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On Software Piracy 187


software firm, the original firm will always deter the pirate and enjoy the monopoly market
simply because monopoly profit is always higher than duopoly profit. To this end,
readers would also like to notice that the presence of the pirate increases the demand of
the original firm through network effect compared to the full protection case. Thus, this
is clearly a positive effect of allowing piracy. Although there exists the dampening effect
on the price under piracy due to competition, but a priori it is not quite clear which effect
dominates and eventually which situation would be more profitable to the original firm.
Digging a little bit deeper and contrasting with previous results in the literature
(discussed earlier), we realize that the market structure, the nature of competition and the
demand structure play a very crucial role to drive these results. For example, when the
market structure is monopolistic with two types of consumers, software piracy allows
price-discrimination among the different classes consumers (see Conner and Rumelt,
1991; Takeyama, 1994; Slive and Bernhardt, 1998).14 On the other hand, when the market
structure is duopolistic (or strategic in general), the results regarding the existence (or
not) of software piracy very much depends on the nature of competition between the
competing firms. For example, when competition takes place between two symmetric firms
(both are original software developer, while their products are differentiated) (see Shy
and Thisse (1999)), then allowing software piracy by one group (typically low-valued
users) of software users could be supported as a non-cooperative equilibrium under
strong network effect. At the same time, when the competition takes place between two
asymmetric firms, i.e., one firm is the original software developer and the other is just a
pirate (as in this case), then allowing piracy (by the pirate) is not a profitable outcome
to the original firm. Therefore, protection remains the only profitable option to the original
developer.
One important distinction that we would like the readers to notice here is that our study
is based on retail piracy (i.e., one single pirate does all the piracy and sells to others),15
while most of the studies (except Banerjee 2003) discussed in the literature (see section
2 and above) so far, are mainly based on end-user piracy (i.e., consumers pirate copies
mainly for their own use). So there is a distinct difference in the act of coping. Hence,
whether the nature of piracy actually leads to alternative outcomes that remain to be seen.
A future research along this will line would be desirable.




Part II

The Case of Sequential Move

So far we have considered a simultaneous move game between the original developer and
the pirate. Now we are going to consider a sequential move game where the original firm
acts as a leader and the pirate as the follower. We believe this market structure is also
very common in many real life situations, where the original producer is an established
firm in the business and is the market leader. In such situation if any pirate comes to




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188 Poddar


operate, it naturally becomes the follower. An analysis of the leader-follower game also
gives us the opportunity to compare the outcomes of the simultaneous move game
scenario, which we had studied in the previous part, with the sequential version of the
game. This also makes our analysis on software piracy in a strategic framework rather
complete.


The Leader-Follower Game of Piracy

Given the distribution of the buyers which we have discussed earlier (see section 3.3),
the profit function of the pirate (follower) is given by:


πFP = DP . P P

qPO ’ PP
= PP . [ ] (For the expression DP see section 3.3)
q(1 ’ q)


qPO
Thus, the reaction function is given by: PFP (PO) =
2
The profit function of the original firm (leader) is:


πO = DO . PO

(1 ’ q )+ θ (qPO ’ PP )’ (PO ’ PP )
(1 ’ q )(1 ’ θ )
= PO . [ ] (for DO see 3.3)



Plugging in the reaction function of the follower in the above expression, we solve for
(subgame perfect) equilibrium prices:


q (1 ’ q )
1’ q
POL = 2 ’ q ’ θq ; PPF = 2(2 ’ q ’ qθ ) (10)


Equilibrium demands are given by:


1
1
; D P = 2(2 ’ q ’ θq )
DO =
F
L

2(1 ’ θ )
(11)




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On Software Piracy 189


The profit of the original software firm is given by:


(1 ’ q )
π = 2(1 ’ θ )(2 ’ q ’ θq)
L—
(12)
O




and that of the pirate is:


q(1 ’ q )
πP— =
F

4(2 ’ q ’ θq )
(13)
2




Comparison between Simultaneous and Sequential Move Game

When we compare the equilibrium expressions in the leader-follower game with the
simultaneous move game, we get the following results.


Proposition 4
(i) In the leader-follower game, the prices of the original firm and the pirate are higher
compared to the simultaneous move game. Formally, POL ≥ PO* and POF ≥ PP*.
(ii) The demand of the original firm becomes lower while the demand of the pirate
becomes higher in the leader-follower game compared to the simultaneous move
game. Formally, DOL < DO* and DPF ≥ DP*.


Proof: (i) Follows after comparing (10) with (4) and (10) with (5) respectively.
(ii) Follows after comparing (11) with (6) and (11) with (7) respectively.


Proposition 5
(i) The profits for both the leader and the follower are higher than respective
simultaneous Bertrand profits. Formally, π O* ≥ π O* and π P * ≥ π P* .
L * F *


(ii) The original firm (leader) gets a higher profit than the pirate (follower).
Formally, π O* ≥ π P * .
L F




Proof: (i) Follows after comparing (12) with (8) and (13) with (9) respectively.
(ii) Follows after comparing (12) with (13).
Note that point (ii) needs some attention. Usually, if the strategies are strategic
complements between the competitors (which is the case here), then the follower
gets higher profit than the leader. Here, that is not happening since the products



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190 Poddar


are vertically differentiated. The leader is selling the high quality product and the
follower is selling the low quality product. The former is true when the products
are horizontally differentiated.


Now, we compare between the profits of the original software firm under protection and
non-protection.


