Software Anti-piracy and Pricing in a Competitive
Environment: a Game Theoretic Analysis
We study a problem of two software firms competing on price in a market where consumers
can choose between purchasing and pirating software. Firms invest in anti-piracy effort to
prevent software piracy. We study both the monopolistic case and the duopolistic one. We
obtain several interesting results under competition. In particular, when the network effect
increases, each firm adopts a stronger anti-piracy measure only if the cross-effect of antipiracy effort on the other firm is high. If both cross-effect and network effect are low , each
firm invests more in anti-piracy with an increase in network effect. Our results show the
importance of considering competition and cross effect when a firm designs an anti-piracy
policy.
Key words: Software piracy, Anti-piracy effort, Cross effect, Game theory
1.
Introduction
Software piracy, the unauthorized copying, distribution, or use of software products, is by far
the biggest problem facing the software industry. According to a global recent survey by The
Software Alliance (also known as BSA) (2014), 43% of the PC software was installed without
without proper licensing in 2013; the total commercial value of the unlicensed installation
approximated to $62.7 billion globally in 2013. In addition, the use of pirated software can
increase security threats, interfere with existing systems and cause system malfunction and
downtime. A recent survey by IDC shows that the annual cost to enterprises for dealing
with malware from pirated software can reach $114 billion (IDC 2013). Pirated software can
be obtained from various sources. According to the same survey (IDC 2013), 45% pirated
software is from online websites and P2P network and 21% from street market.
Facing the threat of software piracy to their revenue and business growth, many companies exert great effort against software piracy.
Software giant Microsoft has built a
worldwide anti-piracy team which works closely with law enforcement agents to support
criminal prosecutions. Microsoft is estimated to spend more than $10 million a year on
its intelligence-gathering operations for anti-piracy and another $200 million on developing anti-piracy technology (New York Times 2010). To reduce the chances of accessing pirated content intentionally or unintentionally by Internet users, Security software
company McAfee has both patented and developed various technologies that detect and
block pirated material from any websites when visited by users (Burgess 2013, Ernesto
2013). Also, many software firms and industrial organizations have links on their websites to encourage the public to report piracy against their products. Software & Information Industry Association (SIIA) offers rewards up to $1 million for reporting piracy
activities (siia.net 2015). BSA also has such reward program to combat software piracy
(https://reporting.bsa.org/r/report/usa/rewardsconditions.aspx).
1.1
Problem Description
We study a problem of two software providers who sell competing products in a consumer
market. Pirated software products are available on the market for free, but consumers incur
cost for using such pirated products. Consumers have heterogeneous valuations for these two
products. They choose either a legitimate product or a pirated version to maximize their
own utilities which also include the contribution of network effect: the more consumers use
2
a particular software product (pirated or purchased), the more valuable this product is to
its users.
A software provider can exert anti-piracy effort which increase the cost of using pirated
software. In our problem, we also consider cross effect of anti-piracy effort. When a provider
exerts anti-piracy effort, not only the cost of using its own pirated software increases, but
the cost of using the pirate version of its competitor’s product will also increase. Cross effect
arises for several reasons. First, anti-piracy technology such as the one developed by McAfee
usually block the access to pirated products in general, including both its own product and
a competitor’s product. Also anti-piracy campaign through shutting down illegal websites
and user education makes pirated software less available and thus more costly to obtain and
use. Software anti-piracy through legal enforcement and raid can increase the chance of users
being caught of using any pirate software, leading to a higher cost of using pirate software
overall.
In the past studies, it is commonly assumed that there is only one software provider
in the market which faces the competition from its pirate software (Conner and Rumelt
1991, August and Tunca 2008, Lahiri and Dey 2012). We study a more realistic setting of
two competing software providers. In this paper, we study mainly three research questions.
First, how will competition among legitimate and pirated products affect the anti-piracy
effort? Second, how will anti-piracy effort be affected by the network effect when there is
competition among legitimate and pirated products? Third, how will the network effect
affect the profit of each firm due to competition?
2.
Literature Review
Software piracy has long been an important topic in the information system research area.
Many papers have studied policies and strategies to combat piracy. Chen and Png (2003)
explores how a government sets the fine for copying, tax on copying medium, and subsidy
on legitimate purchases, while a monopoly publisher sets price and spending on detection.
