Application of complex adaptive systems to pricing of reproducible information goods

Available online at www.sciencedirect.com

Decision Support Systems 44 (2008) 725 – 739
www.elsevier.com/locate/dss

Application of complex adaptive systems to pricing of reproducible
information goods ☆
Moutaz Khouja a,⁎, Mirsad Hadzikadic b,1 , Hari K. Rajagopalan c,2 , Li-Shiang Tsay d
a
Business Information Systems and Operations Management Department, The Belk College of Business Administration,
The University of North Carolina at Charlotte, Charlotte, NC 28223, United States
b
College of Information Technology, The University of North Carolina at Charlotte, Charlotte, NC 28223, United States
c
School of Business, Francis Marion University, Florence, SC 29501, United States
d
Department of Computer Science, Hampton University, Hampton, Virginia 23668, United States

Received 1 August 2005; accepted 1 February 2007
Available online 13 October 2007

Abstract

Piracy of copyrighted information goods such as computer software, music recordings, and movies has received increased
attention in the literature. Much of this research relied on mathematical modeling to analyze pricing policies, protection against
piracy, and government policies. We use complex adaptive systems as an alternative methodology to analyze pricing decisions in
an industry with products which can be pirated. This approach has been previously applied to pricing and can capture some aspects
of the problem which are difficult to analyze using traditional mathematical modeling. The results indicate that advances in
technology make a skimming strategy the least preferable approach for producers. Further, improvements in technology, more
specifically data communications and the Internet, will erode the profitability of a skimming strategy. The analysis also indicates
that complex adaptive systems may provide a useful method for analyzing problems in which interactions between participants in
the systems, i.e. consumers, sellers, and regulating agencies, are important in determining the behavior of the system.
© 2007 Elsevier B.V. All rights reserved.

Keywords: Information goods; Pricing; Piracy; Complex adaptive systems

1. Introduction increase the consumer base for a product and creates
positive network externalities, which refer to a case
Piracy of copyrighted products has become a major where a consumer's utility from a software increases
problem for many firms. Tolerating some piracy may with the number of its users [21,25]. In that respect,
having more consumers use a software makes it more
☆
The authors would like to thank the referees for their helpful
valuable to others. These positive aspects are less im-
comments and suggestions. portant in the recorded music and movie industries.
⁎ Corresponding author. Tel.: +1 704 687 3242; fax: +1 704 687 Conner and Rumelt [10] examined protection strategies
6330. in the presence of positive network externalities. Their
E-mail addresses: mjkhouja@email.uncc.edu (M. Khouja), analysis indicates that, in the presence of positive net-
mirsad@uncc.edu (M. Hadzikadic), hrajagop@fmarion.edu
(H.K. Rajagopalan), li-shiang.tsay@hamptonu.edu (L.-S. Tsay). work externalities, a strategy of no protection can result
1
Tel.: +1 704 687 3124; fax: +1 704 687 6979. in lower price and increased profit. The authors show
2
Tel.: +1 843 661 1501; fax: +1 661 1432. that network externalities have a strong effect under
0167-9236/$ - see front matter © 2007 Elsevier B.V. All rights reserved.
doi:10.1016/j.dss.2007.10.005

726 M. Khouja et al. / Decision Support Systems 44 (2008) 725–739

three conditions: (1) The software is complicated and reduces it. In a monopoly market, which is the case for
difficult to master, (2) the software allows or demands many information goods, the monopolist is certain that
extensive user customization, or (3) the software is useful the entire market demand is its own. Therefore, a
for multiple-user data processing or formal networking. skimming strategy can be used to exhaust the market
For example, a user would rather use Microsoft Word over [12]. The initial price is aimed at consumers for whom
Word Perfect if most users are using Microsoft Word for obtaining the product early is important and who are
word processing. This is because using the software willing to pay a premium for early ownership. As this
makes it easier for a user to share documents with others. segment becomes saturated, price is reduced to increase
Some users may therefore be willing to pay more for the appeal of the product [11]. This strategy is most
Microsoft Word. However, in case of music and movies appropriate when products are highly differentiated, a
the three conditions identified by Conner and Rumelt [10] segment of the market is price-insensitive, and there are
are not present. limited economies to scale or learning curve effects.
Industries susceptible to piracy are usually dominat- Pricing in a skimming strategy maximizes profit based
ed by monopolists who obtain monopoly power through on what the market can bear and the product's worth to
copyright and intellectual property protection. Like buyers [11,21]. The increased margins which skimming
other monopolies, they are viewed unfavorably because brings should be balanced against the decreased sales
they tend to charge higher prices than what would volume.
prevail under competition. For example, while Napster Since a skimming strategy is suitable when a com-
was being shut down after having been accused of pany has a temporary monopoly position [22], it is ideal
contributing to piracy, major record labels in the music for producers of copyrighted products such as movies
industry, such as Sony, and EMI, were accused of and music recordings. These firms enjoy a natural mo-
violating fair trade practices by threatening retailers nopoly position and can skim the market for as long as
not to advertise compact disks (CDs) below certain their intellectual property is protected. However, piracy
prices [4]. may erode monopoly power even without competitors
Among the industries suffering from piracy, recorded entering the market.
music seems to be the worst hit. Pirating music has Determining prices in a market where some piracy is
become much easier due to digitization, the adoption of unavoidable is a complex problem which is difficult to
compression technologies such as MP3, and easy access analyze using traditional mathematical modeling. The
to digitized music files on the Internet. The Recording difficulty arises in modeling the act of piracy itself. For a
Industry Association of America's (RIAA) 2003 sta- consumer to pirate a product, the following prerequisites
tistics show that both the number and the dollar value of are needed: 1) the consumer does not have a copy of the
CD sales have declined since 2001. In 2003, sales of product, 2) the value the consumer attaches to the
music CDs were $11.2 billion compared to a peak of product exceeds the cost of the copying medium and the
$13.2 billion in 2000. Also, since the launch of Napster risk of being caught and penalized, 3) the consumer
in 1999, sales of CD singles have been decreasing at a prefers pirating to purchasing a legitimate product (be-
remarkable rate till 2002. This is, in part, due to the fact cause his/her reservation price is not met or the expected
that compressing one song into an MP3 file makes it gain from piracy exceeds the expected gain from
easy to swap. Although Napster, once the most popular purchase), 4) the consumer knows another consumer,
music-swapping site, was shut down in an effort to i.e. neighbor, with a reproducible copy, and 5) the
prevent piracy by the big record labels, alternative file consumer or one of his/her neighbors has access to the
sharing through P2P networks, such as Kazaa, WinMX, duplication technology. Therefore, the rate of piracy at a
and Gnutella, immediately replaced Napster. These P2P point in time depends on the diffusion of both legitimate
networks do not require a central server to store files, and pirated copies (when copies can be made from
thus avoiding possible litigation. copies) in the market up to that point and on consumer
The marketing and economics literature delineates connectivity. We define consumer connectivity as the
the different pricing strategies a firm can follow under number of neighbors, physical or via a computer
different conditions [22]. These conditions include de- network, that a consumer can share copies with. Com-
gree of product differentiation, the competitive situa- plex adaptive systems (CAS) and agent-based modeling
tion, and the nature of demand. Skimming and (ABM), which is a flexible approach to modeling CAS,
penetration are the classic strategies for pricing new may provide a useful methodology for analyzing pricing
products [22,29]. A skimming strategy is one in which decisions under piracy. CAS and ABM have been
a firm sets a high initial price and then systematically previously applied to pricing problems in a two-firm

