodhue 1995) will call for a
common vendor and can deliver the technical benefits, it may deliver lesser benefits on the non-
technical dimension as compared to a "best-of-breed" system. If best-of-breed systems imply
full user commitment and involvement at the organizational sub-unit level, and common vendor
implies full technical compatibility, our measures can provide a way to compute the efficiency of
each organizational unit under varying system heterogeneity.
Further, identifying the right unit to invest systems resources is of great importance in IS (Keen
1991), and our network model can help guide this decision. For example, one can construct an
intra-organizational network of workflow and resource inter-dependence (Wybo and Goodhue
1995). This network can then be compared to a systems network, with each link representing
component compatibility. Similar to the operationalization of Sociotechnical capital, network
measures can be used to explore the relationship between organizational resource networks and
24

systems compatibility networks. High prominence in the organizational network maybe a
pointer towards greater systems investments.
6.2. Implications for research in other areas
Our work has implications for researchers interested in studying tie-strength of alliances. In the
information systems context, firms exhibit varying degrees of partnerships depending upon their
level on involvement with each other. For example, Oracle (http://partner.oracle.com) facilitates
three levels of partnerships with decreasing levels of access to product knowledge, and
marketing and sales information; Program Member Level Certified Solution Partner (CSP) and
Certified Advantage Partner (CAP) Each of the above implies a different level of commitment
both financial and strategic. The concept of aggregate strength of relationship proposed in our
theory can help model the levels of these strategic partnerships seen in the software industry.
Such a construct can then be used to understand the implications of firm strategies such as the
trade-offs between tight coupling with smaller firms (presumably at a lower cost, and hence a
larger number of them) versus those with select larger firms.
This research also makes significant contributions to research in social network theory. Burt
(2000) says, “Research will better accumulate if we focus on network mechanisms responsible
for social capital effects rather than trying to integrate across metaphors of social capital loosely
tied to distant empirical indicators”. In our research we identify some of these mechanisms by a
grounded study of the software industry through theories that support the underlying the linkage
formation. Our paper contributes to network theory by developing a model of resource transfer
and conceptualizing a new prominence measure that is applicable to any context where resources
can flow from indirectly connected actors, even in the absence of direct investments. The paper
also attempts to answer a call for integrating substantive theories from other disciplines in order
develop network analysis and proceed from a unit level of analysis to a network level (Monge
and Contractor 1998). We have attempted to bring together diverse literature on compatibility
standards; technological change and resource transfer in order to synthesize our network level
theory of resource transfer.
25

6.3. Limitations
A limitation of our research is that we have not explicitly considered adapters and integrators
directly into the network representation as actors. This may be important since a firm gains
prominence through relations with consultants and adapters thus perpetuating the perception of
compatibility. Multi-mode network analysis allows for this inclusion of heterogonous actors.
Similarly we have not explicitly parameterized the number of markets in which firms compete
versus cooperate; this may be needed for an empirical extension to this study. Further,
measurement of knowledge spillover effects, advantages of absorptive capacity and other factors
in the social dimension may be necessary to analytically compute actual social resources. These
limitations may be addressed through an extensive empirical study.
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31

Appendix A
Our goal is to reduce the solution to equation … to an empirically tractable form. Since all our
relationships are normalized, we represent rij as a fraction of vendor j ’s dependence on all other
vendors directly connected to it. Therefore we can construct an adjacency matrix R as a nXn
column stochastic matrix with elements rij , such that for each j , rij = 1.
From equation … and
… we have
∑
c = r s
i ij j
j
∑ ∑∑ ∑∑∑ +
b = r e + r r e + r r r e
i ij j ij jk k ij jk kl l
j j k j k l
We can simplify the benefits equation by using power matrices of R. Consider an array of power
matrices where
0 1 2
1 ( 0) , , ,.... z
n
2
z = = z = r z =∑ r r . In matrix notation z can be
ij i= j i≠ j ij ij ik ij jk in
j
2
represented as z = RR . , and similarly
Therefore equation … can be re-written in matrix notation as
or further reduced to
∑
i
...
(1.5)
p p
z = R where p is the path length between two firms.
i = ∑ ij j + ∑
2
ij j + ∑
3
ij j +−−−∑ P
ij j ⇒
P
i = ∑∑ ik k
j j j j p= 1 k
p e
b r e z e z e z e b z
n
p
b= ∑(
Z . e)
Therefore we can now write the profit maximization problem of a firm as
p=
1
⎡ ⎤
max ( . )
n
⎢
⎣ p= 1
p
Z e −
j
rijsj⎥ ⎦
ik
(1.6)
(1.7)
∑ ∑ (1.8)
We assume that all firms are rational and will allocate their investments r so as to maximize
their profits, so we consider the first order condition of equation (1.8) by differentiating with
respect to r , and re-arranging the terms we have
ij
n−1
p
j = ∑∑ jk k
p= 0 k
e
s z
and in matrix notation this can be written as
32
ij
(1.9)

