Market Partitioning Under
Varying One-Dimensional
Resource Spaces
César E. García-Díaz
Department of International Economics & Business
Faculty of Economics
University of Groningen (The Netherlands)
c.e.garcia@eco.rug.nl
April 21, 2004
1. Introduction
It has been almost three decades since Organizational Sociology witnessed the
emergence of Organizational Ecology (OE), a research program that focus in the
study of populations of organizations and the principal effects on organizational
founding and mortality rates (Hannan & Freeman, 1989; Witteloostuijn, 2000). OE
tries to give answers to the fundamental question “why are there so many kinds of
organizations?” (Hannan & Freeman, 1977: 936) using a Darwinian approach of
environmental selection features (Levins, 1968), by which explicitly opposes to the
classical rational adaptation theories of organizational theory (Kamps, 2000). One
central claim of OE states that, when facing environmental changes, the organizations
of the population not able to fit the new conditions are replaced by new ones and a
population-level adaptation occurs. This also implies that a selection process takes
place at the individual level (Hannan & Freeman, 1977).
In its attempt to understand population-level adaptation through the behavior of
founding and mortality rates and the proliferation of organizational forms,
Organizational Ecology (Hannan & Freeman, 1977, 1989) has brought alternative
views to classical organization theory’s contingency approach regarding optimal
strategies in uncertain environments through the formulation of Niche Width Theory
(Freeman & Hannan, 1983; Péli, 1997; Bruggeman, 1997; Bruggeman & O’Nualláin,
2000; Baum & Amburgey, 2002; Hannan, Pólos & Carroll, 2003), to organizational
change theories through the formulation of Structural Inertia Theory (Hannan &
Market
2 Partitioning Under Varying one-Dimensional Resource Spaces
Freeman, 1984; Péli et al., 1994; Péli et al., 2000; Hannan, Pólos & Carroll, 2003) and
to economists’ neoclassical theory regarding the understanding of markets
composition. Organizational Ecology has also introduced its own vision of market
structures and, as emphasized by Vermeulen & Bruggeman (2002) and Carroll &
Hannan (1995), has proposed opposite perspectives to classical industrial organization
theory views on the role and effect of market concentration, as is the case in Resource
Partitioning Theory (Carroll, 1985).
Carroll (1985)’s seminal paper in Resource Partitioning Theory (RPT) in
Organizational Ecology gives explanation about the coexistence of generalist
organizations with specialist organizations in a two-dimensional resource space
characterized by scale economies and a center. RPT emphasizes that some necessary
(but no sufficient) conditions are needed for such dual market structure: heterogeneity
of resources, the presence of a market center and economies of scale/scope.
Although Witteloostuijn & Boone (2003) develop a market structure typology with
eight typical cases, there is no theoretical investigation that connects the emergence of
such typology with different sets of initial conditions for the n-dimensional resource
space in which such market evolves. A theory to explain the emergence of these
market configurations is needed. Some attempts like the first-order logic model
developed by Vermeulen & Bruggeman (2001) have been made. However, this model
states that resource partitioning occurs independently of organizational mass, sizelocalized competition, diversifying consumer tastes and changes in niche width,
missing important elements needed to fully understand the dynamics process that
generates market partitioning.
Through computer simulation of different one-dimensional resource spaces, which
differ in its level of resource heterogeneity, we want to understand how such different
resource spaces generate specific partitioned markets. We want to explore which are
the thresholds in the degree of homogeneity at the market center that account for
specific levels of generalist concentration (and consequently, it will be our interest to
explore if size-localized competition (Baum & Amburgey, 2002) is effectively related
to size or if it is a consequence of certain levels of homogeneity of the resource
space). In the search of conditions for sufficiency in market partitioning, we also
explore which are the heterogeneity thresholds that allow market partitioning to
appear.
2. Resource Partitioning Theory
2.1. Fundamental ideas
Carroll (1985)’s shaping paper in the theory of resource partitioning gives explanation
about the coexistence of generalist organizations with specialist organizations in a
market characterized by scale economies and a center. Generalist and specialists
organizations are, in the context of resource partitioning theory, differentiated by the
range of resources they take from the resource space: generalists are characterized by
taking a broader portion of resources, while specialists take a narrower segment.
