Application of complex adaptive systems to pricing of reproducible information goods

Available online at www.sciencedirect.com

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

Decision Support Systems

Application of complex adaptive systems to pricing of reproducibleinformation 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 Statesc 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 2007Available online 13 October 2007

Abstract

Piracy of copyrighted information goods such as computer software, music recordings, and movies has received increasedattention in the literature. Much of this research relied on mathematical modeling to analyze pricing policies, protection againstpiracy, and government policies. We use complex adaptive systems as an alternative methodology to analyze pricing decisions inan industry with products which can be pirated. This approach has been previously applied to pricing and can capture some aspectsof the problem which are difficult to analyze using traditional mathematical modeling. The results indicate that advances intechnology make a skimming strategy the least preferable approach for producers. Further, improvements in technology, morespecifically data communications and the Internet, will erode the profitability of a skimming strategy. The analysis also indicatesthat complex adaptive systems may provide a useful method for analyzing problems in which interactions between participants inthe 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

Piracy of copyrighted products has become a majorproblem for many firms. Tolerating some piracy may

☆ The authors would like to thank the referees for their helpfulcomments and suggestions.⁎ Corresponding author. Tel.: +1 704 687 3242; fax: +1 704 687

6330.E-mail addresses: [email protected] (M. Khouja),

[email protected] (M. Hadzikadic), [email protected](H.K. Rajagopalan), [email protected] (L.-S. Tsay).1 Tel.: +1 704 687 3124; fax: +1 704 687 6979.2 Tel.: +1 843 661 1501; fax: +1 661 1432.

0167-9236/$ - see front matter © 2007 Elsevier B.V. All rights reserved.doi:10.1016/j.dss.2007.10.005

increase the consumer base for a product and createspositive network externalities, which refer to a casewhere a consumer's utility from a software increaseswith the number of its users [21,25]. In that respect,having more consumers use a software makes it morevaluable to others. These positive aspects are less im-portant in the recorded music and movie industries.Conner and Rumelt [10] examined protection strategiesin the presence of positive network externalities. Theiranalysis indicates that, in the presence of positive net-work externalities, a strategy of no protection can resultin lower price and increased profit. The authors showthat network externalities have a strong effect under

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http://dx.doi.org/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 anddifficult to master, (2) the software allows or demandsextensive user customization, or (3) the software is usefulfor multiple-user data processing or formal networking.For example, a userwould rather useMicrosoftWord overWord Perfect if most users are using Microsoft Word forword processing. This is because using the softwaremakes it easier for a user to share documents with others.Some users may therefore be willing to pay more forMicrosoft Word. However, in case of music and moviesthe three conditions identified by Conner and Rumelt [10]are not present.

Industries susceptible to piracy are usually dominat-ed by monopolists who obtain monopoly power throughcopyright and intellectual property protection. Likeother monopolies, they are viewed unfavorably becausethey tend to charge higher prices than what wouldprevail under competition. For example, while Napsterwas being shut down after having been accused ofcontributing to piracy, major record labels in the musicindustry, such as Sony, and EMI, were accused ofviolating fair trade practices by threatening retailersnot to advertise compact disks (CDs) below certainprices [4].

Among the industries suffering from piracy, recordedmusic seems to be the worst hit. Pirating music hasbecome much easier due to digitization, the adoption ofcompression technologies such as MP3, and easy accessto digitized music files on the Internet. The RecordingIndustry Association of America's (RIAA) 2003 sta-tistics show that both the number and the dollar value ofCD sales have declined since 2001. In 2003, sales ofmusic CDs were $11.2 billion compared to a peak of$13.2 billion in 2000. Also, since the launch of Napsterin 1999, sales of CD singles have been decreasing at aremarkable rate till 2002. This is, in part, due to the factthat compressing one song into an MP3 file makes iteasy to swap. Although Napster, once the most popularmusic-swapping site, was shut down in an effort toprevent piracy by the big record labels, alternative filesharing through P2P networks, such as Kazaa, WinMX,and Gnutella, immediately replaced Napster. These P2Pnetworks do not require a central server to store files,thus avoiding possible litigation.

The marketing and economics literature delineatesthe different pricing strategies a firm can follow underdifferent conditions [22]. These conditions include de-gree of product differentiation, the competitive situa-tion, and the nature of demand. Skimming andpenetration are the classic strategies for pricing newproducts [22,29]. A skimming strategy is one in whicha firm sets a high initial price and then systematically

reduces it. In a monopoly market, which is the case formany information goods, the monopolist is certain thatthe entire market demand is its own. Therefore, askimming strategy can be used to exhaust the market[12]. The initial price is aimed at consumers for whomobtaining the product early is important and who arewilling to pay a premium for early ownership. As thissegment becomes saturated, price is reduced to increasethe appeal of the product [11]. This strategy is mostappropriate when products are highly differentiated, asegment of the market is price-insensitive, and there arelimited economies to scale or learning curve effects.Pricing in a skimming strategy maximizes profit basedon what the market can bear and the product's worth tobuyers [11,21]. The increased margins which skimmingbrings should be balanced against the decreased salesvolume.

Since a skimming strategy is suitable when a com-pany has a temporary monopoly position [22], it is idealfor producers of copyrighted products such as moviesand music recordings. These firms enjoy a natural mo-nopoly position and can skim the market for as long astheir intellectual property is protected. However, piracymay erode monopoly power even without competitorsentering the market.

Determining prices in a market where some piracy isunavoidable is a complex problem which is difficult toanalyze using traditional mathematical modeling. Thedifficulty arises in modeling the act of piracy itself. For aconsumer to pirate a product, the following prerequisitesare needed: 1) the consumer does not have a copy of theproduct, 2) the value the consumer attaches to theproduct exceeds the cost of the copying medium and therisk of being caught and penalized, 3) the consumerprefers pirating to purchasing a legitimate product (be-cause his/her reservation price is not met or the expectedgain from piracy exceeds the expected gain frompurchase), 4) the consumer knows another consumer,i.e. neighbor, with a reproducible copy, and 5) theconsumer or one of his/her neighbors has access to theduplication technology. Therefore, the rate of piracy at apoint in time depends on the diffusion of both legitimateand pirated copies (when copies can be made fromcopies) in the market up to that point and on consumerconnectivity. We define consumer connectivity as thenumber of neighbors, physical or via a computernetwork, that a consumer can share copies with. Com-plex adaptive systems (CAS) and agent-based modeling(ABM), which is a flexible approach to modeling CAS,may provide a useful methodology for analyzing pricingdecisions under piracy. CAS and ABM have beenpreviously applied to pricing problems in a two-firm

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

market where consumers' purchase decisions are solelybased on price [34].

