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1
Is Pirates’ Loss Consumers’ Gain? Software Piracy and Bundling Strategy
Xiong Zhang
School of Economics and Management, Beijing Jiao Tong University, Beijing, China
Wei T. Yue
Department of Information Systems, City University of Hong Kong, Hong Kong
Wendy Hui
Faculty of Business, Lingnan University, Hong Kong
Abstract
Unlike traditional software products which rely on product keys to manage software
piracy, Internet-enabled software services utilize the Internet infrastructure to
continuously manage and deter the problem. The emergence of Internet-enabled software
services have led to a different approach to piracy management. In this note, we consider
a firm’s bundling decision intertwining with its piracy deterrence strategy. Similar to
findings in the extant product bundling literature, we find that mixed bundling is the
optimal strategy when software piracy is not considered. This result can be extended to
the case where there is piracy but no piracy deterrence. Although pure bundling is not an
optimal strategy, it exhibits greater resiliency against the threat of piracy. The presence
of software piracy also leads to greater surplus for the legitimate users. When piracy
deterrence measures are used, pure bundling may be the optimal strategy due to a
combination of competition and cannibalization effects existing in mixed bundling. At
the same time, consumers may also enjoy greater surplus in pure bundling than in mixed
bundling, making pure bundling the preferred strategy for both the firm and the
consumers. The use of piracy deterring measures generally allows the firm to extract
surplus from consumers more effectively, giving rise to a “pirates’ loss is consumers’
loss” outcome. Our results provide insights into the emerging Internet-enabled software
service phenomenon; and contribute to the long established literature on piracy and
bundling.
Keywords: Software Product, Internet-Enabled Software Service, Bundling Strategy,
Software Piracy, Digital Rights Management
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Is Pirates’ Loss Consumers’ Gain? Software Piracy and Bundling Strategy
1. Introduction
Bundling and piracy are two pervasive phenomena in the software industry. However, few studies have
tied these two phenomena together. Software bundling has been studied under the realm of information
goods (Bakos & Brynjolfsson, 1999; Geng, Stinchcombe, & Whinston, 2005) which exhibit negligible
marginal costs and can be bundled rather easily without much overhead. Indeed, several studies have
noted that bundling information goods can be an optimal strategy for firms if the consumer valuation of
subsequent goods in the bundle does not decrease quickly (Geng et al., 2005). However, information
goods are known to be susceptible to piracy due to the ease of duplication. To mitigate the threat of
piracy, some studies have considered the use of pricing schedules (Sundararajan, 2004), digital rights
management (DRM) (Chen & Png, 2003; Sundararajan, 2004), versioning (Lahiri & Dey, 2013) and
sampling through piracy (Chellappa & Shivendu, 2005).
Following the emergence of the ubiquitous Internet-enabled technology, many firms have begun
to include Internet-enabled auxiliary components in their traditional software products. For example,
Microsoft offers standalone “on-premises” Microsoft Office as well as Office 365, which comprises
additional auxiliary software services. While software firms have long used bundling as a selling
strategy, such Internet-based components introduce new sets of measures for mitigating piracy. This is
because firms typically apply encryption as DRM to protect software distributed through DVD,
regardless of whether the content is a single software product or a software bundle. When software is
distributed through the Internet as a service, the firm can engage in authentication and continuous
monitoring of their software services. The linkage between the on-premises software and the Internet-
enabled components also means that the firm can extend the online DRM to the on-premises software.
For example, Microsoft had previously relied on Volume Licensing Keys (VLKs) to check for on-
premises software licensing. This scheme is being replaced increasingly by Multiple Activation Keys
(MAK) and Key Management Server (KMS) keys—a form of online DRM that facilitates periodic
licensing check1. The new development presents a novel intertwining effect on software bundling and
software piracy, thus underscoring the relevancy of this topic.
Gopal and Gupta (2010) were the first to study the interaction between bundling and piracy. They
put forward the idea that applying pure bundling can potentially mitigate piracy while increasing profit
at the same time. The intuition is that, when products are bundled collectively, it makes it easier for law
enforcement agencies to detect a pirated product, thus generating a greater deterrence effect. Therefore,
all things being equal, deterrence controls will be more effective. Integrating with demand pooling for
software products of different consumer valuations, bundling may allow the firm to earn higher profits
while decreasing the piracy level for all the products in the bundle. More interestingly, higher profits can
result when the piracy level for one of the products in the bundle is higher. These results provide an
important insight into the underlying mechanism that makes bundling a potential piracy deterrence
instrument. However, the study mainly considers consumers buying the products either individually
(pure components) or as a bundle, and does not analyze mixed bundling, i.e., providing consumers with
the option of buying products individually or as a bundle. In the literature, mixed bundling has often
been found to represent a supreme strategy in view of its ability in performing price discrimination (e.g.,
Adams & Yellen, 1976) and improving product cost sharing (Guiltinan, 1987). Thus, our aim here is to
examine which form of bundling (pure or mixed) is more desirable when piracy is present.