M. Khouja et al. / Decision Support Systems 44 (2008) 725–739 727

market where consumers' purchase decisions are solely should have less protection than in the monopoly case
based on price [34]. only if profit margins are expected to decline in sub-
The objectives of this paper are to 1) provide an sequent generations. For the competitive case, less pro-
alternative methodology for analyzing the problem of tection should be used than in the monopoly case.
piracy, 2) find an optimal monopolist's pricing strategy in Haruvy, Mahajan, and Prasad [17] examined how piracy
a market where some piracy is unavoidable, 3) investigate affects the adoption of subscription software. In this
the impact of piracy on consumers, monopolists, and model the producer determines the price and the
artists, and 4) evaluate the applicability of CAS to busi- protection level which maximize the discounted profit
ness problems, and more specifically pricing. stream over the product's life. The results indicate that
The key results are 1) consumer connectivity has a moderate tolerance for piracy can speed up adoption and
strong impact on optimal pricing strategy, 2) strong enables the producer to charge higher prices. Tolerance
consumer connectivity erodes the profitability of a for piracy decreases when market penetration is quick,
skimming strategy, 3) requiring a legitimate product to information is imprecise, and positive network exter-
make a copy does not significantly lessen the impact of nalities are low.
piracy on profit when consumer connectivity is strong, Sundararajan [31] analyzed optimal pricing and
4) deterrent piracy controls must significantly increase piracy protection for a monopolist using price discrim-
consumers' risk and cost of piracy to be effective, and ination among consumers who are willing to buy var-
5) CAS offer an effective platform for understanding the iable quantities of a digital good. The author shows that
combined effects of many variables on pricing. the optimal pricing schedule can be characterized as a
The paper is organized as follows. Section 2 offers a combination of zero-piracy pricing and piracy-indif-
review of the literature. In Section 3, we introduce CAS ferent pricing schedules. Other findings by network
and describe their use in problem solving. In Section 4, externality-based studies [10,28,32] also indicate that
we develop a CAS for analyzing a monopolist's pricing allowing piracy can make the producer more profitable
policy in a market with piracy. In Section 5, we discuss when positive network externality exists.
the results from several experiments conducted using Chen and Png [7] developed a model that incorpo-
the developed system. Section 6 concludes with sum- rates a piracy penalty set by the government. The
mary of findings and future research on applying CAS to monopolist determines price and piracy monitoring rate.
business problems. Users can buy the product, pirate it, or not use it. The
authors show that changes in pricing and monitoring
2. Literature review rates have qualitatively different effects on consumers.
They also show that from a social welfare perspective,
Piracy has had a major impact in the computer soft- price reductions are better than increased monitoring.
ware industry. Research on software piracy mainly deals Chen and Png [8] extended the model to include a tax on
with pricing, copyright protection, and government pol- copying media and equipment and a government sub-
icies. Nascimento and Vanhonacker [21] found that a sidy for legitimate purchases. Consumers are divided
skimming strategy is optimal in the absence of piracy. into ethical and unethical groups. The results indicate
Using the diffusion of innovation model, they also that taxing the copying media is better from a social
found that copy protection is recommended when sales welfare standpoint than penalizing piracy, and that the
grow faster than piracy and the cost of protection best government policy is to subsidize legitimate pur-
does not significantly increase the marginal cost. Givon, chases. Belleflamme [2] considers a case in which
Mahajan and Muller [13] showed a positive side to copies are of lower quality than originals. He shows that
piracy with a software diffusion model. although diffusion through piracy increases social
Prasad and Mahajan [25] examined the relationship welfare, this comes at the expense of the producer's
between the rate of software diffusion and piracy to profits, which may be insufficient to cover the creation
determine the price and the piracy level that should be cost.
tolerated. The authors examined three cases: A monop- Chellappa and Shivendu [5] analyzed the implica-
oly, a monopoly with multiple generations of software, tions of variable technology standards in the movie
and a competitive market. Their results indicate that a industry. They concluded that when piracy is prevalent,
monopoly should have little piracy protection at the maintaining separate technology standards between dif-
early stages of the software's life and impose maximum ferent regions is beneficial to the producer. In addition,
protection in the second half of the life cycle. For multi- it is not only the producer who incurs losses due to
generation software monopolist, the first generation global piracy but also the consumers in regions where