However, our paper focuses how network externality and other factors affect pricing and
anti-piracy decisions in a competitive environment. Chellappa and Shivendu (2005) study
the issue of product sampling when there is piracy. They use a two-stage model of piracy for
a market where consumers are assumed to be heterogeneous in their marginal valuation for
quality and their moral costs. They find that product sampling can internalize any potential
3
benefits of piracy. Sundararajan (2004) investigates how a monopolistic seller should choose
the optimal pricing schedules and technological deterrence levels when digital piracy exists
in the market and the degree of piracy can be influenced by implementing digital rights
management (DRM) systems. Wu and Chen (2007) study the versioning strategy in the
presence of piracy. They find that when there is no piracy, a single version is the optimal
strategy for an information goods provider. However, when piracy exists, firms tend offer
more than one quality through versioning, an effective and profitable instrument to fight
piracy under some conditions. August and Tunca (2008) consider the decision of providing
security patches to users. They find that in the case that piracy tendency is low, only when
the piracy enforcement level is high, vendor’s software security patch restrictions is optimal.
When patching costs are sufficiently low, a vendor should provide patches to pirated software
as well.
Johar et al (2012) investigate a publisher who gain profit through advertisement
when providing content to consumers who have heterogeneous valuation. The publisher
needs to determine two dimensions, the content quality and content distribution delay, in
its content provision strategy. They find that that when piracy exists, the publisher should
improve at least one dimension of content provision.
Another stream of literature on the other hand, studies the potential positive effect
of piracy on software producers. Before Conner and Rumelt (1991), it was believed that
software piracy would decrease software firms’ profits and increase prices, which would harm
the social welfare. Conner and Rumelt (1991) incorporated the network externality into
their model and examine piracy’s effect on software firms’ profit. When more people use one
software, whether legitimate or pirated, consumers can gain higher utility through network
effect, making consumers willing to pay more for the product. Therefore if network effect
is large, then firms can benefit from piracy. Shy and Thisse (1999) extend the monopolistic
results of Conner and Rumelt (1991) to a duopolistic framework. They show that firms will
allow piracy in order to increase the market size. Similarly, they show that if network effects
are strong, then firms can benefit from not exerting anti-piracy effort. Gu and Mahajan
(2005) also investigate piracy’s effect on firms’ profits when competition exist. They show
that piracy can reduce price competition, and can be beneficial to firms when markets have
high wealth gaps. Jain (2008) find that strong network effects may lead to higher levels of
copyright protection in some case. They show that when network effect is strong, stronger
copyright enforcement can reduce price competition. Lahiri and Dey (2012) find when piracy
enforcement is low, the monopolist have more incentive to invest in quality. Tunca and
4
Wu (2013) show that information goods industry, by suing file sharing networks or users
who share copyrighted material on peer-to-peer networks, can sometimes hurt legitimate
publishers of information goods.
In our paper, we assume that a consumer chooses to buy or pirate software based on
his or her utility. One contribution of our paper is to consider anti-piracy’s cross effect
which is not considered in other papers. We obtain several interesting results. For example,
different from previous works (Conner and Rumelt 1991, Jain 2008), we show anti-piracy
effort increases with network effect only if cross effect is high enough.
3.
The Model
Consider two competing firms (denoted by 1 and 2) located at the endpoints of a Hotelling
line [0,1]. Each firm produces one software product with quality qi , i = 1, 2. Using a common
assumption about the cost of information goods, we let the cost of producing an extra copy
of software be 0. Let p1 and p2 be the price of legitimate software products that firms and
2 sell. Both software products have pirated version. We assume the pirated versions are
costless to obtain since nowadays consumers can download pirated software products easily
from many software pirating websites. Table 1 in the appendix contains a summary of key
variables used in this paper.
Consumers are heterogeneous in their taste for a particular software product and we
assume they are uniformly located on the Hotelling line between 0 and 1. Denote t to be the
mismatch cost parameter. Therefore a consumer located at x will incur the mismatch cost
tx for using product 1 and t(1 − x) for using product 2. Furthermore we assume the quality
of both software products are large enough so that the market is fully covered (otherwise
the problem becomes less interesting since each firm could act as a local monopoly). Then
each consumer (for simplicity we use ”he” to refer to a consumer later on) faces four options:
buying software 1, buying software 2, pirating software 1, pirating software 2. Figure 1
depicts consumers’ choices.
