Deciding On Software Pricing And Openness Under Competition
Hazhir Rahmandad, hazhir@vt.edu
Thanujan Ratnarajah, thanujan@vt.edu
Abstract
The success of many open source applications has motivated commercial firms to explore
how they can benefit from opening their software platforms in hope of getting free high
quality contributors and more complementary products. Y et the openness decision is
tightly coupled with the pricing of the software (e.g. openness limits the price that can be
charged) and the reinforcing feedback loops of network effects and complementary
products. In this paper we explore how there interconnections impact the optimum
pricing and openness decision for two firms in competition. Reinforcing loops increase
the value of early market lead and put pressure on the competing firms to seek such
advantage. We show that the competitive equilibrium under strong reinforcing loops calls
for highly open software products with deep early discounts, which may significantly
compromise the profitability of the players in the market. Proprietary platforms and
higher prices are favored in the absence of these loops.
Keywords: software, network effects, complementary goods, open source, Nash
equilibrium
1- Introduction and Problem Definition
Software development is a major part of economy in many advanced and developing
countries. Due to innovative nature of this business and competitive pressures new
development processes and organizational structures routinely emerge in this market.
Opening the code and licensing of a software product has attracted significant attention
over the last few years after the success of many open source projects such as Linux,
Netscape, and Apache. Open source software has proven a strong competitor for many
traditional software businesses. Once only available in marginal markets and simple
products, open source software is increasingly competing with commercially developed
products in complex applications and where high quality and reliability are required. The
result is a significant threat for the traditional software business model which relies
heavily on the sales revenue of the software.
Another major trend in the recent years is strategizing to benefit from network
externalities of software products and the impact of complementary products and
standardization on market performance of a new product. Many firms therefore have
moved towards get-big-fast strategies that by reducing initial price help them take market
share early in the game to enable future success (Oliva, Sterman et al. 2003). Moreover,
these two trends interact in forming business strategy for a firm: for example openness of
a new software impacts its attractiveness for developers of complementary products, the
price that can be charged on it, and the costs of development.
For-profit software companies need to find avenues to adapt their own software
business models to the new challenges and potential opportunities created by open source
movement on the one hand and the strong reinforcing loops active in software business
on the other. We examine how the processes of development, diffusion, and revenue
generation of a software product evolve in interaction with strategic decisions regarding
the business model used by the software company. The research develops a quantitative
model that can help software companies assess tradeoffs involved in selecting different
business models and thus allow for better strategic decisions.
1-1- Openness: A continuum of licensing models
Open source software development has been characterized by highly motivated
communities of developers who on their own time and without direct financial incentives
work on developing software products. These communities openly share the code of the
software and use licensing measures that keep this code in the public domain. Such
development model can lead to significant cost savings compared to traditional software
development model both due to sharing of modules of common code and savings on the
cost of developers. On the other hand status, leaning, and career advancement incentives,
among others, can explain why open source contributors stay engaged in these
communities (Lakhani and von Hippel 2003; Lemer and Tirole 2005). High quality and
reliability of many open source products has further increased their competitiveness in
the market against traditional proprietary mode of software development and distribution.
A second benefit of opening the source code to a product is how that move
encourages other firms and developers to build complementary software that adds value
to the central software. The popular social networking website Facebook (over 175
million users, and growing (Facebook 2009)) provides a good example. In 2007 it opened
its platform to third-party applications that merge with the current system. In less than 6
months over 8000 third party applications were developed and added to the system. This
number has grown to over 52,000 applications by early 2009, and growing with the rate
of 140 applications per day (Facebook 2009).
The facebook example highlights the continuity of openness. While in its pure form
open source software is free and the code is publicly available, there are many different
licensing methods that can put a software product on a continuum of purely open to
completely proprietary. For example the Facebook system is not open source in that
outsiders can not change the structure of Facebook program. Y et it also provides
integration points and access to users for third party applications, thus creating some level
of openness. More generally firms can keep some parts of the code open and benefit from
open source development while keeping other parts propriety (Nilendu and
Madanmohan 2002). Some of the most common licensing arrangements that define
different points on the openness spectrum include (Wu and Lin 2001):
GNU GPL: This particular license emphasizes on the source code of the software always
being open to the community. If a software project is licensed under this model the
community involved in this project will have the rights to make improvements without
the permission of the owner. But any improved work or derived work from the source
code should be made public. This license prevents open source projects being mixed
with proprietary licenses. GPL maintains a pure open source format.
Mozilla Public License (MPL): MPL is considered to be a weaker definition of GPL in
terms of keeping source open. Any open source work should always be licensed freely.
But the open source work could be combined with other licenses (including proprietary
license) as long as the open source portion of the software stays open to the public. The
organization need not publish the other non-open source work existing within the
software, to the public.
BSD Licenses: BSD licenses allow both improved and derived open source work to be
licensed under proprietary licenses. It has no limiting constraints such as GPL. Open
source work could be easily combined with proprietary work.