The objectives of this paper are to 1) provide analternative methodology for analyzing the problem ofpiracy, 2) find an optimal monopolist's pricing strategy ina market where some piracy is unavoidable, 3) investigatethe impact of piracy on consumers, monopolists, andartists, and 4) evaluate the applicability of CAS to busi-ness problems, and more specifically pricing.

The key results are 1) consumer connectivity has astrong impact on optimal pricing strategy, 2) strongconsumer connectivity erodes the profitability of askimming strategy, 3) requiring a legitimate product tomake a copy does not significantly lessen the impact ofpiracy on profit when consumer connectivity is strong,4) deterrent piracy controls must significantly increaseconsumers' risk and cost of piracy to be effective, and5) CAS offer an effective platform for understanding thecombined effects of many variables on pricing.

The paper is organized as follows. Section 2 offers areview of the literature. In Section 3, we introduce CASand describe their use in problem solving. In Section 4,we develop a CAS for analyzing a monopolist's pricingpolicy in a market with piracy. In Section 5, we discussthe results from several experiments conducted usingthe developed system. Section 6 concludes with sum-mary of findings and future research on applying CAS tobusiness problems.

2. Literature review

Piracy has had a major impact in the computer soft-ware industry. Research on software piracy mainly dealswith pricing, copyright protection, and government pol-icies. Nascimento and Vanhonacker [21] found that askimming strategy is optimal in the absence of piracy.Using the diffusion of innovation model, they alsofound that copy protection is recommended when salesgrow faster than piracy and the cost of protectiondoes not significantly increase the marginal cost. Givon,Mahajan and Muller [13] showed a positive side topiracy with a software diffusion model.

Prasad and Mahajan [25] examined the relationshipbetween the rate of software diffusion and piracy todetermine the price and the piracy level that should betolerated. The authors examined three cases: A monop-oly, a monopoly with multiple generations of software,and a competitive market. Their results indicate that amonopoly should have little piracy protection at theearly stages of the software's life and impose maximumprotection in the second half of the life cycle. For multi-generation software monopolist, the first generation

should have less protection than in the monopoly caseonly if profit margins are expected to decline in sub-sequent generations. For the competitive case, less pro-tection should be used than in the monopoly case.Haruvy, Mahajan, and Prasad [17] examined how piracyaffects the adoption of subscription software. In thismodel the producer determines the price and theprotection level which maximize the discounted profitstream over the product's life. The results indicate thatmoderate tolerance for piracy can speed up adoption andenables the producer to charge higher prices. Tolerancefor piracy decreases when market penetration is quick,information is imprecise, and positive network exter-nalities are low.

Sundararajan [31] analyzed optimal pricing andpiracy protection for a monopolist using price discrim-ination among consumers who are willing to buy var-iable quantities of a digital good. The author shows thatthe optimal pricing schedule can be characterized as acombination of zero-piracy pricing and piracy-indif-ferent pricing schedules. Other findings by networkexternality-based studies [10,28,32] also indicate thatallowing piracy can make the producer more profitablewhen positive network externality exists.

Chen and Png [7] developed a model that incorpo-rates a piracy penalty set by the government. Themonopolist determines price and piracy monitoring rate.Users can buy the product, pirate it, or not use it. Theauthors show that changes in pricing and monitoringrates have qualitatively different effects on consumers.They also show that from a social welfare perspective,price reductions are better than increased monitoring.Chen and Png [8] extended the model to include a tax oncopying media and equipment and a government sub-sidy for legitimate purchases. Consumers are dividedinto ethical and unethical groups. The results indicatethat taxing the copying media is better from a socialwelfare standpoint than penalizing piracy, and that thebest government policy is to subsidize legitimate pur-chases. Belleflamme [2] considers a case in whichcopies are of lower quality than originals. He shows thatalthough diffusion through piracy increases socialwelfare, this comes at the expense of the producer'sprofits, which may be insufficient to cover the creationcost.

Chellappa and Shivendu [5] analyzed the implica-tions of variable technology standards in the movieindustry. They concluded that when piracy is prevalent,maintaining separate technology standards between dif-ferent regions is beneficial to the producer. In addition,it is not only the producer who incurs losses due toglobal piracy but also the consumers in regions where


quality is important. In a more recent study, Chellappaand Shivendu [6] assume that consumers are not fullyaware of the true fit of an information good to their tastesuntil consumption. In this model, piracy offers a con-sumption opportunity before purchase. The authors de-velop a two-stage model of a market composed ofheterogeneous consumers in their marginal valuation forquality and their moral costs. Some consumers pirate theproduct in the first stage and based on that experienceupdate their fit-perception which may cause them to re-evaluate their buying/pirating decision in the secondstage. An important result from the model is that piracylosses are more severe for products that are overvalued inthe market and ultimately do not live up to their reputationrather than for products that have been undervalued in themarket and turn out to be a good surprise.

Papadopoulos [23] investigated the relationship be-tween price, copyright law enforcement, and formationof black markets. Data for music recordings was used tofit a regression model to estimate the relationship be-tween legitimate music recording price, black marketdistribution channels and piracy. The author found thatpiracy in a country is most strongly related to the ratio ofaverage hourly wage to the average sound recordingprice and to a lesser degree, to a black market efficiencyindex. Wang [38] analyzed motion picture piracy andfound a positive relationship between perceived cost–benefits of a pirated copy and intent to purchase apirated copy. The likelihood of purchasing a piratedcopy is not dependent on individual income but ratheron the perceived benefit relative to the cost of a piratedcopy. In addition, the results indicate a negative re-lationship between the variables of perception of per-formance risk, ethical concern regarding piracy, andperception of social norms opposed to piracy and theintent to purchase a pirated copy. Other recent behav-ioral studies on piracy in the music and software in-dustry have been undertaken by Chiou, Huang, and Lee,[9] and Moores and Chang [20], respectively.