Market Partitioning Under Varying one-Dimensional Resource Spaces
3
Generalists/specialist definition is slightly different from the original inter-temporal
definition of OE’s niche theory, in which both specialists and generalists define the
width of their niches among range of resources that are not present simultaneously
throughout time (Wezel & Witteloostuijn, 2003).
The resource space might be, for instance, the n-dimensional space of product space
characteristics, where each n-vector represents a specific combination of consumer
preferences (Péli & Nooteboom, 1999).
Resource partitioning assumes that the center of the market is abundant in resources
(it means that the resource distribution is unimodal), so that intensive competition
might be hold around the center. Provided that the total resource space has a fixed
carrying capacity1, such intensive competition will generate two different and
simultaneous outcomes:
a)
Some of the firms that fight for taking resources at the market center will not
succeed and will have to leave the market. It means that the fewer winning
organizations will take over the market center and, as a result, the market
concentration will increase. Those successful organizations could grow big
(generalists) due to the departure of some of their competitors and the
advantages provided by the scale economies, but will be less in number as
well. Also, “generalists tend to differentiate themselves by differentiating
their product offers, positioning their niches apart from each other” (Péli &
Nooteboom, 1999:1135). In other words, “as market concentration rises, the
amount of unique resource space covered by the combination of all
generalist organizations contracts” (Carroll et al. 2003:14).
b) Since the total resource space owned by the all the generalist organizations is
contracted, the peripheries of the resource space will be available for
organizations that might take resources from this non-abundant portion of
the resource space. Those “small” organizations (specialists) might
proliferate as the market concentration rises 2,3. It means that the
1
In their geometrical model, Péli & Nooteboom (1999) assume that the resource space
is constant and homogeneously distributed. Carroll (1985), in the theoretical model that
serves to explain the resource partitioning process of the newspaper industry, implicitly
assumes that the resource space doesn’t change while the concentration is raised.
2 It is important to say that large organizational size is not necessarily related to
generalism (consequently specialism is not necessarily related to small organizational
size). As Carroll (1985:1267) mentions, in non homogeneous resource space
distribution, a single specialist might have abundant resources of their narrow niche,
allowing them to grow bigger than some generalists. This situation leads us again to the
above-mentioned issue about the definition of generalists and specialists. One more
example is seen in Boone, Carroll & Witteloostuijn (2002), in which it is proposed that
the higher the degree of homogeneity and concentration of resources, the higher the
concentration of generalists that compete around the center on the basis of scale.
Again, in a resource space where resources are highly concentrated around the peak, a
firm might be seen as a generalist, since it takes advantage of the economies of scale
and can grow big taking over of the most abundant part of the space, but also it might
Market
4 Partitioning Under Varying one-Dimensional Resource Spaces
consolidation of generalists creates the conditions for specialist proliferation:
“The surviving generalists thus become larger and more general as time
passes. However, because of the ever-widening range of the surviving
generalist’s target area, it become increasingly difficult to secure the entire
free area. This is because doing so involves uncertainty, it might prove very
difficult or more costly than it is worth, or it might entail loss of some of the
organization’s existing target areas because its identity or capabilities would
be undermined” (Boone, Carroll & Witteloostuijn; 2002:272).
So far, there are two explored sources of resource space release for specialists: first,
the intensive competition among generalists, which produces that some of them leave
the market, while others conquer the freed space near the market center (Carroll,
1985; Carroll et al., 2003). Second, the emergence of new tastes due to specialists’
effort to enter the market and differentiate themselves (Carroll & Hannan, 1995). The
latter effect is explained by changes in the dimensionality of the resource space (Peli
& Nooteboom, 1999)4.
2.2. Latest Developments
Hannan, Carroll & Pólos (2004a,b) undertake the task of unifying niche theory and
RPT. They faced many differences and tensions: i) Niche theory defined niches under
absence of competition (fundamental niches) while RPT emphasizes niche
differentiation under competition (realized niches) 5, ii) environmental conditions vary
between two environmental states and depending on variability, grain and
dissimilarity of the environmental states, while RPT consider one single
environmental configuration, or better, several similar resource conditions at the same
time iii) in RPT, generalist can perform simultaneously in the range of environmental
resources in which they define their niches, while in niche theory they alternate their
operations in two non-simultaneous environmental states, iii) niche theory states its
predictions without assuming scale economies or nonhomogenous environmental
distribution, unlike RPT.
be seen as a specialist, because it is enough for this firm to focus on a narrow segment
of the resource space.