Proprietary Licenses: Licensee is permitted to use the software under the conditions
mentioned in the license created by the owner of the software. Using software (under this
license) for improvement activities or derived work is prohibited. It could only be done
with the permission of the owner of the software.
While the more open modes of development have many benefits in terms of
development cost and encouraging complementary products, they pose a significant
challenge in terms of commercial viability. The strictest forms of open source software
are by definition free: if anybody can download and alter the code, you can not charge for
that code. The lower levels of openness may allow for charging for software, yet they
usually bring down the price to accommodate community of developers and
complementary products. As a result, direct sales revenue is negatively impacted by
openness of a software product, even though maintenance and customization of installed
software, and advertising revenue in case of online software, could still provide some
stream of revenue. This poses an important question for the profit oriented developers of
anew software product: given all the tradeoffs involved what level of openness should
they choose to maximize their long-term profit? Given the legal and technical
ramifications of openness question, once settled, it is not easy to change the level of
openness for a product.
1-2- Network effects and pricing in competition
Over the past two decades management scholars and economists have paid increasing
attention to the significance of different reinforcing loops at work in the operation of
firms. Network effects (Katz and Shapiro 1992), word of mouth (Dodson and Muller
1978), learning curves (Argote and Epple 1990), and economies of scale and scope
(Panzar and Willig 1981) are a few of such reinforcing loops. The common denominator of
these mechanisms is that as the size of the company or its market share grow, its unit cost
for further growth goes down. For example more fax machines make the next unit of fax
machine more attractive (network effect), satisfied customers lower the cost of attracting
new customers (word of mouth), accumulating production leads to more efficient
production processes (learning curves), and larger size reduces fixed cost per unit of
product (economies of scale). As a result the larger firms find themselves in a better
position in competition, and can derive the competitors out in “winner take all” dynamics
(Frank and Cook 1995). When these loops are active, early success breads further
advantage to the firm and thus an aggressive policy of expansion is prescribed for firms
competing in markets with strong reinforcing loops (Arthur 1989).
Companies typically can gain early advantage by a combination of entry timing
(those who enter the market earlier get a head start), early discounts, and joining in
networks of complementary goods to increase the value of their product to early adopters
(e.g. one of the reasons why V HS won against Beta max in the video market (Sterman
2000)). Previous research has explored the optimum pricing policy for a firm benefiting
from learning curves (Spence 1981; Cabral and Riordan 1994) and has shown that early
discounts can help firms succeed in competition when learning curves benefits can be
kept inside the firm. Therefore when reinforcing loops are important in a market, pricing
decisions should be made with an eye on these dynamics, and typically efficient prices
change over time depending on market conditions.
Many software products are exposed to multiple reinforcing dynamics including
word of mouth (Dellarocas 2003) (e.g. for viral marketing), network externalities (e.g.
computer games are more attractive when many of your social network are playing them),
complementary software development (e.g. Microsoft Windows platform is largely
attractive because most mass market software firms first develop their product for this
platform), and economies of scale (e.g. most of the cost of software development is fixed
costs and production and distribution costs are often negligible). Therefore a dynamic
pricing policy that considers these feedback effects seems a requirement for software
pricing. Moreover, finding optimal pricing policy for new software products is linked to
the openness question discussed above: openness decision sets a limit on the prices that
can be charged on a product (Hawkins 2004). Thus the two decisions should be
considered simultaneously: what pricing policy and what openness level should a new
firm adopt?
Another complexity in determining optimum pricing policy relates to the
competitive nature of the these decisions. Firms are not making their pricing decisions
independently, rather, their decision directly depends on the decisions of their
competitors. For example a reduction in price can lead the competitor to reduce theirs,
negating the expected benefit of the initial move. Therefore a game theoretic framework
should be employed to find out the Nash equilibriums in such competitions. In such
equilibrium neither player can improve their payoff by changing their pricing (and other)
policies. Finding Nash equilibrium is however typically hard analytically for all but
simplest discrete time models.
The goal of this paper is to advance a solution to the challenge faced by software
firms using a generic dynamic model of software development, sales, and complementary
products in competition between two firms. We model how firms compete using price
and openness to capture a pool of customers and how their success in getting customers
impacts their profits. We then introduce a numerical method for solving the game
theoretic equilibrium problem for these firms and analyze the structure of this solution as
a function of alternative market and technology characteristics.
2- Modeling dynamics of software openness and pricing
Our modeling work draws on data from two case studies and the relevant literature. One
proprietary study by the first author explored the costs and benefits of different openness
decisions that could be pursued by a large software company in positioning one of its
products. Given the proprietary nature of this case we only used it to inform the
formulation of development and market share, however, the parameter values reported
here differ from the case. Anther case using data from the competition of Linux and
Windows operating systems informed the characteristics of reinforcing loops active in
software development. That case is documented elsewhere (Ratnarajah 2008). Both these
cases informed the structural features of the model in terms of software life cycle, factors
determining the attractiveness, and the important feedback processes. They also helped us
determine reasonable ranges for specific parameters. However, the model reported in this
paper does not attempt to reflect any specific product. Capturing some of the most critical
feedback mechanisms involved in determining pricing and openness policies, this model
is used to find general patterns of optimal pricing and openness under alternative market
and technology settings and can be tailored to specific cases as needed.