1 For more details, see https://technet.microsoft.com/en-us/library/ff793434.aspx; https://www.microsoft.com/en-
us/licensing/existing-customer/product-activation.aspx
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We follow the common approach taken in the bundling literature—a monopolist firm making the
choice of selling the software product and associated services using one of the following strategies: pure
components (the software product only), pure bundling (the bundle consisting of the software product
and the auxiliary Internet-enabled component only) and mixed bundling (both the software product and
the bundle). Specifically, we are interested in the following questions: 1. What are the effects of piracy
on the individual selling strategies? 2. How does piracy change the firm’s optimal bundling choice? 3.
What will be the resulting consumer welfare? Essentially, the different selling strategies involve different
combinations of the product and the bundle. The piracy levels are different depending on whether the
choice involves the product and/or the bundle. Our stylized models analytically compare the bundling
strategies under three scenarios: no piracy, piracy is present, and piracy is present while the firm applies
DRM.
Although this work draws much of its inspiration from Gopal and Gupta (2010), our objectives
and analysis approach are very different. First, rather than just illustrating the use of bundling as a piracy
deterrence strategy, we focus on examining whether the existent insights from the bundling literature
would change when piracy is introduced into the problem. Second, our work focuses on the emerging
Internet-enabled service phenomenon, so our problem scope is much more relevant under the new
Internet-enabled cloud-based context. Finally, we do not model the problem using the private goods club
approach, where piracy demand depends on the number of individuals sharing the individual product.
Instead, we follow the model setting of the traditional bundling literature, by presenting the pirated
product as simply another option under the consumer’s choice set, along with the legitimate product.
This approach makes our work more comparable to the extant bundling literature. As bundling models
are known to be notoriously difficult to solve mathematically, our approach also allows us to preserve
the mathematical tractability and thus arrive at more conclusive results.
Indeed, when one does not consider piracy, mixed bundling is generally found to be the superior
strategy. Pure bundling offers only one bundle to the market. The firm needs to set a price to extract as
much surplus from the consumers as possible, while making sure that the demand for the bundle is as
large as possible. The two objectives are in conflict with each other. The optimal bundle price is where
both surplus extraction and the quantity demanded are optimally balanced. With mixed bundling, the
firm can increase the bundle price to extract more surplus from the high type (bundle) consumers, while
at the same time set the product price at a reasonable level to keep the low type (product) consumers.
Hence, the price discrimination allows the firm to address the conflicting objectives more effectively.
When piracy is considered and the firm does not apply DRM, the firm earns lower profits under
all strategies. Although mixed bundling is still the optimal strategy, pure bundling is more resilient to
the threat of piracy, i.e., the decline in profits is less significant. The presence of pirated product in the
market, in essence, creates a “competition” effect to the legitimate product and bundle, thus lowering
the firm’s profits. The effect on profitability is more prominent under mixed bundling because both
segments (the product and the bundle) are affected by piracy, whereas only the bundle segment is
affected under pure bundling. We find that piracy generally increases consumer surplus while bundling
results in a “pirates’ gain is consumers’ gain” outcome at the expense of the firm. Note that this result
holds even if we do not consider the surplus gained by pirates from consuming the pirated product.
Incidentally, Vernik, Purohit and Desai (2011) find the presence of piracy may also lead to higher
consumer surplus due to increased competition (hence lower prices) between different sellers. In our
context, piracy creates a direct competition effect between the authentic and the pirated products.
When DRM is considered, the firm earns higher profits under both pure and mixed bundling.
Compared to the case with no piracy deterrence, DRM increases the piracy cost and allows the firm to
“re-extract” consumer surplus by raising prices under both bundling strategies; it also increases the
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bundle demand for pure bundling. Thus, the introduction of DRM leads to a “pirates’ loss is consumers’
loss” outcome. Contrary to conventional wisdom, pure bundling can turn out to be the optimal strategy.
The intuition is that pirated software can be a close substitute to the product in mixed bundling. The
competition effect forces the firm to set a lower product price. However, a lower product price can
cannibalize the demand of the bundle. If the competition and the cannibalization effects are large and
the online DRM is effective, pure bundling can be more profitable. This result is in contrast to previous
findings, albeit under different modeling settings2, that not applying DRM could lead to higher profits
for the firm due to competition induced price increases (Jain, 2008; Vernik et al., 2011). In our work,
pure bundling does not eliminate piracy completely and can result in a higher consumer surplus than
mixed bundling. Interestingly, this situation can co-exist with pure bundling being the optimal strategy,
due to the competition and cannibalization effects in mixed bundling.
2. Literature Review
Tracing back to the 1960s, one finds an extensive line of studies examining product bundling. The
optimal bundling strategy has been at the center of discussions. The following are some major findings:
mixed bundling has been found to be an optimal strategy under general settings (Adams & Yellen, 1976;
McAfee, McMillan, & Whinston, 1989; Schmalensee, 1984; Stremersch & Tellis, 2002); pure bundling
is the optimal strategy when product values are negatively correlated (Adams & Yellen, 1976; Salinger,
1995); the pure components strategy is the least favorable when the marginal cost is low and the mean
valuation of the product is high (Schmalensee, 1984). When pure bundling and mixed bundling are
compared, mixed bundling is more profitable if the consumers have substantial differences
(heterogeneity) in the valuation of the second product (Pierce & Winter, 1996). Recently, some studies
have extended the bundling studies by incorporating other elements, such as network externalities effect
(Pang & Etzion, 2012; Prasad, Venkatesh, & Mahajan, 2010) and capacity limit (Cao, Stecke, & Zhang,
2015). In this note, we extend the bundling literature by considering piracy, which is especially relevant
to information goods.