quality is important. In a more recent study, Chellappa American Life Project reveals that many artists do not
and Shivendu [6] assume that consumers are not fully feel that digital file sharing hurts them [26].
aware of the true fit of an information good to their tastes Many of the above models have focused on one or
until consumption. In this model, piracy offers a con- two aspects of piracy in order to maintain mathematical
sumption opportunity before purchase. The authors de- tractability. For example, some models have focused on
velop a two-stage model of a market composed of network externalities, some on price and protection
heterogeneous consumers in their marginal valuation for level, some on price and government policy, and some
quality and their moral costs. Some consumers pirate the on varying technology standards. Incorporating several
product in the first stage and based on that experience piracy aspects into a single model complicates the ana-
update their fit-perception which may cause them to re- lysis and makes insights into the interaction effects of
evaluate their buying/pirating decision in the second these factors difficult to obtain. Piracy is a dynamic
stage. An important result from the model is that piracy problem in which the time element is essential. The level
losses are more severe for products that are overvalued in of piracy at a point in time depends both on the number
the market and ultimately do not live up to their reputation of legitimate and pirated copies of the product available
rather than for products that have been undervalued in the in the market. This makes the time of price changes to
market and turn out to be a good surprise. increase revenue a critical part of decision making.
Papadopoulos [23] investigated the relationship be- Finally, products susceptible to piracy are usually short-
tween price, copyright law enforcement, and formation lived products with consumer interest waning quickly
of black markets. Data for music recordings was used to over time. All of these aspects make CAS and ABM a
fit a regression model to estimate the relationship be- useful alternative methodology for incorporating the
tween legitimate music recording price, black market many aspects of piracy.
distribution channels and piracy. The author found that Despite the fact that CAS were introduced over
piracy in a country is most strongly related to the ratio of 30 years ago [18,19], there is little research on their use
average hourly wage to the average sound recording for solving business problems. This is may be due in part
price and to a lesser degree, to a black market efficiency to the difficulty in representing key elements of busi-
index. Wang [38] analyzed motion picture piracy and ness problems such as key levers, constituent “agents”,
found a positive relationship between perceived cost– negotiations, rewards, fitness, etc. There have been some
benefits of a pirated copy and intent to purchase a attempts to advance the state of knowledge of applying
pirated copy. The likelihood of purchasing a pirated CAS to business problems. For example, Ben Said,
copy is not dependent on individual income but rather Bouron, and Drogoul [3] used agent-based modeling
on the perceived benefit relative to the cost of a pirated (ABM) in a consumer market. The authors proposed a set
copy. In addition, the results indicate a negative re- of behavioral primitives for consumer agents which
lationship between the variables of perception of per- include imitation, conditioning, mistrust, and innova-
formance risk, ethical concern regarding piracy, and tiveness. The system incorporates opinion leaders whose
perception of social norms opposed to piracy and the opinions are highly valued by consumers. Consumers
intent to purchase a pirated copy. Other recent behav- learn over time and genetic algorithms are used for the
ioral studies on piracy in the music and software in- evolution of consumers. The authors use ABM to pro-
dustry have been undertaken by Chiou, Huang, and Lee, vide operational and conceptual richness to capture a
[9] and Moores and Chang [20], respectively. broad range of consumer behavior. This study illustrates
Related to copyright protection, an interesting find- the difficulty in capturing and generalizing key elements
ing by Gopal and Sanders [14] is that deterrent controls, of agents' behavior.
which employ educational and legal campaigns, protect ABM and CAS have been used to analyze pricing
the producer's profit better than preventive controls that decisions under limiting assumptions without piracy.
use technology to make piracy difficult. Also, deterrent Tesauro and Kephart [34] analyzed pricing decisions of
controls were shown to be superior from social welfare two firms selling an identical product. Consumers
perspective. were assumed to behave deterministically and prefer the
A unique aspect of the music and movie industries is product with lower price. Sellers alternate in setting price
the royalty system. Record labels usually pay per unit for each period with full knowledge of the competitor's
royalty to artists ranging from 5% to 25% of the sale price and profit. The authors investigated the effects of
price or a fixed amount per unit sold. An artist who gets using Q-learning on the sellers' behavior. Q-learning is an
royalty was once considered one of the victims of algorithm that incorporates long-term rewards into
piracy. However, a recent report from Pew Internet & reinforcement. The results indicate that pricing policies


derived with Q-learning reduce price wars and increase influences the behavior of individual agents. The agents
profitability. The results support earlier conclusions on the interact with the environment as well. CAS are networked
benefits of incorporating long-term consequences of in the sense that agents interact with their neighbors and,
actions into the learning reinforcement [33,37]. ABM occasionally, distant agents, and non-linear in the sense
has been used in other business applications such as to that the whole is greater than the sum of its parts.
study the performance of a supplier selection models [36] The main properties of CAS include self-organiza-
and explore bidding strategies for market-based schedul- tion, emergence, and adaptation. Ant colonies, networks
ing [27]. of neurons, the Internet, the brain, and the global econ-
The proposed application provides a step in the long- omy are a few examples where the behavior of the
term process of effectively applying CAS to business whole is much more complex than the behavior of its
problems. It includes the identification of a) appropri- parts. Agents are autonomous entities with limited per-
ate agents, b) their key properties, c) mechanisms for ception of their environment. They are guided by few
agents' learning, d) agents' goals, e) fitness functions, simple rules and act locally. Agents' overall status and
and f) key performance indicators. The subsequent steps behavior can be tracked and evaluated. The performance
in the development of CAS for solving business prob- of the overall system is derived from the effectiveness of
lems include refinements to the proposed CAS to better the individual agents and their interaction. Agents may
capture the above key elements, the addition of more or may not have a history of their previous interactions
agents to the system such as government and regulating and the ability to learn from them. Information about
agencies, and implementing learning for all agents in the their past performance is used by the agents to deter-
system. mine the type and the degree of improvement in their
behavior.
3. Agent-based modeling and Complex Adaptive Agent interactions are mostly local; namely, they
Systems communicate with their immediate neighbors. Occa-
sionally, as they move about, some agents get a chance
Complex Adaptive Systems and ABM are bottom– to interact with other agents exhibiting plausible prop-
up approaches for analyzing and understanding complex erties, regardless of the distance between the two
systems. We focus on a particular implementation of agents. Their behavior is driven by a few, well-chosen
Complex Adaptive Systems (CAS) known as ABM. rules. It is the interaction between agents, as well as the
Entities in the system are modeled as agents whose interaction between the agents and the environment
behavior mimics that of real entities. Agents act ac- that gives rise to the complexity of the system as a
cording to their rules/schema. Agents can have a high whole.
degree of heterogeneity or be very similar. The actions
and interactions of the agents in the system result in an 4. Complex adaptive systems and pricing under piracy
aggregate behavior of the system [35]. Agents in busi-
ness models are the actual players in the system, which The proposed system is developed for a firm that has a
include firms, consumers, and regulatory agencies. One monopoly for a copyrighted product. Each consumer has
can view ABM as social simulation, which is now his/her value for the product. Thus, each consumer has
possible due to increased computing power [30]. his/her reservation price for the product, which is the
Several advantages of using CAS and ABM have maximum price he/she is willing to pay. This value is
been given in the literature. While these advantages may known to the consumer prior to consuming the product.
not be unique to CAS, their combination makes this While this assumption is similar to assumptions in some
method attractive. ABM does not require assumptions models in the literature [8], others authors assume that
with regard to the behavior of the system [35]. Agents consumers update their fit-perception of the product after
also provide a useful approach for modeling entities in sampling it [6]. If the selling price is equal to or below the
many social problems [1]. The use of ABM enables us reservation price, a consumer will buy the product. If the
to use the wealth of information about agents' behavior, selling price is higher than the reservation price, there is a
motives, and interactions to examine the consequences probability that he/she may pirate the product. The
in terms of aggregate system behavior. Agents also pirating probability depends on several factors including
provide a method for modeling heterogeneity [35]. access to copies that can be pirated, the availability of
CAS exhibit complex non-linear behavior brought duplication technology, and the cost of the copying
about by interaction of agents. Agents influence the medium. A consumer's decision to pirate also depends
behavior of the system while, at the same time, the system on the penalty for pirating and the probability he/she