The profitability of a software business depends on its costs and revenues. Figure
1 outlines the major interactions between the market and the software organizations and
how these shape the costs and revenues in our model. Note that similar structures are
replicated for both firms (though subscripts in Vensim™ simulation environment). The
revenue of a software company relies on the market share, which determines the product
sales, and the installed base that controls service revenue. Revenue directly and indirectly
depends on the openness and pricing decisions. Higher prices increase revenue directly
and openness contributes to revenue indirectly by increasing the market share through
increasing complementary software and thus customer utility. Openness also reduces the
costs by replacing paid employees with open source community of developers. Multiple
reinforcing loops that depend on the installed base can further increase the services
revenue and the attractiveness of strategies that benefit from openness of the software.
On the other hand, the openness of the platform requires a company to allow other
parties access to the result of their development activities. This sharing limits the product
price that can be charged and thus negatively impacts the revenue. Multiple feedback
processes result from these interactions and lead to tradeoffs that influence optimum
pricing and openness decisions.
Consumer
|<—_—_—_—
Market Feature Expectations
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- +
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Formal # +
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Installed Share
# oO
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Installed Base
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Figure 1- The overview of the feedback loops under analysis.
We consider the software development companies to decide on developing new
features (Feature Introduction Rate) based on benchmarking their current features (New
Features Developed) against capabilities of average product in the market (Market
Feature Richness) and trying to move ahead of the market. The market feature richness
partially depends on the features provided by all the players in the market, and partially is
exogenous based on initial consumer expectations. A fter an initial investment period,
introducing new features also depends on profitability of the software: if profitability is
low, investment dries up. The relative feature richness of the product impacts its utility to
consumers.
Both “Open Source Contributors” and “Formal Employees” can contribute to the
development of the software. The numbers of these contributors partially depend on the
number of “Features Under Development”. Number of open source developers also
depends on the openness of the software platform and its current traction in the market.
The firm adjusts its formal employees to finish the features under development in the
planned time, given the current level of open source contributors resulting in the
balancing loop B1:Development. A software product with a large pool of pen source
contributors requires fewer formal employees and thus lower Costs.
Sales of software (Sales Rate of Software: SS) depends on the “Total Adoption”
rate (A), which we assume to be exogenous and determined by a typical product life
cycle model (i.e. a bell-curve over time), and “Market Share” (MS) for each player in the
market. Market share in turn depends on “Utility of the Software” (U) through the
classical Logit model:
ei
MS, re (1)
Utility of the software is determined based on an additive function of “Product Feature
Richness” (F), “Price” (P), “Complementary Software Share” (C), and “Installed Share”
(S) for the product:
Ui=a,F” —ap.P” +acC," +a5.8* (2)
Here , represents the relative weight of factor] in utility of the consumer, and /,
represents the steepness of relationship between different utility determining factors and
overall utility. Forexample £,, 6,, and f, are typically between 0 and 1 (that is, there
is a decreasing retum on features, complementary software and on installed share), while
sensitivity to price is only restricted to positive values. The inputs to utility function (F, P,
C, and S) are normalized by market feature richness, maximum price, total
complementary software, and total installed base, so that they all remain bounded and
robust in the simulations that will follow.
To include the impact of “Openness Decision” (O) and “Pricing Decision” (PD)
on price, we use another parameter, « >0, to determine a maximum feasible price given a
level of openness (1—O*), and the pricing decision (between 0 and 1) specifies the price
to be charged between zero and this maximum feasible price:
Pi=(1-O*).PD, (3)
Connecting the impact of software sales (SS) to installed share (S), we close the
“R1: Network Effects” loop. Software sales accumulates in the installed base (B) which is
drained with some time constant as consumers stop using the product, and installed share
is simply the share of each player of the overall installed base in this market:
B =|(S§-B/z,).dt (4)
B
=p (5)
Ss vB
This feedback mechanism captures both the word of mouth effect and different network
externalities that depend on the installed base of the software: the more the installed base,
the higher the utility, and thus the market share and sales.
The introduction of “Complementary Software” (CS) depends both on the effect
of the openness of the software (EO) and the installed share (S). The dependence on
openness follow the observation that open platforms encourage complementary software
developers to build their products on those platforms. On the other hand, installed share
of products is typically a major motivation for complementary product developers to
build products compatible with the bigger players in the market. Moreover, the
complementary software has a useful life after which it looses its impact on the
attractiveness of the focal software. Finally, Complementary Software Share is
determined by the number of complementary software products for all the players.