3
Niche formation also accounts for explanation of the proliferation of new entrants into
a market (Swaminathan, 1998).
4
In Péli & nooteboom (1999)’s framework, the specialists can proliferate in
homogeneously distributed resource space without scale effects, given that there is an
increase in dimensionality of such space. Moreover, Boone, Carroll & Witteloostuijn
(2002) emphasize that specialists proliferate in a space that doesn’t change, provided
there is a set of heterogeneous resources.
5
In the presence of scale economies, we can think of a positive relationship between
organizational size and the size of the realized niche: provided that a large organization
and a small organization have the same fundamental niche’s size, the large organization
will probably have a larger realized niche than the one the small organization has. This
is, in general larger organizations do not necessarily happen to have larger fundamental
niches (Hannan, Carroll & Pólos 2004a).
Market Partitioning Under Varying one-Dimensional Resource Spaces
5
With the aim of integration of these two fragments, Hannan, Carroll & Pólos
(2004a,b), redefine the principle of allocation, stating that the level of organizational
commitment or engagement is fixed for a population at a given point of time.
Hannan, Carroll & Pólos (2004a,b) make a distinction between two kinds of appeal
(i.e. intrinsic and actual). Intrinsic appeal refers to the degree to which an
organizational offering fits a specific taste due to a socio-cultural affinity. The
intrinsic appeal is the abstract “attraction” between the taste and the offering, which
becomes materialized by factors like availability of the offering or the way it is
presented to customers (i.e. through the capacity of engagement of the organization).
So we can say that the level of actual appeal depends on the capacity of
organizational engagement in the social positions in which it has intrinsic appeal.
Note that it is assumed that every single social position in a social space has a unique
taste and that, consequently, tastes vary among social positions.
Given the above framework, the fundamental niche is redefined as the set of positions
for which an organization’s offering has nonzero appeal (Hannan, Carroll & Pólos
(2004a,b)6. In order to reconcile the niche theory’s fundamental niche perspective
with the RPT’s realized niche viewpoint, the latter is defined as the set of positions
that generate positive returns for the organization. The organization’s return is
calculated by multiplying the organization’s “share” in each social position among all
the organizations that compete for the same taste (which is defined as organization’s
fitness) with the “total expenditure” of each social position (given, for instance, by
number of consumers at that position). Considering that an organization gets positive
returns from the set of positions with nonzero actual appeal, it can be proved that the
organization’s realized niche is a subset of its fundamental niche (Hannan, Carroll &
Pólos, 2004a).
Taking a step further in the explanation of the resource partitioning process, Hannan,
Carroll & Pólos (2004a) divide the market in three distinguishable segments: the
center, the near-center and the periphery, and try to explain why the near-center
organizations, as concentration rises, become prone to failure while the organizations
in the periphery raises their survival chances. Hannan, Carroll & Pólos (2004a) leave
apart the definitions of generalists and specialists, and use the maximum scale
advantage as a proxy for concentration, given that scale is positively correlated to size
(Carroll & Swaminathan, 2000) and that concentration is positively correlated to the
size of the largest organization in the market. For a dynamic perspective, it is
necessary to take into account two kinds of effects in this partitioning process: sizelocalized competition and scale-based competition.
Given size-localized competition effects (Péli & Nooteboom, 1999; Baum &
Amburgey, 2002), the near-center organizations tend to disappear because they face
strong competition with both center-located and peripheral organizations. As
6
It is important to note that this organizational-level definition of fundamental niche
differs from the population-level previous definitions (Hannan & Freeman, 1977, 1989;
Freeman & Hannan, 1984)
Market
6 Partitioning Under Varying one-Dimensional Resource Spaces
mentioned before, specialists and generalists, which are different in size and structure,
don’t compete directly and coexist in the same resource space.
On the other hand, the scale-based competition hypothesis states that “among scalebased (generalist) competitors within an organizational population, the greater the
sum of distances of a firm from each of its larger (generalist) competitors, the higher
its mortality hazard” (Carroll et, al, 2003:12).
Carroll & Swaminathan (2000) point out that there is no contradiction in the two
concepts: while the sized-localized competition applies to every organization in the
population, the scale-based competition applies only to the generalists. As mentioned
before, the small generalists will face the most fierce competition because they will
experience an increase in their mortality rates due to both effects: i) size-localized
competition with specialists and, ii) scaled-based competition with other generalists.