assigns to being caught. Finally, the probability of j 1, 2,.., J, a state condition of the system
pirating is an increasing function of the difference assessed at the end of each period,
between the selling price and copying cost. The goal of ρg,j,t the weight assigned to state/action pair j/g at
the firm is to maximize total profit by periodically the at the end of period t.
adjusting prices over the finite life of the product.
In applying CAS to pricing, or any similar problem, All variables indexed by t are dynamic in terms of
one must first identify the agents in the system and being recalculated each period in the simulation. All
their rules. Agents in this problem include one seller parameters indexed by t are dynamic in terms of the
and N consumers. IF/THEN rules are used to describe simulation being able to handle changes in their values
an agent — the IF part of the rule being the condition from one period to the next. For many of these
or state, and the THEN part is the action. Agents need parameters (ri,t,Ot, and At), the values are kept the
not be homogenous and each agent has its own rules. same during a run of the simulation for the experiments
The effectiveness of the pricing strategy is measured in order to focus on the effects of piracy.
using the seller's profit. The following assumptions are
made: 4.1. Seller's schema

1. There is only one seller. Similar to industry practice, we assume the seller
2. The goal of the seller is to maximize profits over the monitors sales and profit performance. As this data
life of the product. becomes available each period, which can be a week, a
3. Advertising cost is a fixed amount per advertising month, or a quarter, decisions are made and implemen-
campaign. ted. Therefore, we implement a periodic review system
4. Consumers have complete information about the in which time increases in discrete units. A life cycle
current price. consists of T periods. For example, a movie released on
5. Each consumer may obtain only one copy of the DVD may have a life cycle of up to 5 months with price
product, legitimate or pirated. changes allowed monthly. At the end of each period, the
seller will have one of three states (i.e. j = 1,2,3):
The following notation is used:
1. the profit has increased from previous period:
t 1,2,3,…,T, a period index, Zt N Zt − 1,
i 1,2,3,…,N, a consumer index, 2. the profit has decreased from previous period: Zt b Zt − 1,
Zt profit for period t, or
Pt unit selling price during period t, 3. the profit is the same as in the previous period:
Qt number of legitimate products sold in period t, Zt = Zt − 1.
qt number of pirated copies made in period t,
ri,t reservation price of consumer i in period t, The seller may implement one of the following
Ri the risk cost consumer i assigns to pirating the actions at the beginning of period t:
product,
d the cost of pirating which includes the cost of 1. keep the current price unchanged (i.e. do nothing),
the storage medium and excludes the risk cost, 2. discontinue the product,
ci,t probability of consumer i pirating the product 3. change the price to Pt − 1(1 ± 0.05k), k ∈ [1,2,3,4,5,6].
in period t,
hi the number of neighbors of consumer i, The last action has 12 possible price changes re-
At advertising cost incurred in period t, At = A if sulting in a total of 14 possible actions (i.e. g = 1,…14).
Pt ≠ Pt − 1 and 0 otherwise. Multiples of 5% change is most common in practice.
Ot per period operating cost incurred for the product, The above states and actions result in 42 state/action
πt sum of all reservation prices of consumers pairs. The initial selling price is user specified.
without the product at the beginning of period However, a search for the best initial price can be
t, incorporated. The seller advertises the product at the
π1 total reservation prices of all consumers prior beginning of each period with a price change. At the end
to the introduction of the product, of each period, the seller detects the state of the system
g 1,2,3,…,G, an index of an action the seller may and takes an action, which is chosen probabilistically
implement at the beginning of a period, based on the weights assigned to each state/action pair.


To ensure that each action has an equal probability of many lifecycles). Every period, buyers interested in the
being selected for each state at the beginning of a run, product make decisions on buying, pirating, or waiting.
the initial weights of each state/action pair is set to 0.01. The buyer's process is interrupted at the end of the
After executing the selected action, the weight of the period to let the seller evaluate the pricing strategy.
selected state/action pair is changed based on its profit Based on the change in profit during the period, actions
performance. During the run of the simulation, the are rewarded and a decision on which action to
weight assigned to the most profitable state/action pair implement is made. The selection of actions depends
increases until it has a probability close to 100% of on the weights of each state/action pair for the occurring
being selected. The speed of convergence depends on state. A life cycle ends only when the seller implements
the relative profitability of other state/action pairs. If one the “discontinue the product” action. If the seller
state/action pair is significantly more profitable than chooses discontinue the product, the lifecycle ends
others, then the probability of selecting this state/action and all parameters are reset except for the weights of the
pair approaches 100% very quickly. If there are many state/action pairs which the seller retains since they were
state/action pairs with only slightly lower profit than the learned from past experience.
best state/action pair, then this convergence will take We consider two costs: An operating cost incurred
many runs of the simulation. every period, and an advertising cost incurred only
Fig. 1 shows flowcharts explaining the simulation for when there is a price change. Since we deal with in-
one product lifecycle (a run of the simulation includes formation goods, per unit cost of production is very

