Supporting Material is available for this work. For more information, follow the link from
the Table of Contents to "Accessing Supporting Material".
Table of Contents
Go Back
Embedding game-theoretic concepts into system
dynamics models: The case of complementary
products development
E.D. Adamides!, N. Pomonis! and Y. Stamboulis”
‘Department of Mechanical & Aeronautical Eng
University of Patras, Rion 26500, adamides@mech.upatras. gr
Department of Mechanical and Industrial Eng
University of Thessaly, Pedion Areos, Volos 38334, ystambou @uth.gr
Abstract
The problem of mutual resource commitment during the development of complementary products is
modeled as an evolutionary Prisoner’s Dilemma game. To investigate the effect of different pure and
mixed cooperation and/or defection strategies over the period of a technology cycle, a system dynamics
simulation model has been built using the resource-based view of the firm. The dynamics of tangible
and intangible assets, such as customer base and technological learning, were included in the model.
Cooperation and defection payoffs have been assumed to be time-dependent. The model was calibrated
using data from the video games industry. Simulations run for different complementors’ strategies
show the importance of early cooperation during technology cycles. The model can be used in an
interactive mode to evaluate more complex industry-specific strategies.
Keywords system dynamics, evolutionary games, complementary products
1. Introduction
The management of complementary products and assets is one of the most important strategic
activities of the firm. Complements are used to provide greater value to the customers as well
as to protect innovative offerings from imitators [Teece (1990)]. In the case of systemic
innovations, the complementary assets are usually integrated parts of the system offered (e.g.
software-hardware, DVD-DVD player).
Firms offering complementary products and/or services are called complementors [Nalebuff
and Brandenburger (1996)]. Nalebuff and Brandenburger stressed the role of complementors
and defined them in a game-theoretic context as follows: “A player is your complementor if
customers value your product more, when they have the other player’s product than when
they have your product alone”. While competitors divide markets, complementors create or
increase the size of a market. In a specific market segment and/or at a specific time period,
otherwise competitors can be complementors.
The motivations for co-operating with a complementor include the building of a critical mass,
the building of new competencies and the setting of market standards [Doz and Hamel
(1998)]. However, the partnering with a complementor may hide dangers. A complementor
may view the alliance opportunistically as a means to promote long-term private gains against
its counterpart [Khanna, et al. (1998)]. For instance, a complementor may acquire the
specialized skills of its partner and then decide to continue alone. Furthermore, a firm
engaged in such an alliance may find out that the effort put in the alliance is too time- and
cost-consuming resulting in a deterioration of its idiosyncratic skills that it would have been
better to undertake the activities of the complementor itself. Finally, a firm may be too tied to
a specific complementor missing opportunities offered elsewhere by others. These risks are
higher at the technological innovation and product development activities where resource
commitments may be decisive for the future of the firm.
It has been only over the last years that the analysis of this kind of strategic situations — to
cooperate or not over the development of complements — has received considerable attention
from the game-theoretic point of view. To this has contributed the shift in strategic thinking
form the analysis of market specific activities and positions to the durable, firm-specific
factors that underpin differences in the product-market opportunity sets of companies
[Ghemawat (1997)]. Research suggests that interesting product market imperfections, which
lead to different competitive positions, generally rest on factor market imperfections [Baumol
et al., (1982)]. In this framework, resource accumulations and commitments play a central
role in the analysis of competitive advantage. How strategy research met game theory is
explained by the fact that resource commitment has always been a central theme in the
application of game theory to the industrial economics view of strategy (e.g. [Shapiro (1989)],
[Ghemawat (1997)].
Since the decision over the development of complementary products is essentially a resource
commitment decision, in this paper we approach it from a game-theoretic perspective. More
specifically, we investigate this long-term strategic decision “to cooperate or not to
cooperate” within the framework of the evolutionary “Prisoner’s Dilemma” game, which has
been used extensively for the analysis of similar situations. However, we extend this simple
model by embedding it in a system dynamics model to take into consideration the endogenous
(e.g. learning) and exogenous (e.g. market dynamics) evolutionary mechanisms that effect
decisions and outcomes through a specific technology-based product cycle. Although we use
simulation to investigate the effect of pure and mixed strategies of cooperation and defection,
the main objective of the paper is to show how game theory and system dynamics can be
integrated for the analysis of this sort of strategic situations, rather than to explain or provide
prescriptions for specific strategies through the analysis of equilibria. The model developed is
structured and calibrated using the video-games industry as a reference case.