Specifically:
CS = f liye EO.S* - CS /7,).dt (6)
EO, = €0y4, + (1 — €044,,).0" (7)
é- 4 (8)
i xcs CS
Parameters ¢, and ¢, determine the strength of the impact of openness and installed share
on the introduction of complementary software. The parameter eOyjn (between 0 and 1)
represents the rate of development of complementary software for completely closed
platforms, as a fraction of complementary development rate for completely open
platforms with otherwise identical characteristics.
The link from installed share to complementary software and back to sales
introduces a second reinforcing loop: “R2: Complementary Software and
Standardization”. This loop captures the process of development of complementary
products and the standardization of the software as a trusted platform, both of which
follow the installed base with a delay, and thus are captured in a separate loop.
The installed share of the product also impacts the attractiveness of product for
involvement of open source contributors (OC). The larger the current base, the more
attractive the platform becomes for new open source developers as they see a larger
prospect for impact and visibility of their work. For example Wikipedia is far more
attractive for potential contributors than a small open source product with a few hundred
installations. Besides the installed share, the current level of features under development
determines a “Desired Joining Rate” (DJ) which limits the number of open source
contributors joining the community. Finally, by definition the level of openness of a
product has a significant impact on the desire of the potential open source contributors to
join the community. The community members leave after some average residence time.
Specifically:
OC, = f (Min(DJ,, issue ES.0"") — OC, /7,) at (9)
ES = 5, + (15). (10)
The number of formal employees (E) is adjusted towards a desired employee level.
The latter is determined based on the development resources, beyond open source
community, needed to develop the features under development and the resources needed
for service and maintenance of the current installed base. Finally, the profit stream (R)
depend on the costs (employee costs (c;.E) and fixed costs( c;,.)) and revenue from both
sales and services (B.p,,). We use the net present value (NPV) of this profit stream
discounted to the beginning of product life cycle with discount rate ras the main
performance function for the firm:
R = AMS.B. Phex + B-Day ~ Cix — CoE (1)
NPV((t) = f e*R(s).ds (12)
0
Full model with complete variable listing is available in the supplementary material for
replication and further analysis.
3-Analyzing pricing and openness policy for two competing firms
In this section we first provide a base run for the model to create a basic intuition about
the dynamics involved. We then show the results of one firm optimizing its pricing and
openness decisions assuming that the other firm behaves as in the base run. This analysis
provides further insights into what policies can help one firm to succeed and the
mechanisms responsible for effectiveness of those policies. We then layout the general
process for finding the game theoretic equilibrium for this competition and share the
results under the base case parameters of the model. Finally, we discuss the robustness of
these results to different market and product characteristics.
3-1-Base run: Two firms with fixed policies
In the first experiment we simulate two identical firms with a fixed pricing policy (charge
maximum feasible price, i.e. PD=1), and a mixed openness policy: O=0.5. Given the
identical nature of the two firms, their performance over time is identical, therefore we
only show the variables from one of the firms in Figure 2. The behavior of the system is
partly driven by the exogenous A doption Rate (Variable 3 in panel a) which follows a
typical bell-curve pattern for the life cycle demand for the product. Installed base of
software (Variable 2, panel a) follow the adoption, and complementary software (variable
2, panel a) lags further. Revenue (variable 1, panel b) is generated by a linear function of
adoption (i.e. sales) and installed base. The costs (variable 2, panel b) on the other hand
follow a significant initial rise to hire required employees (variable 1, panel 3) for the
development of new initial features, and later goes down to steady state levels dictated by
employees required for maintenance and service. Open source contributors (variable 2,
panel 3) follow a similar pattern as employee do, but go to zero as service and
maintenance are assumed to be done through contracts and by formal employees. The net
present value (variable 3, panel b) goes down initially as profit is negative, but later starts
to recover when sales and maintenance revenue dominate the costs. We focused on a 10
year period for analysis, until the profit tends to move towards zero at the end of the life
cycle and the company would find the continuation of this line of business no more
attractive. Given the identical nature of the two firms in this case, the impact of different
feedback loops on their competition is not salient.
20,000 Software
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Figure 2-The base case behavior of the model with two identical competitors with no strategic
behavior. a)Customers, complementary software, and adoption rate. B)Revenue, costs and net
resent value c)employees and open source contributors.