This situation will eventually generate the partitioning of the market7.
RPT has concentrated in explaining interaction in a fixed environment. The
consideration of changing resource spaces and its effects on market structures will
extend further the theory through the consideration of spatial and temporal changes
in social positions’ tastes. “Market structure and firm conduct are co-determined by
the underlying features of the environmental resource” (Witteloostuijn & Boone,
2003:7).
3. A simple discrete-event simulation model
In this section we present a conceptual framework for a simple discrete-event
simulation for market partitioning in one-dimensional resource spaces, which will
allows us to study the evolution of market concentration, organizational density and
the relative performance of specialist organizations versus generalist organizations8.
This is, we want to investigate the effects on concentration and density under varying
degrees of resource heterogeneity. To keep the model simple, and to use it as a step
stone for future works, we explore the effect of varying heterogeneity in onedimensional resource spaces.
i) Resource space generation: there is a one-dimensional resource space with a market
center, which represents the space of social positions, where it is supposed that there
is a number n of social positions. The space has a Gaussian-like distribution and will
be generated for several degrees of resource heterogeneity (represented by its
7
There is still one additional argument inside OE, not directly integrated with the RPT
framework: the density delay effect. We explain it in the following lines. As mentioned
by Carroll & Hannan (1995a), density effects at the time of founding might affect
organizational blueprints, thus affecting also organizational chances of survival at any
point of its lifetime. Density delay might take place either because of the liability of
scarcity at the time of founding, or because the market crowding effects. As per the
density dependence theory, organizations in the periphery of the market have higher
mortality rates during all their lifetimes.
8
The program code was written in MATLAB.
Market Partitioning Under Varying one-Dimensional Resource Spaces
7
variance, ²). The space is generated as a discrete rendering derived from a Gaussian
distribution. Each social position generated Sj, j=1,…, n, has an associated “budget”
bj, j=1,…,n. This budget represents the amount of resource offered by each S j, j=1,…,
n. For convenience, the possibility of considering a range of tastes in each single
social position Sj is not taken into account. The resource space generation is
represented by two (n x 1) vectors, S and b.
ii) Organizational founding: Simulation horizon is divided equally into T discrete
time intervals i, i= 1,…,T, each of them representing a single iteration in the
simulation environment. Firm will enter the market following with a Poisson process
with an arrival rate (per time interval) of i, which means that P(arrival of any firm at
interval i)= ixe-i/x! Although a more precise model will have the rate i dependent
on the number of organizations in the market, we won’t do this in our model just to
keep it simple. That is, i = , i = 1, 2,,…,T. The dependency of the arrival rate on the
number of firms in the market might be allowed to integrate density dependence
theory and resource partitioning (at least regarding founding rates), since founding
events are somehow related to processes of legitimation, and such founding events are
dependent on crowding effects. Noteworthy to say is that such assumption of
considering i as a function of density will work out to represent density dependence,
but not to prove it. Outcome will be recorded in the (1xT) vector X.
iii) Endowment: Although it might be assumed that firms have some endowment at
the beginning of the simulation, this feature will not be considered, since it is our
interest to primarily focus on studying the process of resource partitioning. Regarding
the way this simulation is built, the inclusion of organizational endowment will delay
the emergence of market partitioning since the firms will be allowed to have some
amount of negative profits and will remain in the market. We think that this inclusion
of endowment will just give us a different cut-off point to select firms out, but won’t
modify the behavior of market formation throughout the simulation runs. Obviously,
if the simulation model includes some other features (e.g. density dependence),
endowment do count for market structure emergence.
In addition, it might be argued that a difference in the final results would be generated
if some firms, in spite they have got losses, are able to survive and re-enter the market
again. For that reason, we assume that a firm with no social positions (provided that it
has positive cumulative profits) will remain in the market and will have the
opportunity to fight again for niche positions (i.e. re-entry costs to market are cero).
iv) Niche center / niche width selection: Let us assume that O i,k is the k-th firm that
appears in the market at iteration i. In general terms, each organization generated in
each step, Oi,k, i=1,…,T; k=1, 2, 3,… chooses a strategy that has two components:
The niche center, pi,k, and the breadth of the niche, wi,k. At iteration i=1 each firm
chooses its niche center, pi,k, whose value will remain constant during the whole time
horizon. Oi,k’s niche width will have an starting value for all organizations, wo, which
will be updated in subsequent interactions, depending on the outcomes of price
competition and economies of scale (i.e. t=2,…,T). The niche position p i,k of each Oi,k
Market
8 Partitioning Under Varying one-Dimensional Resource Spaces
is chosen randomly according to a uniform distribution. The arguments for such
assumptions come next.