Related to copyright protection, an interesting find-ing by Gopal and Sanders [14] is that deterrent controls,which employ educational and legal campaigns, protectthe producer's profit better than preventive controls thatuse technology to make piracy difficult. Also, deterrentcontrols were shown to be superior from social welfareperspective.

A unique aspect of the music and movie industries isthe royalty system. Record labels usually pay per unitroyalty to artists ranging from 5% to 25% of the saleprice or a fixed amount per unit sold. An artist who getsroyalty was once considered one of the victims ofpiracy. However, a recent report from Pew Internet &

American Life Project reveals that many artists do notfeel that digital file sharing hurts them [26].

Many of the above models have focused on one ortwo aspects of piracy in order to maintain mathematicaltractability. For example, some models have focused onnetwork externalities, some on price and protectionlevel, some on price and government policy, and someon varying technology standards. Incorporating severalpiracy aspects into a single model complicates the ana-lysis and makes insights into the interaction effects ofthese factors difficult to obtain. Piracy is a dynamicproblem in which the time element is essential. The levelof piracy at a point in time depends both on the numberof legitimate and pirated copies of the product availablein the market. This makes the time of price changes toincrease revenue a critical part of decision making.Finally, products susceptible to piracy are usually short-lived products with consumer interest waning quicklyover time. All of these aspects make CAS and ABM auseful alternative methodology for incorporating themany aspects of piracy.

Despite the fact that CAS were introduced over30 years ago [18,19], there is little research on their usefor solving business problems. This is may be due in partto the difficulty in representing key elements of busi-ness problems such as key levers, constituent “agents”,negotiations, rewards, fitness, etc. There have been someattempts to advance the state of knowledge of applyingCAS to business problems. For example, Ben Said,Bouron, and Drogoul [3] used agent-based modeling(ABM) in a consumermarket. The authors proposed a setof behavioral primitives for consumer agents whichinclude imitation, conditioning, mistrust, and innova-tiveness. The system incorporates opinion leaders whoseopinions are highly valued by consumers. Consumerslearn over time and genetic algorithms are used for theevolution of consumers. The authors use ABM to pro-vide operational and conceptual richness to capture abroad range of consumer behavior. This study illustratesthe difficulty in capturing and generalizing key elementsof agents' behavior.

ABM and CAS have been used to analyze pricingdecisions under limiting assumptions without piracy.Tesauro and Kephart [34] analyzed pricing decisions oftwo firms selling an identical product. Consumerswere assumed to behave deterministically and prefer theproduct with lower price. Sellers alternate in setting pricefor each period with full knowledge of the competitor'sprice and profit. The authors investigated the effects ofusing Q-learning on the sellers' behavior. Q-learning is analgorithm that incorporates long-term rewards intoreinforcement. The results indicate that pricing policies


derived with Q-learning reduce price wars and increaseprofitability. The results support earlier conclusions on thebenefits of incorporating long-term consequences ofactions into the learning reinforcement [33,37]. ABMhas been used in other business applications such as tostudy the performance of a supplier selection models [36]and explore bidding strategies for market-based schedul-ing [27].

The proposed application provides a step in the long-term process of effectively applying CAS to businessproblems. It includes the identification of a) appropri-ate agents, b) their key properties, c) mechanisms foragents' learning, d) agents' goals, e) fitness functions,and f) key performance indicators. The subsequent stepsin the development of CAS for solving business prob-lems include refinements to the proposed CAS to bettercapture the above key elements, the addition of moreagents to the system such as government and regulatingagencies, and implementing learning for all agents in thesystem.

3. Agent-based modeling and Complex AdaptiveSystems

Complex Adaptive Systems and ABM are bottom–up approaches for analyzing and understanding complexsystems. We focus on a particular implementation ofComplex Adaptive Systems (CAS) known as ABM.Entities in the system are modeled as agents whosebehavior mimics that of real entities. Agents act ac-cording to their rules/schema. Agents can have a highdegree of heterogeneity or be very similar. The actionsand interactions of the agents in the system result in anaggregate behavior of the system [35]. Agents in busi-ness models are the actual players in the system, whichinclude firms, consumers, and regulatory agencies. Onecan view ABM as social simulation, which is nowpossible due to increased computing power [30].

Several advantages of using CAS and ABM havebeen given in the literature. While these advantages maynot be unique to CAS, their combination makes thismethod attractive. ABM does not require assumptionswith regard to the behavior of the system [35]. Agentsalso provide a useful approach for modeling entities inmany social problems [1]. The use of ABM enables usto use the wealth of information about agents' behavior,motives, and interactions to examine the consequencesin terms of aggregate system behavior. Agents alsoprovide a method for modeling heterogeneity [35].

CAS exhibit complex non-linear behavior broughtabout by interaction of agents. Agents influence thebehavior of the systemwhile, at the same time, the system

influences the behavior of individual agents. The agentsinteract with the environment as well. CAS are networkedin the sense that agents interact with their neighbors and,occasionally, distant agents, and non-linear in the sensethat the whole is greater than the sum of its parts.

The main properties of CAS include self-organiza-tion, emergence, and adaptation. Ant colonies, networksof neurons, the Internet, the brain, and the global econ-omy are a few examples where the behavior of thewhole is much more complex than the behavior of itsparts. Agents are autonomous entities with limited per-ception of their environment. They are guided by fewsimple rules and act locally. Agents' overall status andbehavior can be tracked and evaluated. The performanceof the overall system is derived from the effectiveness ofthe individual agents and their interaction. Agents mayor may not have a history of their previous interactionsand the ability to learn from them. Information abouttheir past performance is used by the agents to deter-mine the type and the degree of improvement in theirbehavior.

Agent interactions are mostly local; namely, theycommunicate with their immediate neighbors. Occa-sionally, as they move about, some agents get a chanceto interact with other agents exhibiting plausible prop-erties, regardless of the distance between the twoagents. Their behavior is driven by a few, well-chosenrules. It is the interaction between agents, as well as theinteraction between the agents and the environmentthat gives rise to the complexity of the system as awhole.