2. The evolutionary Prisoner’s Dilemma game and its dynamics
The original Prisoner’s Dilemma Game (PDG) is a formulation of a two-person game in
which players decide simultaneously whether to cooperate or not. Mutual cooperation and
defection yields the highest and lowest collective payoff, respectively, which is shared
equally. However, still higher individual payoffs are achieved by defectors against
cooperators, leaving the latter with the lowest possible payoff. This implies that defection is
always a better decision because defectors always do better than (or at least equal to) the co-
players.
This obvious result is, however, at odds with reality, not only in the business terrain, but also
in the human and animal societies where cooperation emerges under certain circumstances to
prevent the phenomenon known as “the tragedy of the commons” [Soden (1988)], where
individual benefits result in a long-term collective disaster. In reality humans, animals and
their organized forms follow mixed adaptable strategies of cooperation and
competition/defection. To understand the emergence and maintenance of cooperation among
selfish individuals in societies, evolutionary PDGs were introduced in which strategies are
either inherited or adopted through basic imitation rules [Axelrod (1984)], [Hofbauer and
Sigmund (1998)]. However, the application of evolutionary game theory into economic
problems entails a great degree of additional complexity as the dynamics of the evolution
(learning, mutation) must be explicitly taken into account. In addition, the mechanisms of
payoff evolution should be modeled appropriately. As a consequence, richer modeling
formalisms that take into account the whole system’s dynamics are required.
System dynamics is an approach developed by Forrester (1961) for studying the behaviour of
systems exhibiting high dynamic complexity as a result of complex dynamic interactions
among their elements. It uses simulation to investigate the behaviour of feedback loops which
contain stocks (levels) and flows (rates). Stocks represent the state of the system whereas
flows the rate of change of this state. States evolve in time according to their relation to
feedback loops. Negative feedback returns the system to a target state, whereas positive
feedback leads to an ever increasing state value. As we show in the following paragraphs,
system dynamics is used to model and simulate the evolutionary mechanisms within the PDG
framework which represents the decision-making setting over the issue of the development of
complementary products.
System dynamics models have already been used for studying the diffusion of innovations
[Sterman (2000)], the innovation management process [Milling (1996)], the interface between
the product and process development [Stamboulis et al. (2002)], the interacting resource
dynamics of co-opetition (Rabbino, 1998), as well as product-line management strategies
[Adamides et al. (2002)]. The model presented in the following section, builds on this
literature and extends it further by integrating a game-theoretic framework over the issue of
complement development throughout a technology cycle.
As the following case demonstrates, the marriage of system dynamics and game theory
provides a platform for assessing complex strategic situations by means of simulation.
Otherwise, analytic solutions would be very complicated to be derived, as the systems
involved exhibit dynamic behaviour between decision points and only patterns of
performance/payoffs can be observed and input to the decision logic of the next phase.
3. The reference case - Complementary products in the video games industry
The home entertainment industry, and more specifically the video games industry, provides
an interesting reference case where evolutionary game theory can be employed not only to
facilitate understanding of players’ strategies, but also to provide a basis for strategic
experimentation, given the appropriate models exist.
The two complementary players in this industry are console manufacturers and games
producers. Relations between them have changed considerably since the early eighties where
Nintendo monopolistically dominated the market and imposed strict rules of cooperation on
developers. Today, though more fragmented, the market is structured during technology
cycles which continuously shrink. Every new technology (for the consoles this refers to the
technology of the main processor, e.g. 16-bit, 32/64 bit, or 128-bit or, lately, its internet
accessibility, whereas for the games producers to the corresponding graphics technology)
leads to turbulence and new market structures may emerge. At the beginning, as well as
during, a new technology cycle complementors of both sides are faced with the dilemma of
cooperating with a specific partner or not. Decisions to cooperate result in mutual
commitment and resources may be exchanged (for example some console manufacturers
provide software-based development toolkits to developers while the new hardware is still
under development [Thomke and Robertson (1999)]). The incentives for cooperation stem
form the fact that console manufacturers aim at setting an industry standard through increased
sales of a wide range of high quality games, whereas games producers want to have their
games in as many as platforms as possible.