If a consumer located at x chooses to buy, his utility Ui of buying and using a legitimate
software product 1 or 2 is given by
U1 = q1 + k(D1 + D3 ) − tx − p1
(1)
U2 = q2 + k(D2 + D4 ) − t(1 − x) − p2
(2)
or
5
Buy 1
Consumer
choice:
Pirate 1
Pirate 2
Buy 2
0
1
__
Figure 1: Consumer demands in the duopolistic case
where Di (D2+i ) is the demand for legitimate (pirated) software i, i = 1, 2.
If a consumer chooses to pirate, he could get software for free by downloading or copying
it. However, he may not get the fully quality qi by using pirated software. For instance,
software firms may not provide patches for pirated software (August and Tunca 2008), so
that computers using pirated version could be vulnerable for viruses, and a consumer’s utility
could decrease. Also, many software firms provide customer support only to those who
own legitimate software products. Therefore a consumer naturally discounts the quality of
pirated software. Consequently both the network benefit and mismatch cost of using pirated
software decrease as a consumer does not value pirated software so high as legitimate one.
Let θi , i = 1, 2 be such discount factor for product 1 and 2. Then the utility of a consumer
who uses a pirated version of software product 1 can be written in the following form:
U3 = θ1 [q1 + k(D1 + D3 ) − tx] − c1 (e1 , e2 ).
(3)
Penalty cost term c1 (e1 , e2 ) in (3) depends on the probability of a consumer being caught
of using pirated software and subsequently required to pay penalty. As anti-piracy efforts e1
exerted by firm 1 increases, a consumer is more likely to be caught using pirated software 1.
Therefore we expect c1 to increase with e1 , i.e., ∂c1 /∂e1 > 0. Also there is a cross effect by
anti-piracy effort e2 from the other firm and we assume ∂c1 /∂e2 > 0 as well.
Similarly, the utility a consumer obtains by using a pirated software product 2 is given
by:
U4 = θ2 [q2 + k(D2 + D4 ) − t(1 − x)] − c2 (e1 , e2 ).
(4)
To proceed, we use the commonly used linear-quadratic framework to simplify the analysis. That is, we use a linear form of penalty cost
ci (e1 , e2 ) = ai e1 + bi e2 , i = 1, 2
and a quadratic cost of anti-piracy effort: ri e2i , i = 1, 2.
6
(5)
4.
Analysis of the Model and Results
4.1
Benchmark: Monopoly Case
We first analyze the case when there is only one software provider in the market. This
analysis serves as a benchmark for the subsequent duopolistic analysis. Without the loss of
generality, we assume that the monopolist is firm 1 and located at 0 of a Hotelling line where
consumers are uniformly distributed. Penalty cost c1 (e1 , e2 ) becomes c1 (e1 ) = a1 e1 as e1 is
the only anti-piracy effort in the monopolistic case. The time sequence is the following. At
the first stage, the monopolistic firm decides the anti piracy effort e1 . At the second stage,
the firm decide the price of the software product p1 . At the third stage, consumers make
their purchase or pirating decisions. We use backward induction to solve this problem. It
can be shown that in the monopolistic case, the second and third stages can be merged into
one stage and the final decisions will still be the same. For comparison with the duopoly’s
case, we keep two stages separate.
At the third stage, a consumer can obtain a legitimate version, gaining utility U1 given
by Equation (1), or acquire a pirated one, gaining utility U3 given by (3). Let x1 be the point
on the Hotelling line where a consumer is indifferent between purchasing and pirating and
x2 be the point where a consumer is indifferent between pirating or not using the software.
In other words, the total demand is simply given by x2 . Then we have
U1 |x=x1 = U3 |x=x1
(6)
U3 |x=x2 = 0
(7)
q1 − tx1 + kx2 − p1 = θ1 (q1 − tx1 + kx2 ) − a1 e1
(8)
θ1 (q1 − tx2 + kx2 ) − a1 e1 = 0
(9)
and
That is
and
From (9), we can solve for x2 :
x2 =
θ1 q1 − a1 e1
θ1 (t − k)
Plugging (10) into (8), we can get x1 :
p1
q1 k q1
+
−
+
x1 =
t
t (t − k) (1 − θ1 )t
7
(
1
k
1
−
(1 − θ1 )t
t θ1 (t − k)
(10)
)
a1 e1 .