Fig. 1. Flowchart of the simulation.


small and, without loss of generality, we assume it to be actions some time before rewards get large is used so that
zero. Therefore, the profit per period is: no action is eliminated from consideration early in a run.
For all three reinforcement methods, at the end of
Qt Pt À A À Ot If Pt pPtÀ1 period t, if Δg,j,t N 0, then the weight of state/action pair
Zt ¼ ð1Þ
Qt Pt À Ot Otherwise j/g is increased according to:
We tested three reinforcement learning methods: qg; j;t ¼ qg; j;tÀ1 þ Dg;i;t for g and j of t À 1 ð5Þ
Short-term profit reinforcement method (STPRM):
The weight of a state/action pair at the end of a period is Therefore, when the same condition occurs again, an
increased by the amount: action's chance of being selected increases with the
profit it has provided in the past. If Δg,j,t ≤ 0, then a
Zt Qt Pt À Ot À A uðjPt À PtÀ1 jÞ
Dg; j;t ¼ ¼ ð2Þ penalty is charged to the state/action pair by decreasing
p1 XN
its current weight by 10%. Hence, if Δg,j,t ≤ 0, then
ri;1
i¼1 qg; j;t ¼ 0:90 qg; j;tÀ1 for g and j of t À 1 ð6Þ
if Δg,j,t N 0, where u(x) is a unit step function defined as
u(x) = 1 if x N 0 and 0 otherwise. Under this reinforce- Therefore, when the same state is realized in the
ment scheme, each state/action pair is rewarded based future, this action has a lower probability of being
on the profit it brings in the current period relative to the selected. The selection of an action for a state is
maximum total profit the product can bring. therefore based on the following procedure: If state j
Medium-term profit reinforcement method (MTPRM): occurs, then the probability of selecting action g is given
For each consumer who obtains a copy of the product, ri is by the weight of state/action pair j/g divided by the sum
set to zero since he/she is no longer willing to pay any- of the weights for all state/action pairs of state j, which
thing for the product. The weight of a state/action pair is can be written as:
increased by the amount: qg; j;t
pg; j;tþ1 ¼ if state j occurs in period t
Zt Qt Pt À Ot À A uðjPt À PtÀ1 jÞ X
G
Dg; j;t ¼ ¼ ð3Þ qx; j;t
ptÀ1 XN
x¼1
ri;tÀ1
i¼1 ð7Þ
if Δg,j,t N 0. Under this scheme, each action is rewarded 4.2. Rules — N consumer agents
based on the profit it brings in the current period relative to
the total remaining profit the product can bring at the time There are N consumers and all have complete
the action is implemented. information about the current selling price. Each
Long-term profit dynamic reinforcement method consumer has his/her own reservation price. Usually,
(LTPDRM): The weight of a state/action pair is companies use past information or surveys to measure
increased by the amount: reservation prices. We assume that reservation prices
Zt þ pt t have a normal distribution with known mean and
Dg; j;t ¼ 0:001 standard deviation. However, the system can deal with
ptÀ1 E
P
N any known distribution. A consumer purchases the
Qt Pt À Ot À A uðjPt À PtÀ1 jÞ þ ri;t product if his/her reservation price is met, if the
i t
¼ 0:001 reservation price is not met then a consumer may pirate
X
N E
ri;tÀ1 the product (with some probability) if a neighboring
i¼1 consumer has a copy, or wait.
ð4Þ A consumer pirates the product according to the
following scheme. When the selling price is higher than
if Δg,j,t N 0, E is the total number of product life cycle the reservation price of a consumer who knows an agent
runs. Under this reinforcement scheme, a state/action is with a copy, he/she may pirate the product. The pirating
rewarded based on the sum of profit it brings in the probability is calculated using.
current period and the amount of profit it leaves in the
market relative to the total profit remaining in the market
Pt À Ri À d
at the time the action was implemented (i.e. in the ci;t ¼ min max ;0 ;1 ð8Þ
previous period). In this scheme a time pressure giving ri;t