Pricing Decision
3-2- Optimizing a single firm’s pricing and openness
In the second experiment we allow one firm to optimize its
pricing and openness decisions to maximize its final net
present value (NPV at time 120), assuming that the other
firm does not change its pricing or openness policies. In
formulating the optimization problem openness is assumed
to be constant throughout the simulation time. This is
consistent with the nature of openness parameter which
Figure Bunnie of modeling DCE decided, is hard to change due to legal and technical
dynamic prices. Two challenges. On the other hand, pricing policy could be
parameters specify each point. dynamic. In extreme, the prices could change at any point
Connecting these points in time. We simplify this problem by allowing the firm to
provide the overall price at any select N points in time, including beginning and end times,
point in time. with their respective prices. Price at any point in time is
then determined by a linear weighing of the two points
before and after that point in time. Figure 3 provides an example with N=4. In the
reported experiments we use N=9, which we found to provide sufficient degree of
flexibility for all the cases we analyzed. This setting leads to 17 parameters to be
estimated for the firm: 1 for openness, 7 for the points in time (other than initial and end
times) when pricing decision changes slope, and 9 for the pricing decision at the N points.
We use Venism ™ optimization engine for solving this nonlinear optimization problem.
Unit Price Market Share Tistalled base of the Software
ae ag”
Taw Mon
‘ORIBTEEALY SOTA
a ao ei)
oh “Tine (Mon)
Figure 4-Performance of two firms when firm 1 is optimizing its price and openness
Figure 4 reports the results of optimizing firm 1’s net present value, keeping the base
parameters for firm 2. In this case optimum openness comes out at 0.36 (vs. 0.5 for firm
2) and optimum pricing is reported in panel a. The pricing decision (PD) starts from free
distribution of the software for the first few months, to a relatively steep hike in the price
so that by month 26 the company is charging the full price feasible (PD,=1 for t>26).
Given the lower openness of the software, firm 1 can charge more than its competitor,
thus the higher final unit price. The initially strong price advantage for firm 1 leads to
significant market share advantage early on for it (panel b). This helps firm 1 build a
strong installed base (panel c) and thus attract many more complementary software
developers than its competitor (panel d). It is interesting to note how a significant initial
installed base also helps firm 1 receive many more open source contributors, leading to
even further cost advantages despite the fact that firm 2 has a more open architecture
(panel e). Another interesting feature of this experiment is the fact that by increasing the
price firm 1 actually reduces its market share advantage over time in return for getting a
more significant profit margin (panel b). Overall, firm 1 can earn a much higher retum on
its investment and reach a significant net present value where as firm 2 in this setting
becomes profitable only after 3 years and can never reach a positive net present value due
to significant losses early on (panel f).
The reinforcing loops of open source support, network effects, and
complementary software significantly impact the shape of optimum pricing policy. In fact
in the absence of these loops the optimal pricing and openness patterns for the firm will
completely change. The optimum policy for firm 1 when the reinforcing loops R1, R2,
and R3 are deactivated (by setting parameter £,, 85, and veto 0) is to keep the software
largely closed (O=0.06) and charge the highest feasible price (PD;=1) . In fact under
these conditions firm 1 looses market share to the second firm (because it is now offering
a more expensive product), yet it improves its profitability by having much higher
margins. Interestingly, firm 2 also benefits from this policy of the first firm as it gains
market share and thus increases its revenue given its constant price. Overall, the
reinforcing loops of network externality, complementary goods, and open source support
increase the usefulness of open source policies and steep discounts early on.
3-3-Strateqic competition between two firms
In the previous section we assumed firm 1 optimizes its price and openness while firm 2
does not make any adjustment to its base case policy. This is not a realistic assumption in
practice because both firms probably have relatively similar opportunities for finding
improved policies, and therefore they would both try to optimize their own performance,
taking into consideration the actions of the other firm. In extreme, rational firms with full
information about the structure of the competitor firm would find the pricing and
openness policy that can not be improved upon if the competitor is also rational and
looking for such policy. Should such policy exist, it constitutes a Nash equilibrium for the
competition between the two firms. While the selection of Nash equilibrium by both
firms may be behaviorally a strong assumption (given the computational, information,
and coordination limitations of real organizations), finding this equilibrium is informative
in telling us about the tendencies of the firm in adjusting its policy in such markets.
Solving the equilibrium problem analytically is not feasible for the model at hand,
therefore we use an iterative numerical method that was capable of solving the
equilibrium problem for all the experiments in this paper.
The basic idea behind solving the strategic equilibrium problem is simple.
Consider the experiments in the section 3-2, and assume that firm 2 predicts firm 1’s
optimal policy (that we found above) and using that as what firm 1 will do, optimizes its
own pricing and openness policy. Next, firm 1 takes this policy of the second firm as
input, and optimizes its own policy for a second round. This process can continue for as
many rounds as needed until the two firms converge to the same policy’. If they do
4 Convergence to the equilibrium (same policy) is not guaranteed, even if such equilibrium exists.
Convergence may depend on starting points of the search process. Moreover, this process does not provide
converge to such policy, that policy is by definition a Nash equilibrium for the
competition between the two firms: neither firm can improve its performance by
deviating from this policy. In our computational experiments under different parameter
settings the firms converged to the same policy after at most five iterations of the above
process (a total of 10 optimizations).