Our work is also relevant to the stream of studies that examines the economic impact on the use
of piracy mitigation measures on information goods. Gopal and Sanders (1997) investigate the use of
preventive or deterrent controls to fight against piracy and find that the latter approach can lead to higher
profits for the firm. Sundararajan (2004) finds that the ability of the firm to conduct price discrimination
will reduce the protection level of DRM. Chen and Png (2003) find that a tax on copying will induce the
firm to increase price and reduce DRM enforcement, which in equilibrium, will propel the firm to rely
more on lower price rather than DRM to mitigate piracy. Lahiri and Dey (2013) find that the presence
of piracy may increase the incentive for the firm to invest in product quality to differentiate from the
pirated product. Some other studies have found that the presence of piracy can lead to a higher profit for
the firm. For instance, allowing sampling of information goods through piracy can be the optimal
strategy for the firm (Chellappa & Shivendu, 2005). Others have found that the externality effect
generated through piracy makes piracy “beneficial” to the firm (e.g., Conner & Rumelt, 1991). In the
digital entertainment context, Vernik, Purohit and Desai (2011) find the elimination of DRM may reduce
piracy because of competition-induced price declines. However, this reduction in piracy does not
guarantee higher profits for the firm. Our work is related to the studies mentioned above by specifically
considering how piracy affects sales and how the firm uses DRM to tackle piracy by reducing the utility
of the pirated product.
2 Under a duopoly setting, Jain (2008) finds that the two firms choose to remove DRM, which leads to the outcome of less
competition and higher price. Purohit and Desai (2011) consider the sale of information goods (music) throgh either the retail
channel or online channel. The online channel is in direct competition with the priated product. Moeoever, DRM can only be
applied to the online channel. Removing DRM on donwloads (online channel) may lead to price increase and hihger profits.
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3. Model Setting
In this section, we present the general setting of our models. We assume that an individual’s reservation
value for the software product (Product) is homogeneous and is denoted by 𝑟, which is a constant. The
individual’s reservation for the software bundle (Bundle) is given by 𝑟 + 𝜃𝑏, where 𝜃𝑏 is simply the net
additive value of the Bundle compared to that of the Product. It is a random variable 𝜃𝑏 ∈ [0, �̅�𝑏] with
density 𝑓(𝜃𝑏).
The goods of interest include (1) the “on-premises” software product and (2) an associated
auxiliary cloud component, which cannot be sold as a standalone good3. We assume the marginal cost
for the Product is zero and the marginal cost for the Bundle is a small but non-negligible constant. At
the consumer end, piracy does not lead to any product quality degradation4. If the firm does not use
DRM, the piracy cost is negligible. If DRM is used, the piracy cost is increased but the effectiveness of
the on-premises DRM and the online DRM can be different. Each consumer will only buy either the
Product or the Bundle. On the other hand, the firm will offer consumers one of the following options:
Product only (pure components), Bundle only (pure bundling) or both the Product and the Bundle (mixed
bundling). We denote these options as PC, PB and MB, respectively. We present these models in the
next three subsections. We first present the base model (Model 1), where both piracy and DRM are not
modeled. In Model 2, we assume that there is a pirated version of the product. In Model 3, the firm can
implement DRM.
3.1 Model 1: No Piracy, No DRM
In Pure Component strategy, the firm would set its price 𝑝𝑝∗ = 𝑟. All consumers will buy the Product.
With a normalized population of one, the firm’s profit is 𝑟, assuming zero marginal cost of production
for software (Bakos & Brynjolfsson, 1999). The total consumer surplus is 𝐶𝑆∗ = 𝑟 − 𝑟 = 0. Thus, an
increase in 𝑟 increases the Product price and the firm’s profit, but has no effect in the total consumer
surplus.
In Pure Bundling strategy, the firm offers only the Bundle at the price as 𝑝𝑏. An individual buying
the Bundle must satisfy 𝑏 > 𝑝𝑏 − 𝑟. The firm’s profit per Bundle sale is 𝑝𝑏 − 𝑐, where 𝑐 is the cost of
providing a Bundle. The firm’s total profit is 𝜋 = (𝑝𝑏 − 𝑐)[1 − 𝐹(𝑝𝑏 − 𝑟)]. The first order condition is 𝑑𝜋
𝑑𝑝𝑏= 1 − 𝐹(𝑝𝑏 − 𝑟) − (𝑝𝑏 − 𝑐)𝑓(𝑝𝑏 − 𝑟) = 0, or
𝑓(𝑝𝑏−𝑟)
1−𝐹(𝑝𝑏−𝑟)=
1
𝑝𝑏−𝑐. (1)
PB is more profitable than PC if and only if 𝑟 < (𝑝𝑏∗ − 𝑐)[1 − 𝐹(𝑝𝑏
∗ − 𝑟)]. We assume the above
condition, 𝑟 < (𝑝𝑏∗ − 𝑐)[1 − 𝐹(𝑝𝑏
∗ − 𝑟)], to be true. In other words, 𝑐 is small and the proportion of
people valuing the additional cloud service in Bundle reasonably highly is sufficiently large.