4. Complex adaptive systems and pricing under piracy

The proposed system is developed for a firm that has amonopoly for a copyrighted product. Each consumer hashis/her value for the product. Thus, each consumer hashis/her reservation price for the product, which is themaximum price he/she is willing to pay. This value isknown to the consumer prior to consuming the product.While this assumption is similar to assumptions in somemodels in the literature [8], others authors assume thatconsumers update their fit-perception of the product aftersampling it [6]. If the selling price is equal to or below thereservation price, a consumer will buy the product. If theselling price is higher than the reservation price, there is aprobability that he/she may pirate the product. Thepirating probability depends on several factors includingaccess to copies that can be pirated, the availability ofduplication technology, and the cost of the copyingmedium. A consumer's decision to pirate also dependson the penalty for pirating and the probability he/she


assigns to being caught. Finally, the probability ofpirating is an increasing function of the differencebetween the selling price and copying cost. The goal ofthe firm is to maximize total profit by periodicallyadjusting prices over the finite life of the product.

In applying CAS to pricing, or any similar problem,one must first identify the agents in the system andtheir rules. Agents in this problem include one sellerand N consumers. IF/THEN rules are used to describean agent — the IF part of the rule being the conditionor state, and the THEN part is the action. Agents neednot be homogenous and each agent has its own rules.The effectiveness of the pricing strategy is measuredusing the seller's profit. The following assumptions aremade:

1. There is only one seller.2. The goal of the seller is to maximize profits over the

life of the product.3. Advertising cost is a fixed amount per advertising

campaign.4. Consumers have complete information about the

current price.5. Each consumer may obtain only one copy of the

product, legitimate or pirated.

The following notation is used:

t 1,2,3,…,T, a period index,i 1,2,3,…,N, a consumer index,Zt profit for period t,Pt unit selling price during period t,Qt number of legitimate products sold in period t,qt number of pirated copies made in period t,ri,t reservation price of consumer i in period t,Ri the risk cost consumer i assigns to pirating the

product,d the cost of pirating which includes the cost of

the storage medium and excludes the risk cost,ci,t probability of consumer i pirating the product

in period t,hi the number of neighbors of consumer i,At advertising cost incurred in period t, At=A if

Pt≠Pt− 1 and 0 otherwise.Ot per period operating cost incurred for the product,πt sum of all reservation prices of consumers

without the product at the beginning of periodt,

π1 total reservation prices of all consumers priorto the introduction of the product,

g 1,2,3,…,G, an index of an action the seller mayimplement at the beginning of a period,

j 1, 2,.., J, a state condition of the systemassessed at the end of each period,

ρg,j,t the weight assigned to state/action pair j/g atthe at the end of period t.

All variables indexed by t are dynamic in terms ofbeing recalculated each period in the simulation. Allparameters indexed by t are dynamic in terms of thesimulation being able to handle changes in their valuesfrom one period to the next. For many of theseparameters (ri,t,Ot, and At), the values are kept thesame during a run of the simulation for the experimentsin order to focus on the effects of piracy.

4.1. Seller's schema

Similar to industry practice, we assume the sellermonitors sales and profit performance. As this databecomes available each period, which can be a week, amonth, or a quarter, decisions are made and implemen-ted. Therefore, we implement a periodic review systemin which time increases in discrete units. A life cycleconsists of T periods. For example, a movie released onDVD may have a life cycle of up to 5 months with pricechanges allowed monthly. At the end of each period, theseller will have one of three states (i.e. j=1,2,3):

1. the profit has increased from previous period:ZtNZt− 1,

2. the profit has decreased from previous period: ZtbZt−1,or

3. the profit is the same as in the previous period:Zt=Zt− 1.

The seller may implement one of the followingactions at the beginning of period t:

1. keep the current price unchanged (i.e. do nothing),2. discontinue the product,3. change the price to Pt− 1(1±0.05k), k∈ [1,2,3,4,5,6].

The last action has 12 possible price changes re-sulting in a total of 14 possible actions (i.e. g=1,…14).Multiples of 5% change is most common in practice.The above states and actions result in 42 state/actionpairs. The initial selling price is user specified.However, a search for the best initial price can beincorporated. The seller advertises the product at thebeginning of each period with a price change. At the endof each period, the seller detects the state of the systemand takes an action, which is chosen probabilisticallybased on the weights assigned to each state/action pair.


To ensure that each action has an equal probability ofbeing selected for each state at the beginning of a run,the initial weights of each state/action pair is set to 0.01.After executing the selected action, the weight of theselected state/action pair is changed based on its profitperformance. During the run of the simulation, theweight assigned to the most profitable state/action pairincreases until it has a probability close to 100% ofbeing selected. The speed of convergence depends onthe relative profitability of other state/action pairs. If onestate/action pair is significantly more profitable thanothers, then the probability of selecting this state/actionpair approaches 100% very quickly. If there are manystate/action pairs with only slightly lower profit than thebest state/action pair, then this convergence will takemany runs of the simulation.

Fig. 1 shows flowcharts explaining the simulation forone product lifecycle (a run of the simulation includes

Fig. 1. Flowchart of

many lifecycles). Every period, buyers interested in theproduct make decisions on buying, pirating, or waiting.The buyer's process is interrupted at the end of theperiod to let the seller evaluate the pricing strategy.Based on the change in profit during the period, actionsare rewarded and a decision on which action toimplement is made. The selection of actions dependson the weights of each state/action pair for the occurringstate. A life cycle ends only when the seller implementsthe “discontinue the product” action. If the sellerchooses discontinue the product, the lifecycle endsand all parameters are reset except for the weights of thestate/action pairs which the seller retains since they werelearned from past experience.