a
n−1
p
S = ∑ ( Z . e)
p=
0
where S is the column vector of statuses of the firms.
(1.10)
Benefit is a function of the intrinsic capability of a firm, similar to Braun (1997) we assume a
linear form ofb = (1 + n) e −1,
and substituting for cost, we have for any k ,
e
k
1+
ck
1 1
= = .
1+ n 1+
n 1 n j
equation(1.9):
a
+ + ∑ kj j
and in matrix notation we have
p
r s . Multiplying both sides by∑∑
zik
, we have from
n−1 p
∑∑zik n−1
p
∑∑zik ∑rkjsj p= 0 k p= 0 k j
si
= +
1+ n 1+
n
⎛ n−1n p⎞ ⎛ p⎞
⎜ Z ⎟. J + ⎜ Z ⎟.
p= 0 p=
1
S =
⎝ ⎠ ⎝ ⎠
1+
n
∑ ∑ S
n−1
p= 0 k
(1.11)
(1.12)
We can further reduce these terms for empirical assessment. Re-arranging equation (1.12), we
n−1n p p
∑Z∑ Z
−1
p= 0
p= 1
have S = ( I −X)
YJ
where Y = , X = . The power series of S is as follows
n+ 1 n+
1
n
−1
n
p p
⎛ ⎞ ⎛ ⎞
⎜ ∑Z ⎟ Z
n− 1 l=∞ n−1
1 p= 0 ⎛ p⎞ ⎜∑ ⎟
1 p=
1 ⎛ p⎞
S = ⎜I − ⎟ ⎜∑Z ⎟. J = ∑⎜ ⎟ ⎜∑Z ⎟.
J (1.13)
1+ n⎜ 1+ n ⎟ ⎝ p= 1 ⎠ 1+ n l= 0⎜
1+
n ⎟ ⎝ p=
0 ⎠
⎜ ⎟ ⎜ ⎟
⎝ ⎠ ⎝ ⎠
The above power series is valid since
n
p
∑ Z
p=
1
1+
n
confirm the existence of the inverse if the norm
< 1
l
. From Kincaid and Cheney (1996), we can
n
p
∑ Z
p=
0
1+
n
≤1⇒ n
∑
p=
0
p
Z ≤ n + 1,
where
n
p
∑ Z is also
p=
0
33

a stochastic matrix with column sums equal to n . Let
said to exist if and only if
1≤j≤n
i=
1
G
( n + 1)
1 n
n =
∑
p
0
p
Z = G
, then the inverse is always
≤ . MatrixG , being a column stochastic, its norm is
n
n
G = max∑ aij
⇒1.
Since ( n+ 1)
> n in our case, the existence of the inverse is confirmed.
For further empirical measurements e and c can be reduced to:
l l
n n
⎛ p ⎞ ⎛ p ⎞
l ∑Z n−1
1 p=
1 ⎛ ⎞ ∑Z
=∞ ⎜ ⎟ l=∞ ⎜ ⎟ n
p 1 p=
1 ⎛ ⎞
c Rs R. ∑⎜ ⎟ ⎜∑Z ⎟.
J ⎜ ⎟
p
= = = ⎜ Z ⎟.
J
1+ n l= 0⎜ 1+
n ⎟ ⎝ p=
0 ⎠ 1+ n l= 0⎜ 1+
n ⎟ ⎝ p=
1 ⎠
⎜ ⎟ ⎜ ⎟
⎝ ⎠ ⎝ ⎠
n
⎛ p ⎞
−1
⎜ Z
⎛ n− 1
l ⎟
p ⎞
=∞ ∑ 1 p=
1
reduced to e= ⎜∑( Z ) ⎟ S ⇒e=
∑⎜
⎟ J .
⎝ p= 0 ⎠ 1+ n l=
0⎜
1+
n ⎟
⎜ ⎟
⎝ ⎠
34
∑ ∑ . This can be further
l