The risks involved in being committed to an alliance from the very early phases of the
technology development are centred around the possibility that the complementor defects
during the development phase as it finds better and/or cheaper alternative partners, or when it
decides to develop complements alone after gathering, through the alliance, the necessary
complementary assets. Given this rationale the “best” single-step game decision for each
player/complementor is to defect and leave its counterpart going alone in the development,
see its outcome, and probably decide to cooperate at a later stage (in a complementor’s
upgrading effort) when, presumably, its cooperation will be more valuable. However, this
myopic decision framework does not take into account the market evolution and technology
accumulation mechanisms which may prove that in the long run more sophisticated decisions
may be more effective.
4. Model structure and modelling assumptions
The system dynamics model developed explores the interactions between two firms
developing and producing complementary products (consoles and video games). For each
firm, the model is structured around five decisional processes: product and process
development, production, cooperation strategy, market performance and dynamics, and
operational performance measurement. These interact with the market adoption process as it
is represented in the related sub-model (fig. 1). Following, we briefly describe each of the five
sub-models of figure 1.
OPERATING DEVELOPMENT
PERFORMANCE PROCESS
PRODUCTION
COOPERATION
STRATEGY
MARKET
DYNAMICS
Figure 1: The structure of the system dynamics model for a complementor
The DEVELOPMENT PROCESS sub-model
The development and production sub-model represents the essential R&D effort that the firm
needs to put in order to develop and launch a new product into the market (includes both
product and production process development efforts). The effort is assumed to follow a bell-
shaped (inverted U) curve. This is a valid generalized assumption for the majority of
engineering projects, independent of the organization and management style employed
[Maylor (1999)]. Successive projects are then modeled by an inverted (positive only) sine
wave. The rate of activity is slow at the beginning of the project, increasing gradually up to a
maximum, and then falls as the project reaches completion. Assuming that this effort is
directly proportional to the financial resources committed (in €), the corresponding area under
the curve gives its total cost. As development teams complete successive projects in a specific
technology (follow-up incremental innovations or upgrades), they accumulate knowledge and
experience, which in turn result in a gradual shrinkage of the duration of the projects. As a
consequence, the cost of successive projects (in general, the resource commitments required)
is reduced by an amount which is a function of the knowledge and experience accumulation
rate. The gradual decrease of the space of possible improvements/modifications, as time
passes, also contributes to the shortening of the project duration and effort put. The model
deals with overlapping development projects, that is, new projects can commence before the
completion of the preceding ones. The phase difference between successive projects is
adjustable.
The PRODUCTION sub-model
The production sub-model deals with the dynamics of the production activity of new
products. Each new product requires that the firm deploys production capacity, which
embodies a leap in productivity as a result of learning before doing in process R&D. The
productivity of the production function is also affected by the production activity itself. As
production continues, the firm learns by doing and hence its productivity is increased. The
rate of this decrease in effort and cost is adjustable to cater for very sharp drops in costs, as is
the case for software. The production rate of each new product is assumed to be affected by
its demand (demand leads production). Production is assumed to commence immediately
after the development effort is completed and terminates with the introduction of the follow-
up product.