We consider two costs: An operating cost incurredevery period, and an advertising cost incurred onlywhen there is a price change. Since we deal with in-formation goods, per unit cost of production is very

the simulation.


small and, without loss of generality, we assume it to bezero. Therefore, the profit per period is:

Zt ¼ QtPt � A� Ot If PtpPt�1

Qt Pt � Ot Otherwise

�ð1Þ

We tested three reinforcement learning methods:Short-term profit reinforcement method (STPRM):

The weight of a state/action pair at the end of a period isincreased by the amount:

Dg; j;t ¼ Ztp1

¼ Qt Pt � Ot � Au jPt � Pt�1jð ÞXNi¼1

ri;1

ð2Þ

if Δg,j,tN0, where u(x) is a unit step function defined asu(x)=1 if xN0 and 0 otherwise. Under this reinforce-ment scheme, each state/action pair is rewarded basedon the profit it brings in the current period relative to themaximum total profit the product can bring.

Medium-term profit reinforcementmethod (MTPRM):For each consumer who obtains a copy of the product, ri isset to zero since he/she is no longer willing to pay any-thing for the product. The weight of a state/action pair isincreased by the amount:

Dg; j;t ¼ Ztpt�1

¼ Qt Pt � Ot � Au jPt � Pt�1jð ÞXNi¼1

ri;t�1

ð3Þ

if Δg,j,tN0. Under this scheme, each action is rewardedbased on the profit it brings in the current period relative tothe total remaining profit the product can bring at the timethe action is implemented.

Long-term profit dynamic reinforcement method(LTPDRM): The weight of a state/action pair isincreased by the amount:

Dg; j;t ¼ Zt þ ptpt�1

tE0:001

¼Qt Pt � Ot � Au jPt � Pt�1jð Þ þPN

iri;t

XNi¼1

ri;t�1

tE0:001

ð4Þif Δg,j,tN0, E is the total number of product life cycleruns. Under this reinforcement scheme, a state/action isrewarded based on the sum of profit it brings in thecurrent period and the amount of profit it leaves in themarket relative to the total profit remaining in the marketat the time the action was implemented (i.e. in theprevious period). In this scheme a time pressure giving

actions some time before rewards get large is used so thatno action is eliminated from consideration early in a run.

For all three reinforcement methods, at the end ofperiod t, if Δg,j,tN0, then the weight of state/action pairj/g is increased according to:

qg; j;t ¼ qg; j;t�1 þ Dg;i;t for g and j of t � 1 ð5ÞTherefore, when the same condition occurs again, an

action's chance of being selected increases with theprofit it has provided in the past. If Δg,j,t≤0, then apenalty is charged to the state/action pair by decreasingits current weight by 10%. Hence, if Δg,j,t≤0, then

qg; j;t ¼ 0:90 qg; j;t�1 for g and j of t � 1 ð6Þ

Therefore, when the same state is realized in thefuture, this action has a lower probability of beingselected. The selection of an action for a state istherefore based on the following procedure: If state joccurs, then the probability of selecting action g is givenby the weight of state/action pair j/g divided by the sumof the weights for all state/action pairs of state j, whichcan be written as:

pg; j;tþ1 ¼qg; j;t

XGx¼1

qx; j;t

if state j occurs in period t

ð7Þ

4.2. Rules — N consumer agents

There are N consumers and all have completeinformation about the current selling price. Eachconsumer has his/her own reservation price. Usually,companies use past information or surveys to measurereservation prices. We assume that reservation priceshave a normal distribution with known mean andstandard deviation. However, the system can deal withany known distribution. A consumer purchases theproduct if his/her reservation price is met, if thereservation price is not met then a consumer may piratethe product (with some probability) if a neighboringconsumer has a copy, or wait.

A consumer pirates the product according to thefollowing scheme. When the selling price is higher thanthe reservation price of a consumer who knows an agentwith a copy, he/she may pirate the product. The piratingprobability is calculated using.

ci;t ¼ min maxPt � Ri � d

ri;t; 0

� �; 1

� �ð8Þ

Table 1Parameters used in numerical experiments

Parameter Value

Market size 10,000 consumersReservation prices, $ N∼ (15,3)Initial price, $ 8, 10, 12, 13.5, 15, 16.5, 18Risk cost, $ N∼ (6,2), N∼ (3,1), 0Cost of copying medium, $ 1, 2Number of neighbors 0, 1, 2, 4, 8, 16Advertising cost, $ 900, 3600Operating cost per period, $ 1200, 4800Pirating technology Copy from original, copy from copySeller's reinforcement method STPRM, MTPRM, LTPDRM

Table 2Identifying a good pricing strategy using CAS

Numberofneighbors

Optimal pricing Numberof piratedproducts

Number oflegitimateproducts

Profit

0 $16.50→$13.20→$9.90 0 9584 $103,8891 $13.50→$9.45 1123 8740 $93,9202 $12.00 975 8414 $92,5684 $12.00 1228 8414 $92,5688 $12.00 1378 8414 $92,56816 $12.00 1478 8414 $92,568


Eq. (8) implies that if the sum of the copying andconsumer risk costs is greater than the selling price, thenthe consumer will not pirate. Otherwise, the probabilityof pirating increases as the difference between theselling price and the sum of the copying and risk costsincreases. For each buyer, a uniform random variable isdrawn from the interval [0,1] and if the number issmaller than ci,t, then he/she pirates. We assume thatconsumers' pirating risk costs are random variablesfrom a normal distribution, however the system canhandle any specified distribution.

We deal with two cases of the technology of piracy.In the first one, copies can be made only from legitimatecopies and making copies from copies results inunacceptable degradation in quality. This is the casewith audio and videocassette tapes and will be referredto as copy from original (CFO). In the second case,copies can be made from legitimate copies or from othercopies without significant degradation in quality. This isthe case with digital media such as music CDs anddigital video disks (DVD) and will be referred to as copyfrom copy (CFC).

We assume that a consumer may be connected toother consumers (neighbors) and use different sizes ofneighborhoods to observe the effects of technology. Inthe past, a consumer needed to have a physicallegitimate copy of a product in order to copy it. TheInternet and file compression technologies have elim-inated such a requirement. This implies that aconsumer's neighborhood is no longer defined by his/her physical space, but rather by his/her technologicalnetwork. If the number of neighbors is one, then aconsumer located at coordinate (xi, yi) has a neighbor at(xi, yi+1). If there are two neighbors, then there is anadditional neighbor at (xi, yi−1). For four neighbors,there are two additional neighbors at (xi+1, yi) and(xi−1, yi). If a consumer has eight or sixteen neighbors,then they are located closest to him/her on the two-dimensional grid.