Table 1 5. Results from running the system and managerial
Parameters used in numerical experiments implications
Parameter Value
Market size 10,000 consumers The system was developed using JBuilder 9 on a PC
Reservation prices, $ N ∼ (15,3) with a Pentium 4 and 1.0 GHz. Several experiments
Initial price, $ 8, 10, 12, 13.5, 15, 16.5, 18 were conducted to test the system and examine the
Risk cost, $ N ∼ (6,2), N ∼ (3,1), 0
managerial insights it provides. The system was run
Cost of copying medium, $ 1, 2
Number of neighbors 0, 1, 2, 4, 8, 16 with the parameters shown in Table 1.
Advertising cost, $ 900, 3600 The total number of parameter combinations (in-
Operating cost per period, $ 1200, 4800 cluding the pirating technology and the seller's
Pirating technology Copy from original, copy from copy reinforcement method) is 7 × 3 × 2 × 6 × 2 × 2 × 2 × 3 =
Seller's reinforcement method STPRM, MTPRM, LTPDRM
6048. The system was run with each possible parameter
combinations for the same randomly generated popula-
Eq. (8) implies that if the sum of the copying and tion of consumers. Each run consisted of 1000 product
consumer risk costs is greater than the selling price, then life cycles, each with duration T (the time from the
the consumer will not pirate. Otherwise, the probability introduction of the product until the “discontinue the
of pirating increases as the difference between the product” action is selected). Therefore, the simulation
selling price and the sum of the copying and risk costs allows the seller to learn from selling many similar
increases. For each buyer, a uniform random variable is products each having a product life cycle of several
drawn from the interval [0,1] and if the number is periods (weeks or months). The seller's behavior and
smaller than ci,t, then he/she pirates. We assume that results from the most profitable life cycle, which was the
consumers' pirating risk costs are random variables most frequently occurring (learned) seller's behavior for
from a normal distribution, however the system can majority of problems, was used for the analysis.
handle any specified distribution. Of the three seller reinforcement methods, LTPDRM
We deal with two cases of the technology of piracy. (long-term profit dynamic reinforcement method) and
In the first one, copies can be made only from legitimate STPRM (short-term profit reinforcement method) were
copies and making copies from copies results in found to perform best. Surprisingly, MTPRM (medium-
unacceptable degradation in quality. This is the case term profit reinforcement method) did not perform as
with audio and videocassette tapes and will be referred well as STPRM. The differences in the total maximum
to as copy from original (CFO). In the second case, profits from using the different reinforcement meth-
copies can be made from legitimate copies or from other ods were small. For example, LTPDRM outperformed
copies without significant degradation in quality. This is STPRM by 1.55% (in terms of profit) for the CFC case
the case with digital media such as music CDs and whereas STPRM outperformed MTPRM by 0.68%.
digital video disks (DVD) and will be referred to as copy Since LTPDRM and STPRM performed best, we use the
from copy (CFC). results from them for the analysis.
We assume that a consumer may be connected to
other consumers (neighbors) and use different sizes of 5.1. Identifying a good pricing strategy
neighborhoods to observe the effects of technology. In
the past, a consumer needed to have a physical The system can be used to identify a good, possibly
legitimate copy of a product in order to copy it. The optimal, pricing strategy for the seller. For example,
Internet and file compression technologies have elim-
inated such a requirement. This implies that a
Table 2
consumer's neighborhood is no longer defined by his/
Identifying a good pricing strategy using CAS
her physical space, but rather by his/her technological
Number Optimal pricing Number Number of Profit
network. If the number of neighbors is one, then a
of of pirated legitimate
consumer located at coordinate (xi, yi) has a neighbor at neighbors products products
(xi, yi + 1). If there are two neighbors, then there is an
0 $16.50 → $13.20 → $9.90 0 9584 $103,889
additional neighbor at (xi, yi − 1). For four neighbors, 1 $13.50 → $9.45 1123 8740 $93,920
there are two additional neighbors at (xi + 1, yi) and 2 $12.00 975 8414 $92,568
(xi − 1, yi). If a consumer has eight or sixteen neighbors, 4 $12.00 1228 8414 $92,568
then they are located closest to him/her on the two- 8 $12.00 1378 8414 $92,568
dimensional grid. 16 $12.00 1478 8414 $92,568


consumer connectivity on profit is strongest when the
number of neighbors is small (less than 8 neighbors). The
worst scenario for the monopolist is when consumers
have high connectivity and copies can be made from
copies. Unfortunately this is the situation many firms
face today due to the availability of most products in
digitized form, the good quality of compression tech-
nology, the decreased cost of bandwidth, and the low
cost of CD burners. In this respect, piracy reduces the
Fig. 2. Profit as a function of initial price for different consumer monopoly power firms in the music and movie in-
connectivity CFC and STPRM, At = $3600, O = $4800, Ri = 6, and dustries enjoyed in the past.
d = $1.
5.4. Impact of consumer connectivity and initial price
Table 2 shows the optimal pricing strategy for E(Ri) = on diffusion of pirated copies
$6.00, d = $1.00, O = $4800, A = $3600, CFO, and
LTPDRM. As the table shows, under no piracy (i.e. The number of neighbors has a strong impact on the
zero neighbors), it is best to introduce the product at a rate of diffusion of pirated copies in the market, especially
price of $16.50, reduce the price to $13.5 in the next when the initial price is high. As Fig. 4 shows, a
period, and then to $9.90 in the last period before dis- significant increase in the number of pirated copies begins
continuing the product. The total profit in this case is to appear for 4 neighbors as compared to 2 and 1—
$103,889. If each consumer is connected to two neigh- neighbors at an initial price of about $13.50. The implies is
bors, then it is best to use a single price of $12.00 and the that while the number of copies in the market may remains
total profit is $92,568. It is possible to use different relatively unchanged, using high initial price changes the
initial prices to find a better strategy for each level of mix of these products in favor of pirated copies.
consumer connectivity. For example, for the case of 1
neighbor, since $13.50 was the best initial price out of 5.5. Impact of copying medium and risk costs on profit
the seven tested initial prices, an experiment with initial
prices between $12.00 and $15.00 with increments of In many cases, firms selling reproducible products
$0.50 can be performed. such as music CDs increase their deterrent controls to
curtail piracy and to maintain a skimming approach to
5.2. Piracy and the effectiveness of skimming strategies the market. Some governments have even added a tax on
the copying medium and equipment to deter piracy and
Piracy reduces the effectiveness of a skimming strat- compensate the sellers [5]. The success of a skimming
egy, which the literature indicates to be the most suitable strategy will largely depend on the ability of a firm to
strategy for monopolists with no piracy. Before im- increase the piracy risk cost of consumers. Fig. 5 shows
provements in technology led to increased piracy, firms that the increase in the risk cost has to be large in order
operated on or close to the top curve of Fig. 2 (i.e. little for it to have an impact on the success of a skimming
or no piracy). However, as the curve shows, starting strategy. At an initial price of $18.00, an increase of
with a high price and reducing that price over time is less consumer pirating risk cost from 0 to an average of
effective as the number of neighbors increases. When
the number of neighbors is 4 or more, which is common
nowadays due to the Internet, it is best to use a single
price of $12 per unit. The skimming strategy may be
very suboptimal when the number of neighbors is large.

5.3. Impact of consumer connectivity on profit

The number of neighbors, i.e. connectivity of con-
sumers, has a strong effect on profits in both the CFO
and CFC cases. Fig. 3 shows the profit for both CFC and
CFO for different number of neighbors for an initial Fig. 3. Profit as a function of number of neighbors STPDRM, At =
price of $16.50. As the figure shows, the effect of $3600, O = $4800, Ri = 6, d = $1 and P1 = $16.50.