The MARKET DYNAMICS sub-model
This sub-model represents the sales of the firm to its end customers. The sales of each new
product are affected by a variety of factors. First, we assume that there is a pool of potential
customers, the size of which depends on the available new products in the market. A fraction
of the potential customers decides to buy the product of the first firm according to the
combined prices of complementary products. This means that we assume that the decision of
a customer to buy the product of the first firm (e.g. the video game console) is affected not
only by the price of the product itself, but also by the price of the complementary product
(e.g. the video games).Customers who decide not to buy exit the market, while customers
who decide to purchase the product of the first firm, buy the product with a rate that depends
on the existing customers of the firm (the word of mouth effect) as well as on the cooperation
strategy that the firm decided to follow. The rate of customer acquisition of the two
companies is influenced by the degree of modernity (how “new”) of the product (the rate
decreases as time passes), while a fraction of lost customers becomes potential customers as a
new product is introduced to the market. Finally, it should be noted that for the products of
the second firm, the potential customers are the customers that have already bought a product
of the first firm — e.g. the video game console manufacturer. The analogy of one console to
ten video games was assumed in calibrating the sales rates. The influence diagram of the
factors that are involved in customer acquisition for one of the complementors is shown in
figure 2.
, Complementor’s
Complement’s
. cooperation
BNE strategy
* s gy
- Price 8)
v
- cooperation
strategy (rate)
Bxisting: Cistomier
customers acquisition
rate
Ci omplenent s + Product
customers development
“Modernity” strategy (rate)
a
Figure 2. Influence diagram of market dynamics of a complementor
The COOPERATION STRATEGY sub-model
This sub-model implements the Prisoner’s Dilemma payoff matrix. The decisions of the two
potential complementors are simultaneous — i.e. both firms are faced with making decisions at
the same point in time. The payoffs for each strategic decision are shown in Table 1. It is
clear that for both companies the dominant strategy is not to cooperate independent of the
decision of the other. After each development effort is completed, the pay-offs are
materialized in the sales rate of each firm. In essence, the payoffs are the coefficients that
regulate the sales rate for each firm. The values of the payoffs are diminishing as
development efforts are completed (multiplied by a factor inversely proportional to the
number of efforts completed). This is to model the fact that the expected gains of a firm that
cooperates are greater at the beginning of the cooperation, whereas a firm that defects late has
less benefits as it has already invested resources in the cooperation. Defection yields the
highest outcome because the defecting firm can build on its existing market deploying more
marketing resources using a different partner. Mutual defection results in other competitors
valuing the cooperation of both firms less (bargaining power is diminished and the possibility
of forming a highly profitable alliance is reduced).
The OPERATING PERFORMANCE sub-model
The cost and revenue (performance) sub-model deals with the evolution of the operating
profitability of each firm as the production activity is undertaken and new products are
introduced into the market. The firm’s revenues are a function of its sales and the unit’s
selling price. The unit price is variable and is based on the unit cost of the product (adding a
profit markup). The operating cost of a firm includes both the cost of production and the cost
of R&D effort made in order to develop and launch a new product.
Shans Cooperate with Not cooperate with
& Firm B Firm B
Firm B
Cooperate with a = = 7
Firm A B=2 A=2 B=0 A=3
Not cooperate 7 = _ 7
with Firm A B=3 A=0 B=1 A=1
Table 1: The pay-offs of each strategic (cooperation or defection) decision.
5. The use of the model
The model was developed in the system dynamics simulation environment ithink v. 6.0.1.
Simulations were executed for a time period of 240 months (20 years) to cater for a seven
year initial technology development period and thirteen years of upgrades/modifications
overlapping with the sales of the previous versions of the product. Both random and user-
induced strategies were possible. The model was validated with respect to random strategies.
Figure 3 shows the effect of pure strategies on the customer rate for one of the
complementors. Customer rates (sales rates) have been used as performance measures over
net profitability since the real development costs of consoles and games were not available.
As it can be seen in the diagram, a pure cooperation strategy yields overall higher customer
rates (trace 1). This is because the firm fully utilizes the market building dynamics of its
complementor at the initial stages of the cycle whereas the cannibalization effects of the late,
very short development times are balanced by the early long development and sales cycles.
& 5: cust RATE 2: CUST RATE
1 1000000,004
"
1 00000,00-4 i 2
a
2
1 000-12. _— + i H
4.00 60.75 120.60 180.25 240.00
Graph 8 (Untitled) Months 8:40 88 de, 30 €00 2003
Figure 2. Pure strategies of cooperation and defection
In contrast to the single step game, in the repeated game as demonstrated in the figure above,
the dominant strategy for each player is to cooperate.