Figure 5-a reports the successive changes in the optimum pricing policy for firm 1
(optimization rounds 1, 3, 5, 7, and 9), that is, item 1 represents optimum policy for firm
1 if firm 2 is following base case policy, item 2 representing optimum for 1 if firm 2 is
following firm 1’s policy in item 1, and so on. As the competition between the two firms
get closer to a fully rational one, both firms tend to increase their openness (firm 1 going
from O;=0.36 to 0.53, 0.64, 0.68, and 0.69 in the five successive optimizations) and
provide the software for free longer, in the hope of increasing their early market share
advantage over their competitor. Higher discounts and openness however are copied by
the other firm who is also seeking to improve its profits, leading both firms to receive a
lower profit stream (panel b) in a prisoners’ dilemma type of game. In fact with the
current parameter settings net present value for neither firm becomes positive in the final
equilibrium (item 5 in both graphs).
Unit Price
Present value Stream.
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0 2 24 23% 4 6 72 8 9%6
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Figure 5- Successive iterations of optimization to find strategic equlibrium for both firms. Item 5
represents the optimal policy under strategic competition which is identical for both firms. a) The
unit price for firm 1 over time b) The net present value for firm 1.
A comparison between the base case (Figure 2, where no competitive action was
modeled) and the final strategic equilibrium is instructive (Figure 6). In both cases the
market share is equally distributed between the two identical firms, therefore the installed
base for both firms is identical to the base case (Figure 1-a). However, increased
openness of the software in the competitive equilibrium leads to increased
complementary software in this case (Figure 6-a), and reduced prices for both firms
(Figure 6-b). These factors increase the overall utility of the customers benefiting from
these products in this market. Moreover, open source developers become a more
important part of the development process given their higher share in the product
development process (panel c). On the other hand both firms are financially worse off in
the competition (panel d). Overall, moving towards the competitive equilibrium tends to
benefit the users of the software at the expense of the software producing firms, leads to
more open platforms and lower prices or free products.
any direct way to assess the uniqueness of an equilibrium point. In all the experiments reported here
however we did converge to a single policy regardless of the optimization starting point in the policy space.
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Tine (Mout)
96 0a a4
Figure 6- Comparison of base case (item 1) and competitive
equilibrium (item 2) for complementary software (a), unit price (b),
jopen source contributors (c), and net present value over time (d).
3-4- Robustness of results
The preceding analysis used a set of base case parameters to define the strength of
different feedback processes and customer utility function. In this section we analyze
how sensitive the competitive equilibrium results are to some key parametric assumptions.
First we vary seven of the major model parameters around their base levels to assess the
impact of different loops and effects individually. We then combine a few of these effects
to see how completely different market conditions can change the optimal pricing and
openness decisions. Table 1 reports the parameter settings used for this analysis.
Table 1- The parameter settings used in the sensitivity analysis. Full paramters and equations are
available in the attached model.
Parameter Base | Lower | Higher | Equation
Value
Sensitivity of Utility to Price ( Bp) 1 05 | 2 2
Sensitivity of Utility to Installed Share ( /,) 0.5 0.1 0.8 2
Sensitivity of Utility to Complementary Software Share ( ,) 0.5 0.2 1 2
Sensitivity of Complementary Software to Openness ( &, ) 1 0.5 2 7
Sensitivity of Complementary Software to Installed Share(¢,) | 1-5 0.5 3 6
Sensitivity of Open Source Contributors to Installed Share(v,) | 1-5 0.5 3 10
Sensitivity of Price to Openness (« ) 1 0.5 2 3
Figure 7 reports the optimum pricing policy and openness for each sensitivity analysis as
compared to the base case. Item 3 in each graph represents the base optimum policy, item
2 represents the results with the higher value of the parameter, and item 1 represents
results with the lower value. In general, all equilibrium policies continue to have the S-
shaped feature of starting from fully free software and moving towards charging the
maximum price feasible at some point in time. The sensitivity of results to different
parameters, however, differs. For example, how sensitive the open source contributors
are to the installed share of the software has little impact on the competitive equilibrium
(panel f). In contrast, the sensitivity of the customer utility to complementary software
makes a significant difference in the magnitude of openness in equilibrium (panel c): low
sensitivity leads to relatively closed software (O=0.45) compared to when customers
really care about complementary software.
60 100
Ae Seen [
i 5
{
| b) Sensitivity of Utility to Installed Share
80 | a) Sensitivity of Utility to Price (8p )=0.5, 2, 1 || 5° (fel O 305-2 =
15 | Otow= 0.62, Ori=0.64 |} 5 | Opog= 0.82, Ows0.42.— |
/ j |
Q ob
100 180
c) Sensitivity of Utility to Complement d) Sensitivity of Complementary Software to
B Softwar¢ Share (3,.)=0.2, 1, 0.5 160 Opennest (4 )=0.5 21 7
so | Ora 9.45, Ors0.84 ll Oroy= 68 On=0.81 {
25 f 20 |
|
0 I | ol,
e) Sensifivity of Complementary Software to
Installed Share ( ¢, )=0.4, 3, 1.5
"0 | Oaw= 0:93, Oxp=0.82 30 f) Sensitivity of Open Source Contributors to
bo 2 2 s Installed Share ( vg )=0,5, 3, 1.5;
} / ° 0.68, Or=0.68
0 ofl ok.