Fig. 4. Diffusion of pirated copies as a function of initial price for
different consumer connectivity CFC, STPRM, At = $3600, O = $4800,
Ri = 6, and d = $1.
Fig. 6. Combined impact of the consumer connectivity and technology
on profit STPRM, At = $3600, O = $4800 Ri = 6, and d = $2.
$6.00 and an increase in the copying medium cost from
$1 to $2 result in about $5000 increase in profit. For this will soon allow the same for transmission of movies.
investment in deterrent control to be successful, the Therefore, a consumer can have a neighbor provid-
additional revenue from taxing the copying medium and ing a product for piracy who is located in a different
the additional $5000 increase in profit must be larger geographical region. Fig. 6 shows the significant
than the expenditure on deterrent controls needed to combined effect of consumer connectivity and repro-
increase the risk cost. This may explain the strength of duction technology on profit. Earlier technology is rep-
the campaigns of the record labels in litigating against resented by the CFO and N = 1 whereas modern
individual pirates to substantially increase their assess- technology is represented by CFC and N = 16. At high
ment of the risk of being caught and the size of the initial prices, such as 10% above the mean reservation
penalties. However, Fig. 5 indicates that decreasing the price (i.e. $16.50), the decrease in profit due to
initial price is much more effective in increasing profit improved consumer connectivity and reproduction
than increasing the expenditure on piracy controls. technology is $44,949 (51%). Even for an initial price
equal to the average reservation price (i.e. $15), the
5.6. Piracy is becoming a more significant factor with decrease in profit is $25,966 (12%).
time
5.7. Piracy and consumer welfare
In the early 1990s, the major technology for music
and movie distribution was magnetic tapes (audio or From a social welfare perspective, it is optimal to
video). By the late 1990s, CDs became the standard allocate products to all consumers with positive utilities.
technology for music distribution. Now, digital video Assuming the seller uses a profit-maximizing price,
disks DVD is the standard technology for movie Fig. 7 shows the number of consumers with a copy of
distribution. These changes led significant improvement the product, legitimate or pirated, as a function of the
in the ability of consumers to make good copies from initial price. As the figure shows, piracy mitigates the
other copies. At the same time, the Internet allows music effect of the monopolist's pricing on product diffusion.
files to be transmitted between consumers without phys- As the monopolist raises the initial price in an attempt to
ical contact. Increased bandwidth and decreasing cost skim the market, consumers respond by pirating the
product rather than waiting until the selling price drops

Fig. 5. Profit as a function of initial price for different copying and risk Fig. 7. Piracy and product diffusion STPRM, At = $3600, O = $4800
costs CFC, STPRM, At = $3600, O = $4800, and N = 4. Ri = 6, and d = $1.


to or below their reservation prices. It is noteworthy that The results from the system are robust over repeated
the total number of consumers who obtain the product runs in the sense that the best pricing strategy for each
remained stable at about 10,000 over all initial prices in problem (i.e. parameter combination) and the learned
the range of $8–$18. This switch of many consumers to (i.e. most frequently used) pricing strategy were the same
piracy has empirical support in the literature. Peitz and for over 90% of the problems. In other words, the same
Waelbroeck [24] used the data from the International profit-maximizing behavior seems to be learned by the
Federation of the Phonographic Industry (IFPI) World seller for most problems. In addition, in an experiment
Report of 2003 to investigate the legitimacy of the where a new consumer population was generated for
RIAA's claim that music downloads are causing a large each run of a problem, the seller's pricing behavior in
decrease in music sales. Analysis of the data shows that terms of the number of price drops remained the same as
music downloading alone could have caused as high as a in the single consumer population runs. The exact prices
20% reduction in music sales worldwide between 1998 and profit amounts were different due to the randomness
and 2002. This effect does not include the effects of CD of each newly generated consumer population.
burning and organized piracy which may account for The choice of the initial weight to assign to each state/
another significant amount of lost sales. action pair and penalty scheme may have an impact on
how quickly the simulation converges to the best pricing
5.8. Piracy and decrease of royalty for the creator policy. However, its impact on the resulting best pricing
policy and best profit identified by the simulation should
Creators of reproducible goods, such as music be negligible. We experimented with different initial
writers, singers, and actors, are frequently different weights and penalties and found the results to be robust.
from the monopolist selling the product. Creators usu- For example, for problems with CFO, LTPDRM and 1
ally receive royalty for each legitimate product sold. neighbor, initial weights of 0.005 and a penalty of 15%
This royalty can be a fixed amount per unit sold or a resulted in best profits within 0.1% of the profits
percentage of the price. Incorporating this royalty as a obtained with initial weights of 0.001 and penalty of
fixed amount per unit sold does not change the reward 10% for 160 out of the 168 problem instances.
structure of the monopolist, whereas having it as a The developed system can incorporate additional real
percentage of the selling price may change the reward world aspects such as 1) declining interest in the prod-
structure. If the monopolist acts based on the STPRM uct over time, which can be incorporated as a down-
and $3 of royalty is paid to the creator per legitimate ward trend in the average reservation price over time,
product sold, then the total royalty paid to the creator is 2) effects of Internet technology, which can be modeled
shown in Fig. 8. As the figure shows, the creator's as random connections between consumers in the
royalty suffers only a small decrease because of a high system, 3) effects of legal and education campaigns to
initial price when there is only one neighbor and copies deter piracy, which can be modeled as decreases in
can be made only from legitimate products. Again, this consumers' probability to pirate, and 4) the effects of
was the scenario creators had before digitization, the injecting some bad copies in the market to discourage
Internet, and compression technologies. The decline in piracy, which some firms have used to deter piracy.
royalty due a high initial price (i.e. a skimming strategy) Furthermore, we assumed that consumers considers pi-
is much more significant for high consumer connectivity racy only if their reservation prices are not met. The
(N = 16) and improved copying technology (CFC). system can deal with other possibilities such as a
consumer deciding whether to pirate or purchase the
product based on the expected gain, or try to pirate first
and only purchase if unable to pirate, or can use a mix of
these and other rules. However, this will lead to different
results in terms of the experiments. In short, the pro-
posed system is flexible enough to handle many aspects
of the problem that would have been difficult to in-
corporate using different problem solving approaches.