We can say that the fact of picking up a given position p i,k by a firm is partly a
consequence of identifying resource peak points by the firm actors. Those points of
peak intrinsic appeal (Hannan, Pólos & Carroll, 2004a,b) are chosen by
entrepreneurial activities and, supposedly, such activities are more likely to be carried
out in the most abundant regions of the resource space.
As found in empirical research (Boone, Carroll & Witteloostuijn, 2002), the more
concentrated the resources are, the higher the concentration among generalists. It
means that the effects of concentration might be partly a consequence of crowding
along the process of niche center selection. So it is expected that founded firms, at the
beginning, are more likely to locate their niche centers in the most abundant region,
rather than in the peripheral regions. However, when the market gets crowded, the
risk of failure is higher in the region near the center since competition is expected to
be higher in such area respect to the level of competition in non-abundant regions of
the resource space. In the absence of more detailed assumptions, the trade-off
between attractiveness and risk that entrepreneurs leads us to consider that the
generation of niche centers might be distributed uniformly.
As mentioned before, we assume that firms are totally inert, so p i,k remains unchanged
throughout the time horizon, and no possible niche center shifts are possible. Firms
that are not able to maintain themselves in the starting position abandon the market
and leave their niches free. The outcome of niche centers at each iteration t is stored
in a matrix(T x max(X1, X2, X3,..., XT)) named P.
In addition, there is no reason to think that wi,k is defined as resource dependent. On
the contrary, we think that all firms may enter the market with a given fixed “scope”,
which they will be able to expand as soon as the benefit from economies of scale and
competition.
v) Niche overlap and competition dynamics: Each social position will choose one
single option among the presented offerings. Each social position S i at time t will
decide according to both price, ri,k, and appeal loss, pi,k -Si, which represents the
dissimilarity in taste or distance (Hotelling, 1929) between the social position and a
given offering (the firm’s point of peak intrinsic appeal is located at its niche center).
Firms calculate their initial prices according to the amount of resources they expect to
capture in the first iteration, depending on their niche center positions in the resource
space. Given that at the beginning all the firms start with the same niche width and
same startup capacity (i.e. sunk costs that reflect their initial engagement), the initial
price, r1,k, is set according market expectations respect to niche center positioning:
r1,k  (Mup)(SC  K o  C o * (
b
) 
j
{ j S j [ w1, k l , w1, k u ]}
b
)
j
{ j S j [ w1, k l , w1, k u ]}
9
Market Partitioning Under Varying one-Dimensional Resource Spaces
where SC is the (sunk) cost of startup capacity, Ko is the per-period fixed cost, Co is
the average variable cost per unit and (wi,kl, wi,ku) are the lower and upper limits of the
firm’s niche9. In addition, we assume Co = (wo-)² and  as the point of the minimal
efficient scale. Firms use a markup factor (Mup) to compute the price.
w1,k
w1,k
O2,k
O1,k
Sa
Sb
Sc
Sd
Niche overlap
at time i
p1,k
Se
p2,k
Figure 1. Niche overlap
The parameter  will be selected so that it is allowed firms to grow to some extent
until it is not attractive anymore (due to increasing returns to scale). This is, the
variable cost increases exponentially when the niche width surpasses the threshold .
Since price discrimination is not allowed (i.e. each firm offers the same product to its
entire niche), the cost of producing a product with a broad appeal is prohibitive and is
reflected in the variable cost calculation. Below the threshold , firms might enjoy
scale economies effects. Also note that in case of nonconvex niches, the formula
might take into account the niche “holes”, which makes unlikely the possibility of
covering completely apart social positions in terms of profits.
Taking into account that qi,k represents the price offered by Oi,k at iteration i, each
social position Sj will use the following criteria to pick up the best of its offerings:
r
i ,k
*
, pi , k
*

Sj

i  1,..., T ; k  1,.2,3,...; j  1,..., n
9

 arg min ri ,k  pi ,k  S j , for every S j  ( wil,k , wip,k )
The sunk cost is a one-time “charge”.