Figure 3 shows the effect of mixed strategies on customer rates, again for one
player/complementor: initial cooperation up to month 90 and then defection (trace 1) and
initial defection and then cooperation (trace 2). The complementing company is assumed to
be always cooperating. The net effects of both strategies on the customer rate differ
significantly in the range of month 90 to month 120. In the first case, the firm exploits the
market that was cooperatively built (all feedback loops involving Customer acquisition rate
are positive), whereas in the second, the high payoffs of early defection (payoff value 3,
assuming that it can benefit from a different complementor). For longer simulation runs, or
for a delayed change of strategy (150" month), a clearer dominance of the initial cooperation
strategy over the initial defection strategy was observed (the effect of changing strategy is
minor when the market has been built).
& +: cust Rate 2: CUST RATE
1 1000000 004
1 00000,00-4
Si,
1 000-12 i H
1.00 180.25 240.00
‘ Graph 8 (Untitled) Months 8:56 ée™, 302002003
J
Figure 3. Mixed strategies of cooperation and defection
5. Conclusions
In this paper we have extended the Prisoner’s Dilemma formulation by embedding it in a
system dynamics model to take into consideration the endogenous (e.g. learning) and
exogenous (e.g. market dynamics) evolutionary mechanisms that effect complementors’
decisions and outcomes through a specific technology cycle. We have built and used a system
dynamics simulation model to investigate the effect of pure and mixed strategies of
cooperation and defection on the market effectiveness of complementors. Simulation
experiments indicated the importance of early cooperation. However, the main objective of
the paper was to show how game theory and system dynamics can be integrated for the
modeling, analysis and experimentation in such a strategic situation, rather than to explain or
provide prescriptions for specific strategies.
References
Adamides, E.D., Stamboulis, Y., Malakis, T. and Harisoulis, D. (2002). Product R&D,
process R&D and market dynamics: A simulation study, Proceedings of the 2002 IEEE
International Engineering Management Conference, 673-678.
Axelrod, R. (1984). The Evolution of Cooperation, Basic Books, New York.
Baumol, W.J., Panzar, J.C. and Willig, R.D. (1982). Contestable Markets and the Theory of
Industry Structure, Harcourt Brace Jovanovich, New York.
Doz, Y.L. and Hamel, G. (1998). Alliance advantage: The art of creating value through
partnering, Harvard Business School Press, Boston, MA.
Forrester, J.W. (1961). Industrial dynamics, The MIT Press, Cambridge, MA.
Ghemawat, P. (1997). Games Businesses Play: Cases and Models, The MIT Press,
Cambridge, MA.
Hofbauer, J. and Sigmund, K. (1998). Evolutionary Games and Population Dynamics,
Cambridge University Press, Cambridge.
Khanna, T., Gulati, R. and Nohria, N. (1998). The dynamics or learning alliances:
competition, cooperation and relative scope, Strategic Management Journal, vol. 19, 193-
210.
Maylor, H. (1999). Project Management, Financial Times Pitman, London.
Milling, P.M. (1996). Modeling innovation processes for decision support and management
simulation, Systems Dynamics Review, vol. 12, 221-234.
Nalebuff, B.J. and Brandenburger, A.M. (1996). Co-opetition, HarperCollins Business,
London.
Rabbino, H. (1998). Applying the principles of co-opetition with system dynamics tools,
Proceedings of the 16th International Conference of the System Dynamics Society, (CD of
Proceedings).
Shapiro, C. (1989). The theory of business strategy, RAND Journal of Economics, vol. 20,
125-137.
Soden, D. (1988). The Tragedy of the Commons: Twenty Years of Policy Literature, 1968-
1988, Vance Bibliographies, Monticello, IL.
Stamboulis, Y., Adamides, E.D. and Malakis, T. (2002). Modeling the Product-Process R&D
Dynamics, Proceedings of the 20" International Conference of the System Dynamics Society
(CD of Proceedings).
Sterman, J.D. (2000). Business Dynamics. Systems Thinking for a Complex World, Irwin
McGraw-Hill, Boston, MA.