(11)
At the second stage, the firm chooses the selling price p2 to maximize its profit:
π1 (p1 , e1 ) = x1 p1 − r1 e21
(12)
Plugging (11) into the profit function (12) and differentiating the profit with price p1 , we
can get the first order condition with respect to p1 :
∂π1 (p1 , e1 )
q1 k θ1 q1
2p1
1
k
1
=
+
−
+(
−
)a1 e1
∂p1
t
t θ1 (t − k) (1 − θ1 )t
(1 − θ1 )t
t θ1 (t − k)
(13)
from which we can solve for p1 :
1
kq1
1
k
p1 = (1 − θ1 )[q1 +
+(
−
)a1 e1 ]
2
(t − k)
(1 − θ1 ) θ1 (t − k)
(14)
At the first stage, after one substitutes (14) into the profit function (12), the profit
function becomes only a function of decision variable e1 . The firm needs to choose the effort
to maximize its profit:
∂π1
(1 − θ1 )a1
kq1
1
k
1
k
=
[q1 +
+(
−
)a1 e1 ][
−
] − 2r1 e1 (15)
∂e1
4t
(t − k)
1 − θ1 θ1 (t − k)
1 − θ1 θ1 (t − k)
We can get the optimal effort of anti-piracy as:
e∗1
=
q1
q1 + k t−k
8r1 t
ka1
a1
(1−θ1 )[− θ (t−k)
+ 1−θ
]
1
+
ka1
θ1 (t−k)
−
a1
(1−θ1 )
(16)
1
and plugging e1 into (14), we can get p1 .
By using comparative statics analysis, we can study how different parameters can affect
the optimal decision variables and the firm’s profit. The results are summarized in Theorem 1
(Proofs of all theorems are omitted due to space constraint):
Theorem 1. In the monopoly’s case, we have the following results:
1. As network effect increases, the optimal anti-piracy effort decreases, the price increases
and the firm’s profit increases. That is, ∂e∗1 /∂k < 0, ∂p∗1 /∂k > 0, and ∂π1∗ /∂k > 0.
2. As software quality increases, the optimal anti-piracy effort increases, the price increases and the firm’s profit increases. That is, ∂e∗1 /∂q1 > 0, ∂p∗1 /∂q1 > 0, and
∂π1∗ /∂q1 > 0.
3. As perceived quality for using pirated software increases, the optimal anti-piracy effort
increases, the price decreases and the profit decreases. That is, ∂e∗1 /∂θ1 > 0, ∂p∗1 /∂θ1 <
0 and ∂π1∗ /∂θ1 < 0.
8
From Theorem 1.1, as the network effect increases, it is optimal for a software company
to decrease its anti-piracy effort. This is similar to the one found in Conner and Rumelt
(1991). The intuition is the following: as the network effect increases, a software company
has incentive to reduce anti-piracy effort and allow a higher level of piracy so that more
users will join the network even though they might choose to pirate. As a result, the
software company can charge legitimate users a higher price due to increased network size
and its profit increases. Therefore, when the network effect is strong, it is important for a
monopolistic software provider to have a larger user base.
On the other hand, as software quality increases, it becomes more attractive for both
legitimate and pirating users. In this case, it is optimal for a software company to increase
anti-piracy effort to reduce software piracy. At the same time, the company is able to
charge legitimate users a higher price and increase its profit, as shown in Theorem 1.2.
From Theorems 1.3, as quality of pirated software increases, it becomes more attractive to
use pirated software. That means the competition between legitimate and pirated software
becomes stronger. Then a software company’s optimal response is to increase its anti-piracy
effort to discourage the use of pirated software on the one hand, and to decrease its price to
make legitimate software more competitive on the other hand. As a result, the monopolist’s
profit decreases as pirated software becomes attractive.
Comparing Theorems 1.2 with 1.3, it is interesting to see that although anti-piracy effort
always increases for an increase in either q1 or θ1 , the behavior of profit is different. A
monopolist’s profit increases for a higher q1 even with a higher anti-piracy effort since it
becomes more attractive to purchase its product. However for a higher θ1 , it becomes more
attractive to pirate and a firm puts in more anti-piracy effort and gets less profit.
Next we explore a duopolistic case to see whether the same results hold in a competitive
environment.