Market
10 Partitioning Under Varying one-Dimensional Resource Spaces
Based on the previous assumptions, firms gain or lose social positions and readjust
their (realized) niches at every iteration. Firms with no social positions at all can reenter the market if they have positive cumulative profits. Prices are updated according
to values of profits, economies of scale effects and criteria for niche expansion. We
explain briefly each of them.
Returns: If an organization Oi,k is selected for a social position Sj, it will get a return
of bj* ri,k at iteration i. If a firm gets negative cumulative profits at any iteration, it
leaves the market. If i,k represents the set of social positions at which Oi,k is selected,
then Ri,k, that represents the total profits the firm Oi,k gets at iteration i, is calculated as
follows:
Ri , k 
 b r
S j
j i,k
 [ K o  ( wiu, k  wil, k   ) 2
i ,k
 b ]
S j
j
i ,k
i  2,..., T ; j  1,..., n; k  1,2,3,...;
Economies of scale: Scale effects are perceived after returns with some delay
(Hannan, Carroll & Pólos, 2004b). In the computer simulation model, scale
economies effects are seen on prices for the next iteration since the average cost,
input for next calculations, is perceived as a lower amount. In fact, prices get lower in
the current iteration due to scale economies effects in the previous iteration, and that
way the competitive power and the possibilities for engagement are higher (Hannan,
Carroll & Pólos, 2004a,b). Firms will calculate prices in a similar way they calculate
the initial prices. Positive scale effects will be reached only when the firm operates
below the point of minimal efficient scale.
Criterion for niche expansion: At every iteration, a firm will evaluate if it is worth
expanding its niche, either to compete with other firms or to occupy empty social
positions left as a consequence of other’s disbanding. A firm will decide to expand if it
is possible to lower the price to its expanded niche (searching for an increase of its
engagement).
It is an aim of this simulation model to study the evolution of concentration and the
organizational forms as ways of getting a better understanding of the process of
resource partitioning, under different levels of resource heterogeneity. Such
heterogeneity is represented with the variance of the resource distribution.
This model differs from Vermeulen & Bruggeman (2001)’s model in that it is not
assumed the presence of some generalist and specialist organizations at the early stage
of the market. In our model, they are generated at every iteration and selected
according to their offerings, situation that affects the way they proliferate throughout
the runs of the model. Vermeulen & Bruggeman (2001) state that processes of
resource partitioning are independent from size-localized competition and from
diversifying preference tastes.
Market Partitioning Under Varying one-Dimensional Resource Spaces
11
Finally, we argue that this approach is somehow in line with structural inertia
(Hannan & Freeman, 1984, 1989), since inertia is also gained with the sophistication
of routines, and increased in time. This is reflected in the simulation model, since repositioning and niche center shifts are not allowed in the model.
Resource space
Organizational founding






Endowment


Niche center / niche width

Price calculation





Niche competition



One dimensional space of social positions.
Each social position has a unique taste.
Unimodal distribution.
Each social position has a budget or number of consumers.
Follows a Poisson process.
Generalists / specialists are defined according to distance to
market center and possibilities of getting positive scale effects.
Not considered in the simulation model.
Firms with no social positions at any iteration, but with positive
cumulative profits, are allowed to re-enter the market with the
same niche center. Re-entry costs are zero.
Niche centers are chosen at the beginning of the simulation and
remain constant throughout the whole simulation.
Niche centers are generated according to a uniform distribution.
All firms start with the same niche breadth.
Niche expansion is symmetric.
Prices are computed according to market expectations of firm’s
own niche.
Prices are updated at every iteration. Criteria for price updates
are cumulative returns, economies of scale and niche expansion.
Each social position chooses one single offering.
Offerings are selected considering both price and taste
dissimilarity.
Niche “holes” are possible, but unlikely due to possible
increasing returns to scale.
Table 1. Summary of assumptions
4. Simulation results and analysis
The simulation was executed with several degrees of heterogeneity (variance). For all
the simulation runs, outputs in market concentration (measured by the four-firm
concentration ratio), number of specialist and generalists organizations (defined
depending on the distance to market center) seem to reach some stable behavior
within a range of values.
As per resource partitioning theory, market gets more concentrated throughout time
and such increase in concentration is correlated to specialist proliferation. It means
that the total space shared by the generalist firms is contracted. That is, the average
niche size of such firms is increased and the number of them is decreased (Carroll et
al., 2003).