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3 This type of mixed bundling strategy is referred as MB-1 strategy where only {product 1} and {product 1, product 2} are
offered (Prasad et al., 2010). 4 Literature has assumed the application of DRM affects product quality. For example, Sundararajan (2004) assumes the
application of DRM will reduce the quality of the pirated product. Vernik, Purohit and Desai (2011) find that DRM reduces
the utility to legal users consuming digital content.
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𝑓(𝑥)
1−𝐹(𝑥)=
1
𝑥+𝑟−𝑐, (2)
w
h
e
r
e
≡𝑝𝑏−𝑟. Let the solution to Equation 𝑓𝑥1−𝐹𝑥=1𝑥+𝑟−𝑐, (2) be
𝑥∗. An increase in 𝑟 tends to shift the right hand side towards the left, and thus decrease 𝑥∗. If 𝑥∗ is
decreased, 𝐹(𝑥∗) is also decreased and, since 1 − 𝐹(𝑥∗) , which is exactly the Bundle demand, is
increased. Since both the price and demand increases with 𝑟, the firm also earns higher profits with a
higher 𝑟.
Lemma 1a (No piracy, No DRM; Pure Bundling): An increase in 𝑟 increases 𝑝𝑏∗5, the equilibrium demand
1 − 𝐹(𝑝𝑏∗ − 𝑟) and the equilibrium profit (𝑝𝑏
∗ − 𝑐)[1 − 𝐹(𝑝𝑏∗ − 𝑟)].
We now consider the total consumer surplus: 𝐶𝑆∗ = ∫ (𝑟 + 𝜃𝑏 − 𝑝𝑏∗ )𝑓(𝜃𝑏)
�̅�𝑏
𝑝𝑏∗ −𝑟
𝑑𝜃𝑏. The lower
limit 𝑝𝑏∗ − 𝑟, which is 𝑥∗, decreases with r, while the integral (𝑟 + 𝜃𝑏 − 𝑝𝑏
∗ )𝑓(𝜃𝑏) increases with r. This
implies that the consumer surplus grows with 𝑟.
Lemma 1b (No piracy, No DRM; Pure Bundling): The equilibrium total consumer surplus increases with 𝑟.
Lemma 1a suggests that an increase in the valuation of the software product, 𝑟, leads to an
increase in the Bundle price, which increases the monopolistic firm’s profit. However, according to
Lemma 1b, the increase in valuation is not completely transferred to the firm; the consumers also share
part of the value increase.
In Mixed Bundling strategy, an individual has the choice to buy the Product or the Bundle. An
individual buying the Product must satisfy 𝑟 > 𝑝𝑝 and 𝑏 < 𝑝𝑏 − 𝑝𝑝. We assume the first condition to
be true. An individual buying the Bundle must satisfy 𝑏 > 𝑝𝑏 − 𝑟 and 𝑏 > 𝑝𝑏 − 𝑝𝑝.
We assume that the Bundle can be more profitable than the Product, i.e., �̅�𝑏 − 𝑐 > 0, the value-
added by the cloud service is larger than the cost of offering the cloud service for at least some
consumers. The firm’s total profit is 𝜋 = 𝑝𝑝𝐹(𝑝𝑏 − 𝑝𝑝) + (𝑝𝑏 − 𝑐)[1 − 𝐹(𝑝𝑏 − 𝑝𝑝)]. Differentiating
the above equation with respect to 𝑝𝑝 and 𝑝𝑏, we arrive at the following first order conditions:
𝑑𝜋
𝑑𝑝𝑝= 𝐹(𝑝𝑏 − 𝑝𝑝) + (𝑝𝑏 − 𝑐 − 𝑝𝑝)𝑓(𝑝𝑏 − 𝑝𝑝) = 0
𝑑𝜋
𝑑𝑝𝑏= [1 − 𝐹(𝑝𝑏 − 𝑝𝑝)] − (𝑝𝑏 − 𝑐 − 𝑝𝑝)𝑓(𝑝𝑏 − 𝑝𝑝) = 0
If all individuals are willing to buy the Product in the first place, the firm would not offer Bundle unless
it is more profitable than Product, i.e., 𝑝𝑏 − 𝑐 − 𝑝𝑝 > 0. However, if Bundle is more profitable than
Product, we have 𝑑𝜋
𝑑𝑝𝑝> 0. Hence, the firm will set 𝑝𝑝 as high as possible, i.e., 𝑝𝑝
∗ = 𝑟. The firm’s profit
maximization problem then becomes:
max𝑝𝑏𝑟𝐹(𝑝𝑏 − 𝑟) + (𝑝𝑏 − 𝑐)[1 − 𝐹(𝑝𝑏 − 𝑟)]
s.t. 𝑝𝑏 − 𝑐 − 𝑟 ≥ 0
5 This is apart from the special case of Exponential 𝜃𝑏 because the hazard function of Exponential is just a horizontal straight
line. An increase or decrease in the parameter of the function shifts the function to the left or to the right on the Cartesian
plane. If the function is a horizontal straight line, shifting horizontally makes no difference.