4.2
Duopoly Case
We now study the setting that two firm are in the market.They lie at each end of the Hotelling
line. That is, firm 1 lies at point of 0, and firm 2 at 1. The time sequence is similar to the
monopoly case: At the first stage, both firms determine their anti-piracy effort e1 and e2 ; at
the second stage, both firms set prices p1 and p2 ; at the third stage, consumers choose which
type of software to use and whether to pirate or not.
9
At the third stage, a consumer located at point x1 will get the same utility whether he
uses pirated software product 1 or legitimate software product 1, as shown in Figure 1. Then
U1 in Equation (1) equals U3 in (3) at x = x1 . That is,
q1 + k(D1 + D3 ) − tx1 − p1 = θ1 [q1 + k(D1 + D3 ) − tx1 ] − c1 (e1 , e2 )
(17)
Similarly, U2 in Equation (2) equals U4 in (4) at x = x3 :
q2 + k(D2 + D4 ) − t(1 − x3 ) − p2 = θ2 [q2 + k(D2 + D4 ) − t(1 − x3 )] − c2 (e1 , e2 )
(18)
and a consumer at point x2 will get the same utility whether using pirated product 1 or 2.
Then,
θ1 [q1 + k(D1 + D3 ) − tx2 ] − c1 (e1 , e2 ) = θ2 [q2 + k(D2 + D4 ) − t(1 − x2 )] − c2 (e1 , e2 ) (19)
As shown in Figure 1, the total demand for software product 1 is x2 , including pirated
version and legitimate version and the total demand for software product 2 is 1 − x2 . We
shall have:
D1 + D3 = x2
(20)
D2 + D4 = 1 − x 2
(21)
From (19), (20) and (21), we can solve for x2
x2 =
θ1 q1 − θ2 q2 + (t − k)θ2 − c1 (e1 , e2 ) + c2 (e1 , e2 )
(θ1 + θ2 )(t − k)
(22)
From (17), we can get x1 which is the demand for legitimate product 1 D1 ,
D1 = x1 =
(1 − θ1 )q1 + (1 − θ1 )kx2 − p1 + c1 (e1 , e2 )
(1 − θ1 )t
(23)
and from (18), we can get x3 :
x3 = 1 − D2 = 1 −
(1 − θ2 )q2 + (1 − θ2 )k(1 − x2 ) − p2 + c2 (e1 , e2 )
(1 − θ2 )t
(24)
from which we can get the demand for legitimate product 2:
D2 =
(1 − θ2 )q2 + (1 − θ2 )k(1 − x2 ) − p2 + c2 (e1 , e2 )
.
(1 − θ2 )t
(25)
The profits of firms 1 and 2 are given by:
π1 (p1 , e1 ) = D1 p1 − r1 e21 =
(1 − θ1 )q1 + (1 − θ1 )kx2 − p1 + c1 (e1 , e2 )
p1 − r1 e21
(1 − θ1 )t
10
(26)
π2 (p2 , e2 ) = D2 p2 − r2 e22 =
(1 − θ2 )q2 + (1 − θ2 )k(1 − x2 ) − p2 + c2 (e1 , e2 )
p2 − r2 e22
(1 − θ2 )t
(27)
By solving p1 and p2 from ∂π1 (p1 , e1 )/∂p1 = 0 and ∂π2 (p2 , e2 )/∂p2 = 0, We can get prices of
two software products at the Nash equilibrium:
(1 − θ1 )q1 + (1 − θ1 )kx2 + c1 (e1 , e2 )
2
(28)
(1 − θ2 )q2 + (1 − θ2 )k(1 − x2 ) + c2 (e1 , e2 )
2
(29)
p1 =
p2 =
After plugging (28) and ci (e1 , e2 ) = ai e1 + bi e2 into (26), we get the first order conditions
of π1 (p1 (e1 , e2 ), e1 ) with respect to e1 :
1 )k(−a1 +b1 )
2[(1 − θ1 )q1 + (1 − θ1 )kx2 + a1 e1 + b1 e2 ][ (1−θ
+ a1 ]
∂π1
(θ1 +θ2 )(t−k)
=
− 2r1 e1 = 0
∂e1
4(1 − θ1 )t
(30)
Similarly, we have
2 )k(a2 −b2 )
2[(1 − θ2 )q2 + (1 − θ2 )k(1 − x2 ) + a2 e1 + b2 e2 ][ (1−θ
+ b2 ]
∂π2
(θ1 +θ2 )(t−k)
=
− 2r2 e2 = 0 (31)
∂e2
4(1 − θ2 )t
We can jointly solve the equilibrium anti-piracy efforts e1 and e2 from the first-order
conditions (30) and (31). However, the expressions are too complicated to gain any analytical insights. To gain further insights, we consider the following two cases: a symmetric
case where both firms’ parameters are the same and an asymmetric case where both firms’
parameters are the same except that software quality is different between two products.