We assume that the generalists are those firms which have their niche centers in the
surrounding area of the market center. The firms that have their niche centers in the
Market
12 Partitioning Under Varying one-Dimensional Resource Spaces
periphery of the market are named specialist. Those firms that have their niche centers
neither in the vicinity of the market center nor the periphery are named middle firms.
Figures 2, 3, 4 and 5 show some samples of simulation runs under several degrees of
heterogeneity. The behavior of concentration, specialist and generalist proliferation
are displayed. At the early stages of the simulation runs, we can see a drop of market
concentration, while both the number of specialist and generalists increase. The
number of generalists and specialists keep a stochastic variation after an initial sharp
increase. Such sharp increases are result of the appearance of firms at the early stages
of the market, when proliferation is easy without facing strong competition. All the
firms start the market with the same capacities, but with a different niche center,
which is generated according to a uniform distribution, as mentioned before. That
way, we can say that the raise on the number of specialists and generalists during the
first iterations are due to an effect of the initial conditions established in the program
code, when the selection mechanism is weak because the market is not crowded. As
the simulation runs longer, both the number of specialists and generalists seems to
find a somehow stable region of values.
However, there are two important caveats worth to mention. First, the complete
resource space corresponds to the potential market the firms can get, but it doesn’t
mean that the market is fully occupied by the firms since the start of the simulation.
That is, the market grows as the simulation runs. For that reason, the observed
behavior of the share of the largest firms doesn’t exactly mean that the generalist
market contracts. Second, we can say that, along with a proliferation of specialist and
generalists throughout time, there is also a kind of replacement of themselves
throughout the computer experiment.
Results also show that, for lower degrees of heterogeneity (i.e. a market with more
concentrated resources), the number of generalists in the long run is slightly lower,
meaning that the more concentrated the resources, the more concentrated the market
and the less the number of large firms (see also figure 6). For instance, for a relatively
high heterogeneous market where the resources are more widespread across the social
space is possible that the number of generalists would result higher.
It was also tested that, in a simulation where the definition of generalists and
specialists are related to the covering of social positions (niche breadth) and when the
model was run with a very low level of heterogeneity (e.g. 0.6), the generalists just
disappeared from the market. This is somehow consistent with the idea that a
complete homogeneous market (a market with only one single social position), only
one firm will dominate (such firm cannot be named generalist as per the definition
here used, since such a market has no center).
Next, we examine the behavior of market concentration, density and relative
performance of specialists versus generalists across different resource landscapes.
Table 2 summarizes the effects of several degrees if heterogeneity on such variables.
Averages on values of the last twenty iterations were taken in order to generate the
figures 7, 8 and 9.
Market Partitioning Under Varying one-Dimensional Resource Spaces
Figure 2. Simulation outcome with heterogeneity = 0.6
Figure 3. Simulation outcome with heterogeneity = 1.2
13
Market
14 Partitioning Under Varying one-Dimensional Resource Spaces
Figure 4. Simulation outcome with heterogeneity = 1.4
Figure 5. Simulation outcome with heterogeneity = 2
Market Partitioning Under Varying one-Dimensional Resource Spaces
Heterogeneity
0.60
0.70
0.80
0.90
1.00
1.10
1.20
1.30
1.40
1.50
1.60
1.70
1.80
1.90
2.00
Average
Concentration*
0.26
0.33
0.23
0.30
0.27
0.20
0.23
0.29
0.22
0.28
0.21
0.20
0.26
0.21
0.28
Average
Density*
45.57
34.43
47.43
44.00
42.19
50.90
50.00
39.71
52.19
40.10
46.57
49.19
40.71
48.10
46.95
15
Relative performance
Specialists vs.
Generalists**
1.59
1.85
1.76
3.04
1.59
1.82
1.59
2.18
1.56
2.34
1.58
1.27
2.20
1.66
2.82
*Taken over the last twenty iterations
**Takes the average ratio (over the last twenty iterations) of the number of specialists versus the number of
generalists
Table 2. Results across different levels of heterogeneity
As seen in figure 6, concentration decreases as heterogeneity increases. When the
resource space is more diverse in terms of taste preferences, the market structure gets
less concentrated (Boone, Carroll & Witteloostuijn, 2002). This means that, in this
simulation model, the flattening of the resource space (and subsequent increase in
heterogeneity) will lower the effect of the partitioning (Carroll & Hannan, 1995a;
Carroll et al., 2003). It might lead to think that heterogeneity has a range of values for
which market partitioning appears: enough heterogeneity leads to partitioning, but
high heterogeneity leads to market fragmentation.