7
Lemma 2a (No piracy, No DRM; Mixed Bundling): An increase in 𝑟 increases 𝑝𝑝∗ = 𝑟 and 𝑝𝑏
∗ , but does not
affect the equilibrium Product demand 𝐹(𝑝𝑏∗ − 𝑟) or the equilibrium Bundle demand 1 − 𝐹(𝑝𝑏
∗ − 𝑟). As a
result, the firm’s equilibrium profit is increased.
Those buying the Product get zero surplus, while those buying the Bundle at least zero surplus.
The total consumer surplus is 𝐶𝑆∗ = −𝑥∗ + �̅�𝑏 − ∫ 𝐹(𝜃𝑏)�̅�𝑏
𝑥∗ 𝑑𝜃𝑏, where 𝑥∗ ≡ 𝑝𝑏∗ − 𝑟 is the consumer
who is indifferent between buying the Product and buying the Bundle.
Lemma 2b (No piracy, No DRM; Mixed Bundling): The equilibrium total consumer surplus is not affected by
an increase in r.
According to the proof of Lemma 2a, the position of the marginal consumer does not change
with r. With increasing 𝑟, those who buy the Product will continue to get zero surplus because the
monopolistic firm’s tendency to set the Product’s price to r. Interestingly, those buying the Bundle do
not enjoy an increase in surplus either. This is because the firm would be able to increase the price of
Bundle by an amount equal to the increase in 𝑟. This result contrasts that of Lemma 1a in the previous
subsection and highlights the superiority of MB in extracting surplus from a heterogeneous consumer
market.
Lemma 2b suggests that the relative reliance on the Product versus the Bundle in terms of sales
quantity does not change because of 𝑟. The increase in 𝑟 allows the firm to raise the prices of both the
Product and the Bundle. A raise in price in both goods does not alter the relative attractiveness of either
goods. Hence, the demand for the Bundle is not affected. The main driver of the increase in profitability
is the increase in prices rather than demand. We now summarize the results from the three bundling
strategies.
Proposition 1 (No piracy, No DRM):
(i). The firm’s optimal strategy is to offer both versions, i.e., {Product, Bundle}.
(ii). The equilibrium total consumer surplus is higher in PB than in MB.
This result is consistent with extant studies in that MB allows the firm to extract the most surplus
(Salinger, 1995; Schmalensee, 1984). Furthermore, if the cost of cloud services is sufficiently low, the
firm would prefer PB over PC. This result is consistent with Venkatesh and Mahajan (2009). In MB, the
Bundle’s price is higher than that in PB, but the Bundle demand is lower. Thus, the total consumer
surplus of Bundle buyers is lower in MB. Furthermore, the total consumer surplus of Product buyers is
zero in MB. Therefore, in this benchmark setting, the total consumer surplus in PB is higher than in MB.
The consumer surplus associated with PC is the lowest.
3.2 Model 2: With Piracy but No DRM
We now consider that piracy is present in the market. We assume that a pirated copy of the Product is of
the same quality as that of the legitimate Product. Since the auxiliary service component is not sold
separately, we assume that piracy of the Bundle is not possible (although consumers can still pirate the
Product component of the bundle). In the next subsection, DRM will impose a cost (negative value) for
the consumers who consume the pirated product.
We first consider the Pure Component strategy. Since the piracy cost is assumed to be less than
the price of the Product, all consumers will use the pirated software. In reality there could be ethical
users who refuse to use pirated software, but the point of this section is to show the worst-case scenario
that acts as a baseline for comparison. Hence, all consumers choose piracy. The firm’s profit is 0. The
total consumer surplus is 0 for legitimate users, while the total consumer surplus is 𝑟 for all users
(including both legitimate users and piracy users).
8
In Pure Bundling strategy, an individual buying the Bundle must satisfy 𝑏 > 𝑝𝑏 − 𝑟 and 𝑏 >𝑝𝑏. The firm’s profit is 𝜋 = (𝑝𝑏 − 𝑐)[1 − 𝐹(𝑝𝑏)].
In the following analysis, we use subscripts to denote the bundling strategy (PC, PB or MB) of
the respective model as (1, 2, or 3). For example, 𝑝𝑏,𝑝𝑏,2 denote the Bundle price in pure bundling in
Model 2.
Lemma 3 (With piracy but No DRM; Pure Bundling): The presence of piracy decreases the optimal Bundle
price in PB, decreases the equilibrium Bundle demand, increases the equilibrium piracy demand and decreases
the equilibrium profit. If we include the welfare of pirates, the presence of piracy would increase the equilibrium
total consumer surplus. If we do not include the welfare of pirates, the presence of piracy would increase the
equilibrium total consumer surplus if and only if 𝑟𝐹(𝑝𝑏,𝑝𝑏,2∗ ) < 𝑝𝑏,𝑝𝑏,1
∗ − 𝑝𝑏,𝑝𝑏,2∗ + ∫ 𝐹(𝜃𝑏)
𝑝𝑏,𝑝𝑏,2∗
𝑝𝑏,𝑝𝑏,1∗ −𝑟
𝑑𝜃𝑏.
The surplus per consumer must increase because every legitimate user now enjoys a lower
Bundle price. The total consumer surplus seems to be decreased under some conditions simply because
the welfare of pirates is not included in the calculation.