5. Results from running the system and managerialimplications

The system was developed using JBuilder 9 on a PCwith a Pentium 4 and 1.0 GHz. Several experimentswere conducted to test the system and examine themanagerial insights it provides. The system was runwith the parameters shown in Table 1.

The total number of parameter combinations (in-cluding the pirating technology and the seller'sreinforcement method) is 7×3×2×6×2×2×2×3=6048. The system was run with each possible parametercombinations for the same randomly generated popula-tion of consumers. Each run consisted of 1000 productlife cycles, each with duration T (the time from theintroduction of the product until the “discontinue theproduct” action is selected). Therefore, the simulationallows the seller to learn from selling many similarproducts each having a product life cycle of severalperiods (weeks or months). The seller's behavior andresults from the most profitable life cycle, which was themost frequently occurring (learned) seller's behavior formajority of problems, was used for the analysis.

Of the three seller reinforcement methods, LTPDRM(long-term profit dynamic reinforcement method) andSTPRM (short-term profit reinforcement method) werefound to perform best. Surprisingly, MTPRM (medium-term profit reinforcement method) did not perform aswell as STPRM. The differences in the total maximumprofits from using the different reinforcement meth-ods were small. For example, LTPDRM outperformedSTPRM by 1.55% (in terms of profit) for the CFC casewhereas STPRM outperformed MTPRM by 0.68%.Since LTPDRM and STPRM performed best, we use theresults from them for the analysis.

5.1. Identifying a good pricing strategy

The system can be used to identify a good, possiblyoptimal, pricing strategy for the seller. For example,

Fig. 2. Profit as a function of initial price for different consumerconnectivity CFC and STPRM, At=$3600, O=$4800, Ri=6, andd=$1.

Fig. 3. Profit as a function of number of neighbors STPDRM, At=$3600, O=$4800, Ri=6, d=$1 and P1=$16.50.


Table 2 shows the optimal pricing strategy for E(Ri)=$6.00, d=$1.00, O=$4800, A=$3600, CFO, andLTPDRM. As the table shows, under no piracy (i.e.zero neighbors), it is best to introduce the product at aprice of $16.50, reduce the price to $13.5 in the nextperiod, and then to $9.90 in the last period before dis-continuing the product. The total profit in this case is$103,889. If each consumer is connected to two neigh-bors, then it is best to use a single price of $12.00 and thetotal profit is $92,568. It is possible to use differentinitial prices to find a better strategy for each level ofconsumer connectivity. For example, for the case of 1neighbor, since $13.50 was the best initial price out ofthe seven tested initial prices, an experiment with initialprices between $12.00 and $15.00 with increments of$0.50 can be performed.

5.2. Piracy and the effectiveness of skimming strategies

Piracy reduces the effectiveness of a skimming strat-egy, which the literature indicates to be the most suitablestrategy for monopolists with no piracy. Before im-provements in technology led to increased piracy, firmsoperated on or close to the top curve of Fig. 2 (i.e. littleor no piracy). However, as the curve shows, startingwith a high price and reducing that price over time is lesseffective as the number of neighbors increases. Whenthe number of neighbors is 4 or more, which is commonnowadays due to the Internet, it is best to use a singleprice of $12 per unit. The skimming strategy may bevery 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 CFOand CFC cases. Fig. 3 shows the profit for both CFC andCFO for different number of neighbors for an initialprice of $16.50. As the figure shows, the effect of

consumer connectivity on profit is strongest when thenumber of neighbors is small (less than 8 neighbors). Theworst scenario for the monopolist is when consumershave high connectivity and copies can be made fromcopies. Unfortunately this is the situation many firmsface today due to the availability of most products indigitized form, the good quality of compression tech-nology, the decreased cost of bandwidth, and the lowcost of CD burners. In this respect, piracy reduces themonopoly power firms in the music and movie in-dustries enjoyed in the past.

5.4. Impact of consumer connectivity and initial priceon diffusion of pirated copies

The number of neighbors has a strong impact on therate of diffusion of pirated copies in the market, especiallywhen the initial price is high. As Fig. 4 shows, asignificant increase in the number of pirated copies beginsto appear for 4 neighbors as compared to 2 and 1—neighbors at an initial price of about $13.50. The implies isthat while the number of copies in themarketmay remainsrelatively unchanged, using high initial price changes themix of these products in favor of pirated copies.

5.5. Impact of copying medium and risk costs on profit

In many cases, firms selling reproducible productssuch as music CDs increase their deterrent controls tocurtail piracy and to maintain a skimming approach tothe market. Some governments have even added a tax onthe copying medium and equipment to deter piracy andcompensate the sellers [5]. The success of a skimmingstrategy will largely depend on the ability of a firm toincrease the piracy risk cost of consumers. Fig. 5 showsthat the increase in the risk cost has to be large in orderfor it to have an impact on the success of a skimmingstrategy. At an initial price of $18.00, an increase ofconsumer pirating risk cost from 0 to an average of

Fig. 4. Diffusion of pirated copies as a function of initial price fordifferent consumer connectivity CFC, STPRM, At=$3600, O=$4800,Ri=6, and d=$1.

Fig. 6. Combined impact of the consumer connectivity and technologyon 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 thisinvestment in deterrent control to be successful, theadditional revenue from taxing the copying medium andthe additional $5000 increase in profit must be largerthan the expenditure on deterrent controls needed toincrease the risk cost. This may explain the strength ofthe campaigns of the record labels in litigating againstindividual pirates to substantially increase their assess-ment of the risk of being caught and the size of thepenalties. However, Fig. 5 indicates that decreasing theinitial price is much more effective in increasing profitthan increasing the expenditure on piracy controls.