4.2.1
Duoplistic Competition with Symmetric Firms
When two firms are identical, we can get each firm’s equilibrium effort as
esym =
(2q + k)(1 − θ1 )
8r1 t
− 2(a1 + a2 )
−a1 +a2
a
k
+ 1
2θ1 (t−k)
(32)
1−θ1
and the equilibrium price as
psym =
(1 − θ1 )q1 +
(1−θ1 )k
2
+ (a1 + a2 )esym
2
Then we can show the following result from comparative statics analysis:
Theorem 2. In the symmetric monopolistic case, we have the following results:
11
(33)
1. As network effect increases, both the equilibrium anti-piracy effort and price increase
when the cross effect of anti-piracy effort is high. That is, ∂esym /∂k > 0 and ∂psym /∂k <
0 when the cross effect parameter a2 is large enough.
2. As software quality increases, the equilibrium anti-piracy effort the price and the firm’s
profit all increase. That is, ∂esym /∂q1 > 0, ∂psym /∂q1 > 0, and ∂πsym /∂q1 > 0.
3. As perceived quality for using pirated software increases, the equilibrium anti-piracy effort increases; both the price and the profit decrease. That is, ∂esym /∂θ > 0, ∂psym /∂θ <
0, and ∂πsym /∂θ < 0.
Some results remain the same even in the duopolistic setting: Theorem 3.2 and 3 are
the same as Theorem 1.2 and 1.3 in the monopolistic case. However, the result in Theorem
3.1 is quite interesting and different from Theorem 1.1 in the monopolistic case. On the one
hand, a higher network effect makes anti-piracy effort less desirable, as one could see in the
monopolistic case. On the other hand, under competition, a higher network effect could lead
to a higher anti-piracy effort which could reduce the demand for the competitor’s product
(both legitimate and pirated). when the cross effect of anti-piracy effort is high, the second
effect dominates the first effect and anti-piracy effort increases with network effect.
Anti-piracy effort
0.4
0.2
0
0
0.25
0.5
0.75
1
k
Figure 2: Anti-piracy effort without cross effect
Even if the cross effect does not exist, i.e, coefficients of a2 = b2 = 0 in ci , we still obtain
a result (shown in Figure 2) that is different from what one might have expected under the
12
monopolistic case. The result in Figure 2 is quite interesting. In the small network effect
(k) region, when k increases, anti-piracy effort increases even though there is no cross effect
from anti-piracy effort. Then such increase in anti-piracy effort is purely due to competition.
When k further increases, network effect dominates the competition effect. Then anti-piracy
effort decreases and each firm tries to increase its network by adopting a more lenient antipiracy policy.
Furthermore, we also study how the change in the cross effect of anti-piracy effort influences the equilibrium results.
Theorem 3. In the symmetric monopolistic case, an increase in the cross effect of the antipiracy effort leads to an increase in the equilibrium anti-piracy effort, the equilibrium price
and each firm’s profit. That is, ∂esym /∂a2 > 0, ∂psym /∂a2 < 0, and ∂πsym /∂a2 < 0.
The result in Theorem 3 seems simple but is not that straightforward. When the cross
effect of anti-piracy effort increases, anti-piracy effort becomes more effective in increasing
the cost of using competitor’s pirated software, not its own pirated software. Then why
does a firm still have incentive to increase anti-piracy effort? Also how can a firm even
increase its price? The reason is due to the competitive effect. As the competitor’s pirated
software becomes less attractive, the competitor can increase its price; in turn the first firm
can increase price as well. So anti-piracy effort indirectly benefits the firm itself when the
cross effect increases. Then each firm is motivated to increase anti-piracy effort even if the
direct benefit goes to its competitor, knowing that its competitor is also motivated to do
the same; ultimately, both firms benefit. Theorem 3 discovers the interesting role that the
cross effect plays – an increase in the cross effect can weaken the competition between two
software firms.