In Mixed Bundling strategy, an individual buying the Bundle must satisfy 𝑏 > 𝑝𝑏 − 𝑟, 𝑏 >𝑝𝑏 − 𝑝𝑝 and 𝑏 > 𝑝𝑏. No individual will buy the Product. The firm’s profit is 𝜋 = (𝑝𝑏 − 𝑐)[1 − 𝐹(𝑝𝑏)]. Thus, the mixed bundling problem is now reduced to the pure bundling problem.
Lemma 4 (With Piracy and No DRM; Mixed Bundling): All Product buyers switch to piracy. The presence
of piracy decreases 𝑝𝑏∗ , but does not affect the equilibrium Bundle demand, decreases the equilibrium profit. If
we include the welfare of pirates, the presence of piracy would increase the equilibrium total consumer surplus.
If we do not include the welfare of pirates, the presence of piracy would increase the equilibrium total consumer
surplus if and only if 𝑟𝐹(𝑝𝑏,𝑚𝑏,2∗ ) < 𝑝𝑏,𝑚𝑏,1
∗ − 𝑝𝑏,𝑚𝑏,2∗ + ∫ 𝐹(𝜃𝑏)
𝑝𝑏,𝑚𝑏,2∗
𝑝𝑏,𝑚𝑏,1∗ −𝑟
𝑑𝜃𝑏.
With piracy, MB is reduced to PB. This leads to the same Bundle price 𝑝𝑏,𝑝𝑏,2∗ = 𝑝𝑏,𝑚𝑏,2
∗ . In other
words, the difference in Bundle price due to piracy is less for PB than for MB. This also means that the
left hand side of the inequalities in both lemmas are the same. On the right hand side, given that the
difference in price is less for PB than for MB, the right hand side of Lemma 3 is smaller than the right
hand side of Lemma 4. In other words, the condition is more easily satisfied under MB, meaning that the
presence of piracy is more likely to result in a greater increase in total consumer surplus under MB.
Proposition 2 (With Piracy but No DRM):
(i). Regardless of the selling strategy adopted, piracy negatively affects profitability. However, PB shows
greater resilience against the threat of piracy in terms of percentage change in profitability.
(ii). If we do not consider the surplus from pirates, the presence of piracy is more likely to increase the total
consumer surplus under MB.
We find that the firm will always be worse off regardless of the bundling strategy. This effect is
stronger under MB because the Product is in direct competition with the pirated product. Therefore, we
also see that the consumers are more likely to enjoy higher gains in surplus under MB. The presence of
piracy can be the “friend’ of the consumers. In terms of the benefit of piracy, previous studies have found
that piracy may allow the would-be consumer to sample the product and lead to greater number of
consumers buying the product (Chellappa & Shivendu, 2005).
3.3 Model 3: With Piracy and DRM
We assume the effectiveness of DRM in Product and that in Bundle is different. In Pure Component
strategy, we assume that that DRM increases the piracy cost to 𝜇. An individual buying the Product must
9
satisfy 𝑟 > 𝑝𝑝 and 𝑝𝑝 ≤ 𝜇. It is obvious that the firm would set the Product price to 𝜇 and earn a profit
of 𝜇 from all consumers. The total consumer surplus is 𝑟 − 𝜇 . Therefore, 𝑝𝑝∗ = 𝜇 , 𝑑𝑝
∗ = 1, 𝜋∗ = 𝜇 ,
and 𝐶𝑆∗ = 𝑟 − 𝜇.
Lemma 5 (With piracy and DRM; Pure Component): In the presence of piracy, 𝜇 increases the optimal
Product price and the equilibrium profit for PC; it decreases the equilibrium total consumer surplus as well, if
pirates’ welfare is included. All consumers would choose the Product, i.e., no one would choose piracy.
Contrary to the case where DRM is not considered, the introduction of DRM allows the firm to
set a higher price when the cost imposed on the pirates are higher. At the same time, the firm sets the
price such that all consumers would choose the Product over the pirated product.
In Pure Bundling strategy, we assume that DRM in Bundle increases the piracy cost by 𝑡. An
individual buying the Bundle must satisfy 𝑏 > 𝑝𝑏 − 𝑟 and 𝑏 > 𝑝𝑏 − 𝑡.
Piracy is completely eliminated if t is sufficiently large such that t ≥ r. To allow for the analysis
of the more general case where piracy threat continues to exist, we assume 𝑡 ≤ 𝑟. Hence, the firm’s
total profit is 𝜋 = (𝑝𝑏 − 𝑐)[1 − 𝐹(𝑝𝑏 − 𝑡)]. The first order condition with respect to 𝑝𝑏 is 𝑑𝜋
𝑑𝑝𝑏= 1 −
𝐹(𝑝𝑏 − 𝑡) − (𝑝𝑏 − 𝑐)𝑓(𝑝𝑏 − 𝑡) = 0, or
𝑓(𝑝𝑏−𝑡)
1−𝐹(𝑝𝑏−𝑡)=
1
𝑝𝑏−𝑐. (3)
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Lemma 6: In the presence of piracy, 𝑡 increases 𝑝𝑏∗ , increases the equilibrium Bundle demand 1 − 𝐹(𝑝𝑏
∗ − 𝑡),
decreases the equilibrium piracy demand 𝐹(𝑝𝑏∗ − 𝑡), and increases the firm’s equilibrium profit. If we include
the welfare of pirates, 𝑡 decreases the equilibrium total consumer surplus. If we do not include the welfare of
pirates, an increase in 𝑡 would increase the equilibrium total consumer surplus if and only if
𝑟𝐹(𝑝𝑏,𝑝𝑏,2∗ ) − (𝑟 − 𝑡)𝐹(𝑝𝑏,𝑝𝑏,3
∗ − 𝑡) > 𝑝𝑏,𝑝𝑏,3∗ − 𝑝𝑏,𝑝𝑏,2
∗ + ∫ 𝐹(𝜃𝑏)𝑝𝑏,𝑝𝑏,2
∗
𝑝𝑏,𝑝𝑏,3∗ −𝑡
𝑑𝜃𝑏.