5.6. Piracy is becoming a more significant factor withtime

In the early 1990s, the major technology for musicand movie distribution was magnetic tapes (audio orvideo). By the late 1990s, CDs became the standardtechnology for music distribution. Now, digital videodisks DVD is the standard technology for moviedistribution. These changes led significant improvementin the ability of consumers to make good copies fromother copies. At the same time, the Internet allows musicfiles to be transmitted between consumers without phys-ical contact. Increased bandwidth and decreasing cost

Fig. 5. Profit as a function of initial price for different copying and riskcosts CFC, STPRM, At=$3600, O=$4800, and N=4.

will soon allow the same for transmission of movies.Therefore, a consumer can have a neighbor provid-ing a product for piracy who is located in a differentgeographical region. Fig. 6 shows the significantcombined effect of consumer connectivity and repro-duction technology on profit. Earlier technology is rep-resented by the CFO and N=1 whereas moderntechnology is represented by CFC and N=16. At highinitial prices, such as 10% above the mean reservationprice (i.e. $16.50), the decrease in profit due toimproved consumer connectivity and reproductiontechnology is $44,949 (51%). Even for an initial priceequal to the average reservation price (i.e. $15), thedecrease in profit is $25,966 (12%).

5.7. Piracy and consumer welfare

From a social welfare perspective, it is optimal toallocate products to all consumers with positive utilities.Assuming the seller uses a profit-maximizing price,Fig. 7 shows the number of consumers with a copy ofthe product, legitimate or pirated, as a function of theinitial price. As the figure shows, piracy mitigates theeffect of the monopolist's pricing on product diffusion.As the monopolist raises the initial price in an attempt toskim the market, consumers respond by pirating theproduct rather than waiting until the selling price drops

Fig. 7. Piracy and product diffusion STPRM, At=$3600, O=$4800Ri=6, and d=$1.


to or below their reservation prices. It is noteworthy thatthe total number of consumers who obtain the productremained stable at about 10,000 over all initial prices inthe range of $8–$18. This switch of many consumers topiracy has empirical support in the literature. Peitz andWaelbroeck [24] used the data from the InternationalFederation of the Phonographic Industry (IFPI) WorldReport of 2003 to investigate the legitimacy of theRIAA's claim that music downloads are causing a largedecrease in music sales. Analysis of the data shows thatmusic downloading alone could have caused as high as a20% reduction in music sales worldwide between 1998and 2002. This effect does not include the effects of CDburning and organized piracy which may account foranother significant amount of lost sales.

5.8. Piracy and decrease of royalty for the creator

Creators of reproducible goods, such as musicwriters, singers, and actors, are frequently differentfrom the monopolist selling the product. Creators usu-ally receive royalty for each legitimate product sold.This royalty can be a fixed amount per unit sold or apercentage of the price. Incorporating this royalty as afixed amount per unit sold does not change the rewardstructure of the monopolist, whereas having it as apercentage of the selling price may change the rewardstructure. If the monopolist acts based on the STPRMand $3 of royalty is paid to the creator per legitimateproduct sold, then the total royalty paid to the creator isshown in Fig. 8. As the figure shows, the creator'sroyalty suffers only a small decrease because of a highinitial price when there is only one neighbor and copiescan be made only from legitimate products. Again, thiswas the scenario creators had before digitization, theInternet, and compression technologies. The decline inroyalty due a high initial price (i.e. a skimming strategy)is much more significant for high consumer connectivity(N=16) and improved copying technology (CFC).

Fig. 8. Piracy and creator's royalty STPRM, At=$3600, O=$4800Ri=6, and d=$1.

The results from the system are robust over repeatedruns in the sense that the best pricing strategy for eachproblem (i.e. parameter combination) and the learned(i.e. most frequently used) pricing strategy were the samefor over 90% of the problems. In other words, the sameprofit-maximizing behavior seems to be learned by theseller for most problems. In addition, in an experimentwhere a new consumer population was generated foreach run of a problem, the seller's pricing behavior interms of the number of price drops remained the same asin the single consumer population runs. The exact pricesand profit amounts were different due to the randomnessof each newly generated consumer population.

The choice of the initial weight to assign to each state/action pair and penalty scheme may have an impact onhow quickly the simulation converges to the best pricingpolicy. However, its impact on the resulting best pricingpolicy and best profit identified by the simulation shouldbe negligible. We experimented with different initialweights and penalties and found the results to be robust.For example, for problems with CFO, LTPDRM and 1neighbor, initial weights of 0.005 and a penalty of 15%resulted in best profits within 0.1% of the profitsobtained with initial weights of 0.001 and penalty of10% for 160 out of the 168 problem instances.

The developed system can incorporate additional realworld aspects such as 1) declining interest in the prod-uct over time, which can be incorporated as a down-ward trend in the average reservation price over time,2) effects of Internet technology, which can be modeledas random connections between consumers in thesystem, 3) effects of legal and education campaigns todeter piracy, which can be modeled as decreases inconsumers' probability to pirate, and 4) the effects ofinjecting some bad copies in the market to discouragepiracy, which some firms have used to deter piracy.Furthermore, we assumed that consumers considers pi-racy only if their reservation prices are not met. Thesystem can deal with other possibilities such as aconsumer deciding whether to pirate or purchase theproduct based on the expected gain, or try to pirate firstand only purchase if unable to pirate, or can use a mix ofthese and other rules. However, this will lead to differentresults in terms of the experiments. In short, the pro-posed system is flexible enough to handle many aspectsof the problem that would have been difficult to in-corporate using different problem solving approaches.

6. Conclusion and suggestions for future research

Experiments indicate that CAS and ABM are usefultools for firms in pricing products under piracy. The


system can be used to identify the best pricing policy interms of the best initial price and subsequent pricechanges. Numerical experiments suggest that undermoderate to strong piracy, which is characterized byhigh consumer connectivity and ability to make copiesfrom copies, the skimming strategy becomes unprofi-table and it is better to have a single price. In addition,discouraging piracy by taxing the copying medium andequipment and by increasing deterrent control may notwork well. Specifically, the results suggest that for thiskind of control to work, consumers' perception of theprobability of being caught and the size of the penaltythey will incur must substantially increase.

Interestingly, piracy causes the number of products,legitimate or pirated, in the market to be relativelyindependent of the monopolist's pricing policy. If themonopolist raises prices, consumers respond by morepiracy. In this respect, piracy erodes the power monopo-lists have had in some industries. The ultimate victim ofpiracy may be the creator of the information good whogets a fixed dollar amount per legitimate product sold inroyalty. Therefore, many consumers thinking that piracyis a victimless crime may be mistaken, especially forproducts like music CDs.