6. Conclusion and suggestions for future research

Fig. 8. Piracy and creator's royalty STPRM, At = $3600, O = $4800 Experiments indicate that CAS and ABM are useful
Ri = 6, and d = $1. tools for firms in pricing products under piracy. The


system can be used to identify the best pricing policy in [a1, a2]. For example, a range of [.95,1] implies that the
terms of the best initial price and subsequent price reservation prices decrease on average by 2.5% every
changes. Numerical experiments suggest that under period, and 3) examining global piracy and its
moderate to strong piracy, which is characterized by implications. Under global piracy there are many
high consumer connectivity and ability to make copies relatively homogenous agents within regions and
from copies, the skimming strategy becomes unprofi- heterogeneous agents between regions in terms of
table and it is better to have a single price. In addition, disposable income and cultural dimensions which
discouraging piracy by taxing the copying medium and influences piracy. Furthermore, there are considerable
equipment and by increasing deterrent control may not variations in the environments of different regions in
work well. Specifically, the results suggest that for this terms of the existence and the degree of enforcement of
kind of control to work, consumers' perception of the piracy control laws. Varying technology and quality
probability of being caught and the size of the penalty standards between regions further complicates the
they will incur must substantially increase. problem. Because of the complexity arising from all
Interestingly, piracy causes the number of products, of these factors, CAS may be a good approach to un-
legitimate or pirated, in the market to be relatively derstanding global piracy, which in turn will enable
independent of the monopolist's pricing policy. If the better decision making by policy makers.
monopolist raises prices, consumers respond by more For the proposed model to be used in industry, mea-
piracy. In this respect, piracy erodes the power monopo- sures of the parameters must be obtained. Some parameter
lists have had in some industries. The ultimate victim of estimates such as the one for connectedness may be
piracy may be the creator of the information good who estimated based on available data. Internet access statistics
gets a fixed dollar amount per legitimate product sold in may give a good idea of how connected consumers in a
royalty. Therefore, many consumers thinking that piracy particular region are. For example, according to Internet
is a victimless crime may be mistaken, especially for World Statistics [16], 68.1% of Americans are Internet
products like music CDs. users. Other data such as assessment of consumer risk cost
The proposed system has several limitations. The may require market research.
product modeled in this system does not lose value since In developing CAS for pricing, several issues were
the time of its release. This implies that the product does found to be key to successfully applying this method-
not undergo deterioration and is not subject to obso- ology to business problems. One important issue is
lescence. An inventoried item subject to obsolescence designing the reward/reinforcement methods for firms.
incurs little or no physical damage until moment of The key questions here include: 1) how should different
obsolescence, whereas an inventoried item subject to actions be rewarded. Some actions may optimize short
deterioration will degrade overtime, thereby reducing its term performance, but significantly sub-optimize long-
market value [15]. Furthermore, learning on the part of term performance, 2) how should the reward/reinforce-
consumers is not incorporated into the system. Some ment methods balance the objectives of having emer-
consumers, after observing pricing patterns of products, gence to the best actions while at the same time not
may be willing to wait for one or more price reductions reinforcing actions quickly causing other good actions
before purchasing a product. to be eliminated prematurely. For example, suppose two
CAS methodology provides many opportunities for actions (A and B) out of several actions for the same
further analysis of pricing under piracy. Several ex- state have the best long-term profits with action B
tensions of our model are planned including 1) allowing having larger profit. If action A is selected more fre-
agents to move in the system (such movement of con- quently in the beginning of the simulation than action B
sumers is common and it may lead to further diffusion due to chance, then its future chances of being selected
of piracy), 2) incorporating consumers' declining may increase very quickly relative to action B and may
interest in the product over time. For many information therefore emerge as the best action for that state. An-
goods, life cycles are short and products compete with other important issue is the representation of consumer
many others for limited consumer disposable income; agents. The key questions here are 1) is there a gener-
consumers' declining interest in the product can be al approach for representing consumers which can be
modeled as a stochastic downward trend in reservation used in different applications, and 2) how do consum-
prices over time. Such a decrease in the consumer ers learn from each other, market leaders, and other
interest can be incorporated in the simulation using new sources, and 3) how to incorporate consumers' memory
reservation prices given by ri,t = δiri,t − 1 every period, into the system and how does that memory effect their
where δi is generated from a uniform distribution on behavior?


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Dr. Mirsad Hadzikadic joined the UNC Dr. Li-Shiang Tsay earned her M.S. and Ph.
Charlotte faculty in 1987 after receiving his D. degrees in Computer Science and Informa-
Ph.D. in Computer Science from Southern tion Technology from the University of North
Methodist University where he was a Fulb- Carolina at Charlotte in 2003 and 2005,
right Scholar. In addition to publishing his respectively. Her research has been published
scholarship, he has made presentations at in journals and books including Foundations
national and international conferences, lead- of Data Mining, Data Mining: Foundations
ing information technology firms, and uni- and Practice, Encyclopedia of Data Ware-
versities. His research/scholarship activities housing and Mining, and Journal of Experi-
have been primarily focused on three areas: mental and Theoretical Artificial Intelligence.
data mining, cognitive science, and medical Her research has also been presented at
informatics. From 1991 to 1997, he served as international conferences including IEEE GrC, IEEE ICDM Work-
the Director of the Department of Medical Informatics and Department shop, IEEE/WIC/ACM, IIS, SPIE, and ISMIS. She has served and is
of Orthopedic Informatics of the Carolinas HealthCare System. In serving on several Program Committees of international conferences,
1998, he joined Deloitte and Touche Consulting Group as Manager in including ISMIS'06, IRMA'07, and RSEISP'07. She is an Assistant
the Health Systems Integration Service Line. He returned full time to Professor of Computer Science at Hampton University since January
the University in January 1999 to assume the chair position in 2006.
Computer Science and serve as Director of the Software Solutions Lab.
Currently, he is serving as the Dean of the College of Computing and
Informatics.

Dr. Hari K. Rajagopalan earned his PhD in
Information Technology from the University
of North Carolina at Charlotte in 2006. Apart
from his PhD he also has an MBA in Finance
and an MS in Computer Science. His research
interests include locating emergency response
systems, pricing of digital products and
obsolescence in the high technology industry.
His research has published in the European
Journal of Operational Research, Computers
and Operations Research and other journals.
He is also an active participant at INFORMS, Decision Sciences and
European Working Group in Transportation Meeting and Mini EURO
Conferences. He is currently the Assistant Professor in Management at
Francis Marion University.

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