In the next subsection, we explore how relaxing the symmetric assumption can produce
richer results.
4.2.2
Duoplistic Competition with Asymmetric Quality
We first study how two companies with software of different qualities react by focusing on
anti-piracy effort.
Theorem 4. In an asymmetric case with different software quality qi ,
1. both firm 1’s anti-piracy effort e1 and firm 2’s effort e2 increase with either software
1’s quality q1 or software 2’s quality q2 ; That is, ∂e1 /∂qi > 0 and ∂e2 /∂qi > 0, i=1,2.
13
2. the firm with higher quality software exerts more anti-piracy effort; The difference in
effort increases with quality difference.
When firm 1’s software quality increases q1 , it becomes more tempting to pirate the
software. Firm 1 has an incentive to increase anti-piracy effort to reduce piracy and make
purchasing the software more desirable. When firm 1 exert more anti-piracy effort, it is more
costly to using pirated software product 1, leading to more users using pirated software 2.
In turn, firm 2 will exert more effort in anti-piracy to shift some pirate users to legitimate
users. In other words, each firm’s anti-piracy effort increases even if only one firm’s software
quality increases, as Theorem 4.1 shows.
Then which firm will spend more effort in preventing piracy? As Theorem 4.2 shows, the
higher quality firm should put more effort since its product is more likely to be the target for
piracy. This matches our daily experience: larger software firms are more actively involved
in anti-piracy lawsuits, as their software has more functionalities and is more likely to be
pirated.
Theorem 5. In an asymmetric case with different effort cost ri ,
1. both firm 1’s effort and firm 2’s effort will decrease with either firm’s effort cost. That
is, ∂e1 /∂ri < 0 and ∂e2 /∂ri < 0, i=1,2.
2. the firm with higher effort cost exerts less anti-piracy effort; the difference in effort
increases with cost difference.
The result that a firm’s anti-piracy effort decreases with its effort cost is obvious. When
its cost of anti-piracy is high, a firm will choose to decrease anti-piracy. However, it is not
immediately clear why the other firm will decrease its effort as well, as Theorem 5.2 shows.
The explanation is the following. When one firm’s anti-piracy effort decreases, more users
tend to pirate this firm’s product. The pressure of piracy for the other firm will decrease, so
the other firm is able to decrease its anti-piracy effort.
5.
Conclusion
In this paper, we analyzed the problem how software firms should price their products and
invest in anti-piracy measures to prevent piracy in a competitive environment.
14
In a symmetric duopolistic setting, we show that when cross effect exists, the anti-piracy
effort by a firm involved in price competition may increase or decrease with the network
effect, which is different from previous results. Even without cross effect, anti-piracy effort
may increase or decrease with the network effect in a competitive setting. Another interesting
result is that when cross effect increases, each firm increases its anti-piracy effort. Although
such increase benefits a competitor directly, this competitor can then increase price since
there is less pressure from piracy; the first firm in turn can do the same, benefiting from
cross effect ultimately.
In an asymmetric duopolistic setting, we find that an increase in one product’s quality
causes two firms to increase anti-piracy effort, with a higher quality firm putting more
effort. On the other hand, when anti-piracy cost becomes more expensive for one firm, then
interestingly both firms will decrease anti-piracy effort due to the effect of competition.
Our contributions are in two ways. First, we introduced the cross effect concept which
commonly exists in reality and has not attracted enough interests in software piracy literature. Second, we find that anti-piracy effort may increase when network effect increases in
some circumstances. This result is theoretically interesting, because, it contradicts the previous belief that firms can take advantage of high network effect and exert less anti-piracy
effort. The implication to software companies is that when competition exists, they may
need to exert more effort if the cross effect of anti-piracy effort is high.
There are several extensions possible to our paper. First, we use a Hotellting model to
study competition between two software products. Although many papers use this model, in
reality, vertical competition on quality also widely exists. Second, it might be interesting to
extend our study to include software versioning which is another strategy to combat piracy.
15
References
August, T., & Tunca, T. I., Let the Pirates Patch?
An Economic Analysis of Software Security Patch Restrictions. Information Systems Research, 19(1), 48-70 (2008).
doi:10.1287/isre.1070.0142.