The proposed system has several limitations. Theproduct modeled in this system does not lose value sincethe time of its release. This implies that the product doesnot undergo deterioration and is not subject to obso-lescence. An inventoried item subject to obsolescenceincurs little or no physical damage until moment ofobsolescence, whereas an inventoried item subject todeterioration will degrade overtime, thereby reducing itsmarket value [15]. Furthermore, learning on the part ofconsumers is not incorporated into the system. Someconsumers, after observing pricing patterns of products,may be willing to wait for one or more price reductionsbefore purchasing a product.

CAS methodology provides many opportunities forfurther analysis of pricing under piracy. Several ex-tensions of our model are planned including 1) allowingagents to move in the system (such movement of con-sumers is common and it may lead to further diffusionof piracy), 2) incorporating consumers' declininginterest in the product over time. For many informationgoods, life cycles are short and products compete withmany others for limited consumer disposable income;consumers' declining interest in the product can bemodeled as a stochastic downward trend in reservationprices over time. Such a decrease in the consumerinterest can be incorporated in the simulation using newreservation prices given by ri,t= δiri,t− 1 every period,where δi is generated from a uniform distribution on

[a1, a2]. For example, a range of [.95,1] implies that thereservation prices decrease on average by 2.5% everyperiod, and 3) examining global piracy and itsimplications. Under global piracy there are manyrelatively homogenous agents within regions andheterogeneous agents between regions in terms ofdisposable income and cultural dimensions whichinfluences piracy. Furthermore, there are considerablevariations in the environments of different regions interms of the existence and the degree of enforcement ofpiracy control laws. Varying technology and qualitystandards between regions further complicates theproblem. Because of the complexity arising from allof these factors, CAS may be a good approach to un-derstanding global piracy, which in turn will enablebetter decision making by policy makers.

For the proposed model to be used in industry, mea-sures of the parameters must be obtained. Some parameterestimates such as the one for connectedness may beestimated based on available data. Internet access statisticsmay give a good idea of how connected consumers in aparticular region are. For example, according to InternetWorld Statistics [16], 68.1% of Americans are Internetusers. Other data such as assessment of consumer risk costmay require market research.

In developing CAS for pricing, several issues werefound to be key to successfully applying this method-ology to business problems. One important issue isdesigning the reward/reinforcement methods for firms.The key questions here include: 1) how should differentactions be rewarded. Some actions may optimize shortterm performance, but significantly sub-optimize long-term performance, 2) how should the reward/reinforce-ment methods balance the objectives of having emer-gence to the best actions while at the same time notreinforcing actions quickly causing other good actionsto be eliminated prematurely. For example, suppose twoactions (A and B) out of several actions for the samestate have the best long-term profits with action Bhaving larger profit. If action A is selected more fre-quently in the beginning of the simulation than action Bdue to chance, then its future chances of being selectedmay increase very quickly relative to action B and maytherefore emerge as the best action for that state. An-other important issue is the representation of consumeragents. The key questions here are 1) is there a gener-al approach for representing consumers which can beused in different applications, and 2) how do consum-ers learn from each other, market leaders, and othersources, and 3) how to incorporate consumers' memoryinto the system and how does that memory effect theirbehavior?


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Dr.MoutazKhouja is a Professor ofOperationsManagement in the Belk College of BusinessAdministration at the University of NorthCarolina at Charlotte. He received his PhD inOperations Management from Kent State Uni-versity. His publications have appeared in manyleading journals including Decision Sciences,IIE Transactions, European Journal of Opera-tional Research, International Journal of Pro-
duction Research, International Journal ofProduction Economics, Journal of the Opera-tional Research Society, and OMEGA.
http://www.econ.qmul.ac.uk/papers/doc/wp463.pdf

http://www.econ.qmul.ac.uk/papers/doc/wp463.pdf

http://www.internetworldstats.com/index.html

http://www.internetworldstats.com/index.html

of Orthopedic Informa1998, he joined Deloitte


Dr. Mirsad Hadzikadic joined the UNC

international conferenc

Charlotte faculty in 1987 after receiving hisPh.D. in Computer Science from SouthernMethodist University where he was a Fulb-right Scholar. In addition to publishing hisscholarship, he has made presentations atnational and international conferences, lead-ing information technology firms, and uni-versities. His research/scholarship activitieshave been primarily focused on three areas:data mining, cognitive science, and medicalinformatics. From 1991 to 1997, he served as

the Director of the Department of Medical Informatics and Department
tics of the Carolinas HealthCare System. Inand Touche Consulting Group as Manager ingration Service Line. He returned full time to the Health Systems Inte
the University in January 1999 to assume the chair position inComputer Science and serve as Director of the Software Solutions Lab.Currently, he is serving as the Dean of the College of Computing andInformatics.

Dr. Hari K. Rajagopalan earned his PhD inInformation Technology from the Universityof North Carolina at Charlotte in 2006. Apartfrom his PhD he also has an MBA in Financeand an MS in Computer Science. His researchinterests include locating emergency responsesystems, pricing of digital products andobsolescence in the high technology industry.His research has published in the EuropeanJournal of Operational Research, Computersand Operations Research and other journals.

He is also an active participant at INFORMS, Decision Sciences andEuropean Working Group in Transportation Meeting and Mini EUROConferences. He is currently the Assistant Professor in Management atFrancis Marion University.

Dr. Li-Shiang Tsay earned her M.S. and Ph.
D. degrees in Computer Science and Informa-tion Technology from the University of NorthCarolina at Charlotte in 2003 and 2005,respectively. Her research has been publishedin journals and books including Foundationsof Data Mining, Data Mining: Foundationsand Practice, Encyclopedia of Data Ware-housing and Mining, and Journal of Experi-mental and Theoretical Artificial Intelligence.Her research has also been presented at es including IEEE GrC, IEEE ICDM Work-IIS, SPIE, and ISMIS. She has served and is shop, IEEE/WIC/ACM,
serving on several Program Committees of international conferences,including ISMIS'06, IRMA'07, and RSEISP'07. She is an AssistantProfessor of Computer Science at Hampton University since January2006.

Documents

Application of complex adaptive systems to pricing of reproducible information goods