Just as in the PC case, when the firm is able to impose higher costs on pirates with DRM, the
firm’s profit can be protected with a higher price. In the meantime, the firm can decease the piracy
demand; some consumers may choose to consume the Bundle legitimately. In general, increasing the
piracy cost (higher 𝑡) will increase 𝑝𝑏,𝑝𝑏,3∗ and increase the Bundle demand. In such a case, the condition
in Lemma 6 is more likely to be satisfied, in which the total consumer surplus is more likely to increase.
When MB is adopted, the Product is still available for sale as a standalone product. For this
standalone product, product keys are typically used. For the Bundle offered, the firm can use the regular
license check approach as described above. Thus, a person considering piracy can consider pirating the
product in the Bundle or the Product as a standalone good. The surplus from piracy is therefore 𝑟 − 𝑡 or
𝑟 − 𝜇, whichever is larger. Denote min[𝜇, 𝑡] as 𝜇′. An individual buying the Bundle must satisfy 𝑏 >𝑝𝑏 − 𝑟 and 𝑏 > 𝑝𝑏 − 𝜇′ . An individual buying the Product must satisfy 𝑟 > 𝑝𝑝 and 𝑝𝑝 < 𝜇′ . The
firm’s optimal Product price is 𝑝𝑝 = 𝜇′ . The firm’s profit is 𝜋 = 𝜇′𝐹(𝑝𝑏 − 𝜇′) + (𝑝𝑏 − 𝑐)[1 −
𝐹(𝑝𝑏 − 𝜇′)].
10
Lemma 7 (With piracy and DRM; Mixed Bundling): An increase in 𝜇′ increases 𝑝𝑏∗ . An increase in 𝜇′ does
not affect the equilibrium Product demand 𝐹(𝑝𝑏∗ − 𝜇′) or the equilibrium Bundle demand 1 − 𝐹(𝑝𝑏
∗ − 𝜇′). The
equilibrium piracy demand is 0. 𝜇′ increases the equilibrium profit and decreases the equilibrium total
consumer surplus.
As with PC and PB, we see that the use of DRM will increase the firm’s profit more when a
greater piracy cost is imposed. Moreover, unlike with the PB case, the firm can remove piracy completely
under MB and the total consumer surplus will further decrease through stricter DRM. The resulting
decrease in the total consumer surplus can be easily verified since an increase in 𝜇′ increases 𝑝𝑏∗ , but
does not change 𝑝𝑏∗ − 𝜇′.
In the case of no DRM, we find that PB can never be better than the MB strategy. However, when
DRM is considered, the firm may make higher profit with PB.
Proposition 3 (With piracy and DRM): PB will be more profitable than MB if and only if
(𝑝𝑏,𝑝𝑏,3∗ − 𝑐)[1 − 𝐹(𝑝𝑏,𝑝𝑏,3
∗ − 𝑡)] > 𝜇′𝐹(𝑝𝑏,𝑚𝑏,3∗ − 𝜇′) + (𝑝𝑏,𝑚𝑏,3
∗ − 𝑐)[1 − 𝐹(𝑝𝑏,𝑚𝑏,3∗ − 𝜇′)].
A necessary condition is that 𝑡 > 𝜇.
Intuitively, when 𝑡 > 𝜇, 𝜇′ = 𝜇, piracy is easier in MB than in PB. The pirated software is a
close substitute to the Product. The competition effect forces the firm to set a low Product price. On the
other hand, a low Product price can cannibalize the Bundle. If the two effects are large, PB can be more
profitable than MB. Furthermore, a higher 𝑡 would lead to a higher 𝑝𝑏,𝑝𝑏,3∗ and lower 𝐹(𝑝𝑏,𝑝𝑏,3
∗ − 𝑡);
thus, the left hand side of the above inequality in Proposition 3 will be higher. The right hand side will
be the same since μ does not change. Therefore, the condition will be more easily satisfied. If 𝑡 does not
change, but 𝜇 decreases, 𝜇′ will be lower, 𝑝𝑏,𝑚𝑏,3∗ − 𝑐 will be lower and so the right hand side will be
lower, and this condition will also be more easily satisfied. In other words, the piracy curbing effect is
higher under PB, either through a higher 𝑡 or a lower 𝜇. Thus, an important implication of the analysis
in this subsection is that PB does not need to eliminate piracy completely for it to be the optimal bundling
strategy for the firm. If it makes piracy significantly more difficult or inconvenient, PB can be more
profitable than MB.