Teece, D.J. (1990). Profiting from technological innovation: Implications for integration,
collaboration, licensing and public policy, in The Competitive Challenge: Strategies for
Industrial Innovation and Renewal, (D.J. Teece, ed.), Longman Higher Education, London,
185-219.
Thomke, S. and Robertson, A. (1999). Project Dreamcast: Serious Play at Sega Enterprises
Ltd. (A), Case 600-028, Harvard Business School, Boston, MA.
SD Game DOCUMENTATION
A. ABOUT THE 3 DIFFERENT PROGRAMS
ly
FINAL - SWITCH
This program gives the user two options. The first is to choose the random
numbers (strategy followed) for each product manually. This can be done by
setting the switch placed in graph #3 to the OFF position and pressing the button
“TO RANDOM NUMBERS” which is placed under graph #3. Thus the user can
first select the strategy of the company for each one of the 10 products and then
run the simulation. The second option is to turn the switch to the ON position.
Then the program stops every time a new R&D effort for a new product has
begun. So, the user can change the random numbers (strategy followed) or other
parameters of the model every time the program stops.
FINAL - STRATEGY1
This program gives the user two options. The first is to select a random number
(with the slider under graph #3) which will be the COMMON strategy for all the
products of the company. This can be done by turning the switch, in graph #3, to
the OFF position. The second option is to turn the switch to the ON position.
Then the program follows a pre-selected strategy. This strategy can be
summarized as: “The second company cooperates only if the first company has
cooperated in the previous product. Or, the second company betrays only if the
first company has betrayed in the previous product.”
FINAL - STRATEGY2
This program is actually the same with the previous program with one only
difference. The pre-selected strategy of the program when the switch is turned ON
can be summarized as: “The second company cooperates only if the first company
has betrayed in the previous product. Or, the second company betrays only if the
first company has cooperated in the previous product.”
B. DOCUMENTATION OF THE PROGRAMS
The 3 programs above have the same logic and are based on the same model with slight
differences only in the procedure of the selection of the strategy. Therefore, the
documentation is the same for all 3 programs.
The model has 4 main sub-models for each company (the main company and the
complementary company). These sub-models are:
a) The Production & Development Process sub-model.
b) The Market Dynamics sub-model.
c) The Cooperation Strategy sub-model.
d) The Operating Performance sub-model.
a. THE PRODUCTION & DEVELOPMENT PROCESS SUB-MODEL
The production and development process sub-model calculates the production rate
and the processes R&D effort that each company dedicates for the development of
the new products. The production is driven by the customer rate of the company
(demand driven). The processes R&D effort is based on a sine wave function the
amplitude of which is determined by the R&D intensity of the company. The time
span of the sine wave is determined by the R&D capability of the company and
by the time that is needed to develop the proce: The capability of the
companies changes over time because of learning by doing (experience curve).
This sub-model also calculates the price of the products. The price is calculated
by adding a profit markup (30%) to the unit cost. The unit cost decreases as
production continues because of the experience curve. Here, we should note that
the unit cost for the second company is much smaller than for the first company
and that it decreases much more sharply as production continues. This is because
the product of the second company (video game cassettes) can be produced rather
cheaply after the production of the first product. However, it should be noted that
the unit price of the cassettes does not fall as much as the unit cost falls. At first
the price of the cassettes is high (€85) to cover the R&D costs, but then it falls to
€55 and does not fall any further. Therefore, the profit markup of the second
company increases to more than 30% after a period.
Finally, we should mention that the companies can begin the R&D effort for
every new product before the previous effort has ended. Therefore the companies
can “run” two or more projects simultaneously. The time when every new effort
begins can be changed by the user with the slider named “TIME OF NEW
EFFORT”. The slider gives the percentage of the previous effort when the new
effort will begin. So, if the slider is set at 80, this means that the new R&D effort
will begin at 80% of the previous effort.
b. THE MARKET DYNAMICS SUB-MODEL
The market sub-model is actually the customer rates of the two companies. The
sub-model works as follows:
First, there is a flow of incoming customers. We assume that the flow is steady at
100,000 customers per month.
Then there is a customer base named “Potential Customers”. These customers can
either buy a product from the first company or from another competitor. The
percentage of the Potential Customers that will become Customers of the first
company is influenced not only by the price of the products of the company itself
but also by the price of the complementary products of the second company.