0 12 24 36. AB 60. 72 84 96 108121
80 Look a | Figure 7- Results of sensitivity analysis, changing
bo g i ensitivity of Price to Openness ( «° )=0.5, jone parameter at a time. In each panel item 1
r | represents the low level of parameter, item 2 the
ia Otow= oF Op=0,75, high level, and item 3 the base case. Optimum
Id lopenness levels are also reported on each graph.
Sensitivity of utility to installed share (panel b) also shows a significant impact: the
higher this sensitivity, the more openness is induced in the equilibrium. Therefore one
can expect that in markets with significant word of mouth effects and network
externalities, the balance tilts towards companies with more open platforms and lower
prices. Weak network effects promote more proprietary platforms with higher prices. The
strength of reaction of complementary software developers to openness is also influential:
the stronger this reaction, the more open the equilibrium platform (panel d), resulting in
lower prices. Such sensitivity is likely to be higher when complementary software should
be directly integrated with the focal software, such as integration of social network
platforms with their applications. In contrast, modular complementary software that does
not need access to internal workings of a software is less sensitive to its level of openness
(e.g. most operating systems). Complementary software is also influential through its
sensitivity to installed base: when complementary software producers want to only work
with the market leader, the overall market dynamics favors open source and free products
(panel e). Again, this would typically be the case when the focal software integrates with
the complementary products and therefore a lot of development work for complementary
product is unique to the platform in question.
These effects suggest that the stronger the reinforcing loops of network
externality and complementary products, the more the market tips towards the open
source business model where price is low (or product is free), most of the work is done
by the open source community, and the major source of revenue is the service and
maintenance fees. The third reinforcing loop, open source support, proves less
consequential however. This loop acts through the design of new features. Y et in the
absence of open source developers the company will hire enough paid employees to keep
up with the market. As a result the real effect of openness in gaining market share does
not come from the use of open source community, rather, through the reduced price of
the product when it is open source, and through the impact of complementary products.
Two other experiments need further explanation. First, as panel a shows, the main
difference between higher and lower sensitivities of utility to price is in the timing of
price change. With high parameter values ( 2, =2) the equilibrium price is increased
earlier (in fact from the beginning of the simulation) compared to the low , case in
which equilibrium price increases more abruptly and later than base case. To understand
this effect we need to note that in equation 2 , operates on a price metric that is
normalize against its maximum value and thus is always smaller than one. With higher
than one #, and smaller than one price index (P,), the impact of utility on price will
remain very small compared to other utility factors. For example P; of 0.2 vs. 0.3 leads to
effects of 0.04 vs. 0.09 when f, is 2, both very small effects. As a result the model
allows for faster and earlier increase in the price. Y et the overall price is largely bound to
openness level which remains fairly high in light of its impact on complementary
software development. Therefore intuitively, price sensitive customers also further push
the equilibrium of competition towards free software. Finally, the sensitivity of price to
openness reflects how much price should be reduced if openness is increased. A low
value for « leads to a strong reaction (see equation 3 and note that O is smaller than 1)
while a high value leads to less impact. As a result higher prices are feasible with higher
openness levels when « =2, leading to an equilibrium in which both price and openness
increase (panel g, item 2).
These experiments, therefore, suggest that removing the reinforcing loops of
network externality and complementary software (R1 and R2 in Figure 1) could change
the optimum firm policy in this market considerably. To test this hypothesis we conduct
an experiment in which both these feedback loops are cut, thatis, 8. =, =0, while all
other parameters remain the same as those in the base case. The results are reported in
Figure 8. As anticipated, the shift in the optimum policy is very significant: the optimum
openness shifts to zero, while full price is charged from the beginning to the end (PD=1)
for both firms. The firms are no more under significant pressure to sacrifice their
profitability or open up their source code to gain an initial lead in the market share, and as
a result they end up with significant improved profitability (panel b, compare to Figure 2).
This comes despite the fact that the firm no more benefits from open source contributors
(panel c). Moreover, with a fully closed architecture in a completely proprietary model
fewer complementary software products are written for it (panel a).
Sotbvare Financrals Human Resources
beard a 400,000 7 c
6.00 ay ae
ai ar a
30,000 4a TT nae
2 1yAnstalled Base ~~—.____| | 200200
008 | ; Complementary Software|| ~~
of! _// 3+ Adoption Rate. |
0
0 400,000,
0 2 28 36 48 60 72 OF 96 108 12
La
0 2 m@ 36 4 00 72 € 96 ioe ay 0
Tine (Month)
Tod to
Tine (Mon)
Figure 8-The competitive equilibrium in the absence of complementary product and network
externality reinforcing loops a)C ustomers, complementary software, and adoption rate. B)Revenue,
costs and net present value c)employees and open source contributors.