Burgess, Rick. 2013. McAfee Patents Anti-piracy Filter. Last retrieved February 24, 2015. http:
//www.techspot.com/news/52363-mcafee-patents-anti-piracy-filter.html.
Chellappa, R. K., & Shivendu, S., Managing Piracy: Pricing and Sampling Strategies for Digital
Experience Goods in Vertically Segmented Markets. Information Systems Research, 16(4),
400-417(2005). doi:10.1287/isre.1050.0069.
Chen, Y., & Png, I., Information Goods Pricing and Copyright Enforcement: Welfare Analysis.
Information Systems Research, 14(1), 107-123(2003). doi:10.1287/isre.14.1.107.14762.
Gu, B., & V. Mahajan, How Much Anti-piracy Effort is Too Much? A Study of the Global Software
Industry. Working paper, University of Texas, Austin (2005).
International Data Corporation (IDC). 2014. The Dangerous World of Counterfeit and Pirated Software. Last retrieved February 24, 2015. http://news.microsoft.com/download/presskits/
antipiracy/docs/idc030513.pdf.
Jain, S., Digital Piracy: A Competitive Analysis. Marketing Science, 27(4), 610-626(2008).
doi:10.1287/mksc.1070.0313.
Johar, M., Kumar, N., & Mookerjee, V., Content Provision Strategies in the Presence of Content
Piracy. Information Systems Research, 23(3-part-2), 960-975(2012).
Lahiri, A., & Dey, D., Effects of Piracy on Quality of Information Goods. Management Science,
59(1), 245-264 (2012). doi:10.1287/mnsc.1120.1578.
New York Times. 2010. Chasing Pirates: Inside Microsofts War Room. Last retrieved February
24, 2015. http://www.nytimes.com/2010/11/07/technology/07piracy.html.
Reavis Conner, K., & Rumelt, R. P., Software Piracy: An Analysis of Protection Strategies. Management Science, 37(2), 125-139(1991). doi:10.1287/mnsc.37.2.125
Shy, O. & Thisse, J.-F., A Strategic Approach to Software Protection. Journal of Economics &
Management Strategy, 8: 163190(1999). doi: 10.1111/j.1430-9134.1999.00163.x
siia.net. 2015. SIIA’s Corporate Anti-Piracy Reward Program. Last retrieved February 24, 2015.
http://www.siia.net/piracy/report/tos.asp.
Sundararajan, A., Managing Digital Piracy: Pricing and Protection. Information Systems Research,
15(3), 287-308(2004). doi:10.1287/isre.1040.0030
The Software Alliance (BSA). 2013. The Compliance Gap: BSA Global Software Survey. Last
retrieved February 24, 2015. http://globalstudy.bsa.org/2013/index.html.
torrentfreak.com.
threat.
2013.
Last
McAfee Brands The Pirate Bay as a security
retrieved
February
24,
2015.
http://torrentfreak.com/
16
mcafee-brands-the-pirate-bay-as-a-security-threat-131110/.
Tunca, T. I., & Wu, Q., Fighting Fire with Fire: Commercial Piracy and the Role of File Sharing
on Copyright Protection Policy for Digital Goods. Information Systems Research, 24(2), 436453(2013). doi:10.1287/isre.1120.0430
Wu, S., & Chen, P., Versioning and Piracy Control for Digital Information Goods. Operations
Research, 56(1), 157-172(2007). doi:10.1287/opre.1070.0414
17
Appendix
Table 1: Summary of notation
Notation
Description
Parameters
qi
θi
quality of software product i, where i ∈ {1, 2}
discounted quality of pirated software relative to a legitimate
version, where i ∈ {1, 2}
k
coefficient of a software product’s network externality
x
a consumer’s location on the Hotelling line
t
coefficient of a consumer’s mismatch cost of using a legitimate
version
′
t
coefficient of a consumer’s mismatch cost of using a pirated
version
πi
profit of software firm i, where i ∈ {1, 2}
Ui
utility a consumer gets from using ith legitimate software
product i ∈ 1, 2
U2+i
utility a consumer gets from using pirated software
product i, where i ∈ 1, 2
Di
demand of legitimate software product i, where i ∈ {1, 2}
D2+i
demand of pirated software product i, where i ∈ {1, 2}
Decision Variables
pi
price of software product i, where i ∈ {1, 2}
ei
anti-piracy effort exerted by software company i,
where i ∈ {1, 2}
18