The customer rate is also influenced by a factor that indicates the ‘antiquity’ of
the products. The nature of the video game consoles and video game cassettes is
such that they become outdated fairly soon after their entrance in the market.
Therefore, the model takes into account this fact and actually decreases the
customer rate of the products as time passes from their introduction in the market.
Another factor that influences the customer rate of the companies is the word of
mouth effect. These products target mainly the market of young children and
young adults (ages 6 — 20). For these ages the word of mouth effect plays a
significant role as children play together, are influenced by one another and
exchange video game cassettes. So, they want these cassettes to be compatible
and therefore play in each others consoles. As a result they tend to be influenced
by their friends and end up buying the same console and games with their friends.
Another factor that influences the customer rate is the strategy that each company
follows, namely to cooperate with or to betray the other company. The logic
behind the calculation of the strategic decisions of the two companies will be
analyzed is the next paragraph named “The Cooperation Strategy Sub-model”.
Finally, a factor that influences the customer rate of the company is the customers
of the complementary company. The more the customers of the second company
for products that work on a certain version of the product of the first company, the
more the sales of the specific product of the first company. The magnitude of the
influence between the two companies is determined by the factor in the slider
named “influence of company 2 on company 1”.
Therefore, according to the customer rate some Potential customers become
Customers of the first company and the rest are “lost” by the company and
become “Lost Customers”. However, every time that the company produces and
markets a new product, a percentage of the lost customers become again Potential
Customers. These are the converts who decide to buy the new product and
therefore are again potential customers for the company. The percentage of the
lost customers who become converts each time a new product is introduced can
be determined by the user using the slider named “Percentage of converts”.
Finally, a percentage of the customers of the company may decide to purchase a
new product when introduced, from either the company or from a competitor.
This percentage is assumed to be high at the beginning and become less as time
from the introduction of the new product passes.
As far as the customer rate of the second company is concerned, it follows the
customer rate of the first company and is influenced by the strategy that the
second company decides to follow.
THE COOPERATION STRATEGY SUB-MODEL
This sub-model implements the Prisoner’s Dilemma payoff matrix. The decisions
of the two potential complementors are simultaneous — i.e. both firms are faced
with making decisions at the same point in time. The payoffs for each strategic
decision are shown in Table 1.
Cooperate with | Not cooperate with
FirmB Firm B Firm B
Cooperate with B=? A=2 B=0 A=3
Firm A
Not cooperate _ _ _ _
with Firm A Bes A=0 BSL ASI
Table 1: The pay-offs of each strategic (cooperation or defection) decision
The pay-offs are materialized, after the development effort has been completed, in
the sales rate of each firm. In essence, the payoffs are the coefficients that regulate
the sales rate for each firm. The values of the payoffs are diminishing as
development efforts are completed (multiplied by a factor inversely proportional
to the number of efforts completed). This is to model the fact that the expected
gains of a firm that cooperates are greater at the beginning of the cooperation,
whereas a firm that defects late has less benefits as it has already invested
resources in the cooperation. Defection yields the highest outcome because the
defecting firm can build on its existing market deploying more marketing
resources using a different partner. Mutual defection results in other competitors
valuing the cooperation of both firms less (bargaining power is diminished and
the possibility of forming a highly profitable alliance is reduced).
d. THE OPERATING PERFORMANCE SUB-MODEL
The cost and revenue (performance) sub-model deals with the evolution of the
operating profitability of each firm as the production activity is undertaken and new
products are introduced into the market. The firm’s revenues are a function of its
sales and the unit’s selling price. The unit price is variable and is based on the unit
cost of the product (adding a profit markup). The operating cost of a firm includes
both the cost of production and the cost of R&D effort made in order to develop and
launch a new product.
The structure of the model is shown in the figure below.
OPERATING DEVELOPMENT
PERFORMANCE PROCESS
a
PRODUCTION
|< COOPERATION
x STRATEGY
MARKET
jg——___
DYNAMICS
Figure 1: The structure of the system dynamics model for a complementor