4-Discussion
In this paper we analyzed pricing and openness decisions for software firms exposed to
different reinforcing loops in the software market. A few general themes emerge. First,
the network and complementary product effects significantly influence the desired firm
policy. When strong reinforcing loops are present, the firms need to do all it takes to
build an initial installed base and attract complementary software producers. It can do so
by both giving the product for free, and opening up its platform to benefit from open
source contributors and encourage complementary developers. The pricing will later be
shifted towards charging for the software, yet the charged amount is much less given the
openness of the product that does not allow for high prices. These themes are most salient
when we consider the strategic competition among two firms, where the Nash
equilibrium of their competition dictates significant openness and discounts. When
network and complementary effects are absent, optimum policy could favor the
completely proprietary model with maximum chargeable price.
Secondly, deciding on the right level of openness is tightly coupled with the
pricing decision and the reinforcing loops discussed. The increasing popularity of open
source software has motivated many commercial software producers to look into
profitable opportunities in alternative business models that benefit from openness. Our
results suggest that those opportunities are limited: openness, as a business move, is
beneficial where strong reinforcing loops of network and complementary product exist,
yet the very same market structures require significant discounts that hurt profitability
significantly. Head to head competition therefore significantly limits potential returns in
these markets.
On the other hand, if a firm benefits from early mover advantage, which allows it to
grow significantly before competitors consider the market, openness could prove a
profitable business move. This is because openness leads to strong barriers to entry for
later competitors and thus allows the firm to rip the benefits of a large installed base (e.g.
through service and maintenance) without coping with all the competitive pressures.
Gaining such early mover advantage however is not easy. In a market replete with smart
entrepreneurs, where information travels very fast, players have access to similar
technologies, and capital costs are limited, good ideas rarely remain secrete of one player.
Therefore despite the huge buzz around success stories of get-big-fast strategy in
emerging online market, from Amazon to Y ouT ube and Facebook, the fact is that only a
handful of firms have successfully traversed this path and for each successful case there
are hundreds of failed businesses.
The research also provides some insights about the structure of software markets with
strong reinforcing loops. Early in the market life cycle many things remain unknown:
what is the market size, how many competitors will join, and what prices could be
charged to make the venture profitable. Bright ideas and promises of fast growth can lure
investors and entrepreneurs into exploring such market opportunities without full
appreciation of the odds involved in light of the competitive pressures above. Start up
firms start with deep discounts and free products to gain the early advantage in the
market, hoping that soon they will be able to switch to a profitable model by charging
higher prices for their product, or for the complementary services. Y et as the competitors
join the market with their own discounts, these plans have to change and profitability
should be delayed in hope of driving the competition out. The fierce competition often
continues until seed money runs out and investors pull out. Sometimes in this time frame
a firm reaches large enough a market share and size that it can sustain its business and
become one of the few success stories. More often however, all the players find the
market niche to be too costly to make it worth the effort. Such markets may completely
be abandoned as a result. On the other hand, the price sensitivity of the consumers in this
market increase as they get used to products that are free when they are the most novel.
Such increasing price sensitivity further reinforces the dynamics above. It is not clear
how such market structures would impact long term consumer utility: on the one hand
discounts and large complementary networks of products benefit consumers significantly,
on the other hand the dynamics discussed could keep more mature players from ever
addressing some needs and market opportunities. So far the consumers have largely
benefited from these trends, it should be seen whether the negative effects will catch up,
e.g. through a crash in different Web 2.0 market that has been a hot market with
significant reinforcing loops.
The framework and the model developed in this paper can also be used for analyzing
the options available to a specific firm in a specific market. Such analysis requires
empirical estimation of multiple parameters of the model based on the market and firm
characteristics. In also requires insights into the decision making process and firm
characteristics of competitors. This data may be hard to obtain, but the resulting analysis
can move a long way towards better market entry decisions and pricing and openness
policies for incumbent firms.
This research is limited on multiple fronts. First, the analysis focused on a constant
market life cycle that is not impacted by the different factors influencing the utility of
consumers. In practice the market also grows (or shrinks) depending on the features,
quality, price, complementary products, and other characteristics of the competition.
Inclusion of the feedback to market size can potentially change the structure of optimum
policies for firms involved. Several other relevant dynamics, such as learning effects
where also excluded in this analysis.
Furthermore, we focused on two identical competitors starting at the same time in this
market. Entry timing, competitor heterogeneity, and multiplicity of competitors can
change some of the dynamics discussed. For example late entrants, facing strong
competition, may continue to provide discounts on their product, pushing the other firms
to retain low prices longer. Despite these limitations, we hope our analysis provides some
insights into the complex inter-relationship of openness, pricing, and reinforcing
feedback loops in software business.
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