Regarding density, it seems to be that the higher the heterogeneity, the closer the
market gets to its carrying capacity (figure 7). High heterogeneity seems to give more
survival chances to more firms in the market. Intuitively, high heterogeneity seems to
reflect the situation in which firms are limited to cover widespread areas of the
resource space, giving the opportunity to more firms to enter the market and capture
some regions. This situation is unlikely in markets with concentrated resources (in
Market
16 Partitioning Under Varying one-Dimensional Resource Spaces
this model, with low heterogeneity), since just a few of them will take over the more
abundant regions.
Average Concentration
0.35
Avg. four-firm
Concentration
0.30
0.25
0.20
0.15
0.10
0.05
0.00
0.00
0.50
1.00
1.50
2.00
2.50
Heterogeneity
Figure 6. Behavior of concentration under varying heterogeneity
Average Density
60.00
Avg. density
50.00
40.00
30.00
20.00
10.00
0.00
0.00
0.50
1.00
1.50
2.00
Heterogeneity
Figure 7. Behavior of density under varying heterogeneity
2.50
17
Market Partitioning Under Varying one-Dimensional Resource Spaces
Relative performance Specialists vs. Generalists
Relative Performance
3.50
3.00
2.50
2.00
1.50
1.00
0.50
0.00
0.00
0.50
1.00
1.50
2.00
2.50
Heterogeneity
Figure 8. Relative performance under varying heterogeneity
Figure 8 shows the relative performance of specialist organizations versus generalist
organizations. It is assumed that performance is directly related to the proliferation of
the organizational forms. For higher levels of heterogeneity, it is shown that the
increased diversity of tastes stimulate the proliferation of specialist organizations.
As per the simulation results, we cannot assert that the middle market firms received a
strong effect due to varying heterogeneity. This effect is partially offset by the
random uniform generation of entering firms. However, we suspect that under
density-dependent generation of entering firms, size-localized competition will be a
product of resource concentration, but not mere fact related to size.
5. Final remarks
Although it is clear that the variation of the degree of heterogeneity is key to
understand the effect of resource space changes on market structures, in the
exploration of necessary and sufficient conditions for market partitioning, some
assumptions need to be tuned up for future models.
The simulation exercise allowed exploring the market emergence behavior under
varying one-dimensional resource spaces. Specifically, the four-firm concentration
ratio, number of specialists and number of generalists were observed.
Market
18 Partitioning Under Varying one-Dimensional Resource Spaces
In the search of conditions for market partitioning, our attempt to explore how much
the degree of heterogeneity affects the partitioning of the market, lead us mainly to
observe effects in specialist proliferation, increasing density and decreasing level of
concentration.

Changes in price strategy





Random generation of entering firms


Definition of specialist / generalists
Endowment



Niche shift

Learning features
neighboring strategies
Inclusion of density dependence effects
Generation
using
non
uniform
distributions.
Definition according to niche covering
Inclusion of reserve capacity for
starting organizations.
Inclusion of some degree of niche repositioning and adaptability.
Table 3. Alternative changes to simulation model
For instance, changing the price strategy might generate different outcomes and
effects on the market structure. One alternative is to change the current way of
calculating prices at each iteration and consider different price strategies. This would
generate different consequences on niche expansion and will test the sensitivity of the
outcomes of the model versus different price strategies.
There is one specific learning from this simulation exercise: as mention before, the
inclusion of density dependence on founding rates might produce effects on firm
proliferation and force the market to a faster equilibrium. The assumption of having
all firms starting with the same capacity seems fair but has the problem of measuring
a real proliferation of the specialist’s organizations. Such founding rates have to
include a more complex pattern, depending on contemporary crowding of the market
and perhaps consideration of liabilities of scarcity (affecting in a heterogeneously way
firm endowment) to simulate a more realistic world.
Finally, in line with RPT, it is seen from the simulation results that low heterogeneity
doesn’t allow any partitioning at all, but high heterogeneity is not enough to guarantee
it either, since it leads to market fragmentation. A more precise evaluation of other
conditions for market interaction is needed.
Market Partitioning Under Varying one-Dimensional Resource Spaces
19
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