Protection versus Non-Protection

We begin with the following interesting observation:


1
DO = = D*NP,
L

2(1 ’ θ )


where D*NP is the demand under protection.
Also:


1’ q 1 —
P = 2 ’ q ’ θq < = PNP ,
L*
O
2


where P*NP is the monopoly price under protection.
Hence, we have the following result.


Proposition 6
In this leader-follower case with the presence of network externality, presence of the
pirate does not make any difference to the demand of the original firm. It remains exactly
the same as it was under protection, yet the price is reduced due to competition.


This implies total profit of the original firm under the leader-follower game must be less
than the total profit under protection. Thus, we arrive at the main result for this part.


Proposition 7
In the presence of network externality given a choice between employing protection
and non-protection, it is always profitable for the original software developer to
protect its software, even when it is the market leader.




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On Software Piracy 191


Proposition 8
The ranking of profits of the original firm in three different regimes (i.e., (i) simulta-
neous move under no protection, (ii) sequential move under no protection, and (iii)
protection) respectively is as follows: π O— < π O— < π NP .
— —
L




Thus, moving from a simultaneous move game to a sequential move game as a leader
improves the original firm™s profit, yet the improved profit is still lower than the profit
under protection. Hence, protection remains the optimal policy to the original developer
under all circumstances.
Like the simultaneous case, the following result is also true in the sequential game.


Proposition 9
The original software developer has a greater incentive to protect its product in the
presence of network externality as oppose to the case without any network externality.


Proof: As before, the incentive to protect increases with the degree of network
externality. Gain from protection under network externality is:


q 2 (1 ’ q )
2(1 ’ θ )(2 ’ q ’ θq )(4 ’ q ’ 3θq )
1
2 = G (say).




Observe that G1 is an increasing function of θ. Q.E.D.




Part III

Welfare Analysis

Now we are ready to do some welfare analysis. Assume that in the set up, that is,
discussed in previous two parts (I and II), there is a social planner (say, the government)
whose objective is to maximize society™s welfare. What would be the policy recommen-
dation with respect to piracy? In other words, the question is, whether allowing piracy
is welfare improving or welfare reducing from the society™s point of view. To analyze that,
first we list the consumer surplus and the social welfare under various cases.




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192 Poddar


Software Protection (No Piracy)

1
CS 1 = (14)
8(1 ’ θ ) 2

3 ’ 2θ
1 1
W1 = + = (15)
8(1 ’ θ ) 2 4(1 ’ θ ) 8(1 ’ θ ) 2


No Software Protection (Piracy) - The Simultaneous Game

8θ 2 q 2 + θ 2 q ’ 14θq + 5q ’ 4θq 2 + 4
CS 2 = (16)
2(1 ’ θ ) 2 (4 ’ q ’ 3θq ) 2



12 ’ 8θ ’ q ’ 18θq + 11θ 2 q + 8θq 2 ’ 2θ 2 q 2 ’ 2q 2
W2 = (17)
2(1 ’ θ ) 2 (4 ’ q ’ 3θq ) 2


Comparisons

Comparing between (15) and (17), we get the following result.


Proposition 10
Under network externality, the society is better off with the pirate. Formally:


W2 > W1.


Proof: It can be shown that W 2 is increasing in q for all θ ∈ (0, ½). It is also true that
W 1(θ) = W 2(θ)¦q=0. Thus, combining these two we get the result.


No Software Protection (Piracy) - The Sequential Game

Here again, we list the consumer surplus and the welfare for the case when the original
developer is the leader in the market, while the pirate is the follower.


3θ 2 q 2 + 2θq 2 + θ 2 q ’ 10θq + q ’ q 2 + 4
CS 3 = (18)
8(1 ’ θ ) 2 ( 2 ’ q ’ θq ) 2




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On Software Piracy 193


12 ’ 8θ ’ 9q ’ 6θq + 7θ 2 q + q 2 + 6θq 2 ’ 3θ 2 q 2
W3 = (19)
8(1 ’ θ ) 2 (2 ’ q ’ θq ) 2


Comparisons

Comparing between (15) and (19), we get the following result.


Proposition 11
The society is better off with the pirate under network externality, i.e.:


W3 > W1.


Proof: Like before, it can be shown that W 3 is increasing in q for all θ ∈ (0, ½). It is also
true that W 1(θ) = W3(θ)¦ q=0. Thus, combining these two, we get the result.


Discussion

Thus, in our models, we find that the existence of the pirate is always better for the society.
This is true for both the simultaneous and sequential version of the game under network
externality. But at the same time, we would like to warn our readers to be more careful in
order to generalize this result in other situations. First of all, here we only capture a
situation of retail piracy in a particular demand environment. Generally, the impact of
piracy on social welfare is a far more complex issue than we captured here. For that matter,
we would like to draw the readers™ attention on a comprehensive study by Chen and Png
(2003) on copyright enforcement and pricing of information goods and welfare aspects.
Software is one of the information goods that we are interested here. Chen and Png deal
with general information goods, where the primary question was “ how should the
government use its various policy instruments “ penalties, taxes, and subsidies “ in the
market for information good? This question is especially difficult because the govern-
ment, in setting policy, must consider how legitimate producers will adjust their pricing
and enforcement in response to government policy. So the study addresses the impact
of government policy on the software publisher™s price and detection expenditure and
then analyzes the consequences for social welfare. One distinct difference from their
study to our study here is that in their study the pirates are end-users (consumers) and
there is no retail piracy. The main findings from the study can be summarized as follows.
While the publisher may consider a price reduction and an increase in detection as simply
two alternative ways to boost legitimate demand, the two changes have qualitatively

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