Lemma 8 (With piracy and DRM): MB is more affected by the effectiveness of DRM than PB.
Since the success of MB is more dependent on the effectiveness of DRM, the profitability
advantage of MB over PB decreases with increasing ease of piracy. Now, we compare the consumer
surplus between PB and MB.
Proposition 4 (With piracy and DRM): PB could be the optimal strategy from the perspectives of both firms
and consumers when
(i). Surplus from both legitimate users and pirates (𝑝𝑏,𝑚𝑏,3∗ − 𝜇′ − 𝑐)𝐹(𝑝𝑏,𝑚𝑏,3
∗ − 𝜇′) −
(𝑝𝑏,𝑝𝑏∗ − 𝑐)𝐹(𝑝𝑏,𝑝𝑏,3
∗ − 𝑡) > 𝑝𝑏,𝑚𝑏,3∗ − 𝑝𝑏,𝑝𝑏,3
∗ > ∫ 𝐹(𝜃𝑏)𝑝𝑏,𝑚𝑏,3
∗ −𝜇′
𝑝𝑏,𝑝𝑏,3∗ −𝑡
𝑑𝜃𝑏.
(ii). Surplus form legitimate users (𝑝𝑏,𝑚𝑏,3∗ − 𝜇′ − 𝑐)𝐹(𝑝𝑏,𝑚𝑏,3
∗ − 𝜇′) − (𝑝𝑏,𝑝𝑏,3∗ − 𝑐)𝐹(𝑝𝑏,𝑝𝑏,3
∗ − 𝑡) >
𝑝𝑏,𝑚𝑏,3∗ − 𝑝𝑏,𝑝𝑏,3
∗ > ∫ 𝐹(𝜃𝑏)𝑝𝑏,𝑚𝑏,3
∗ −𝜇′
𝑝𝑏,𝑝𝑏,3∗ −𝑡
𝑑𝜃𝑏 + 𝐾,where 𝐾 = (𝑟 − 𝑡)𝐹(𝑝𝑏,𝑝𝑏,3∗ − 𝑡) is the surplus from
piracy users in pure bundling.
In Proposition 3, we see that with strong competition and cannibalization effects, PB would be
the better strategy than MB for the firm. From the perspective of the consumers, due to the competition
effect, consumers enjoy a high surplus when buying the Product under MB. However, compared to PB,
11
Bundle buyers get a lower surplus in MB because the Bundle price is higher in MB than in PB. Thus,
when the Bundle demand in PB is much higher than the Bundle demand in MB, and the Bundle price is
much lower in PB than in MB, the total consumer surplus will be higher in PB than in MB. Hence, the
situation where the total consumer surplus may be highest for PB can co-exist with pure bundling being
the firm’s optimal strategy. The intuition is similar when we consider the surplus from both legitimate
users and pirates or just the legitimate users. The only difference is that Proposition 4 (ii) is a more
stringent condition given we only consider the surplus from legitimate users.
4. Discussion and Conclusion
The emergence of Internet-enabled software services has added to the relevancy of studying the software
piracy problem together with the bundling strategy. Based on a general model, our work has sought to
contribute to two well-established but disconnected streams of research. Prior studies have found that
network externality can make pure bundling more profitable (Prasad et al., 2010). Moreover, pure
components may be optimal when the marginal cost is high (Venkatesh & Kamakura, 2003). In this
note, we have added another dimension to the discussion; i.e., with piracy and DRM considered, pure
bundling, instead of mixed bundling can be the optimal strategy. The results have generally confirmed
Gopal and Gupta’s (2010) finding that pure bundling can be a desirable strategy when piracy is
considered. However, we have derived our results based on comparisons to mixed bundling instead of
pure components, which is a more stringent requirement.
Our note contributes to the overall discussion on piracy and bundling of information goods. Pure
bundling strategy has been regarded to give firms with market power an unfair competitive advantage
(Kobayashi, 2005). With limited component options, consumers have argued that they are “forced” to
buy bundles with components that they may not need. For example, many Adobe users complained when
Adobe switched to a model of exclusively providing service based software subscription6 (Shankland,
2013). In our stylized setting, we provide an alternative perspective that, taking into consideration piracy
and DRM, pure bundling may be a desirable outcome for both the firms and the consumers. Moreover,
although we use software industry as the focus of our discussion, given that more and more products
have Internet-enabled extensions (such as toys, cars, home appliances), our results may be extended to
other products where the piracy or counterfeiting applies.
Motivated by the phenomenon of Internet-enabled service, the objective of this note has been to
study the intertwining effects that exist in software bundling and software piracy. With a view to
maintaining mathematical tractability, many potential relevant issues have been abstracted away in our
stylized models. For instance, considerations of industry competition, such as under a duopoly setting,
may provide additional interesting insights to the topic. Moreover, part of the excitement about the
Internet-enabled service phenomena is the potential to extend software functionalities to the massive
Internet-enabled collaborative environment, in which network externality may play an important role. It
could be interesting to consider these issues in future studies.
Acknowledgement
This work was partially supported by grants from National Natural Science Foundation of China (Grant
71801014) and Beijing Social Science Foundation (Grant 17GLC069).
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