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Competing Platforms and Third Party Application Developers

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Technology firms often decide between being open or closed to third party application development. Building on a two-sided market model with competing platforms, I show that firms might prefer to restrict third party application development despite the fact that allowing it is free and increases the value of the product to consumers. The reason is that restricting third party application development removes network effects and thereby relaxes competition between platforms. From a social welfare perspective, firms sometimes restrict third party application development even though total welfare would be higher if development was possible.iscussion about five propositions that should be on the agenda of research and implementation for Living Lab founders in the coming years.
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Electronic copy available at: http://ssrn.com/abstract=1559094
COMMUNICATIONS & STRATEGIES, no. 74, 2nd quarter 2009, p. 95.
Competing Platforms
and Third Party Application Developers
Joacim TÅG (*)
Research Institute of Industrial Economics (IFN), Stockholm, Sweden
Abstract: Technology firms often decide between being open or closed to third party
application development. Building on a two-sided market model with competing platforms,
I show that firms might prefer to restrict third party application development despite the
fact that allowing it is free and increases the value of the product to consumers. The
reason is that restricting third party application development removes network effects and
thereby relaxes competition between platforms. From a social welfare perspective, firms
sometimes restrict third party application development even though total welfare would be
higher if development was possible.
Key words: platforms; software; two-sided markets.
"Tech firms today are caught in a bind, between being open (to attract
a community of developers) and closed (to ensure high standards and
maintain their traditional business models)." The Economist 1
hy are some products open to third party development while others
are closed? As the quote above underscores, it may be a trade-off
between having applications that raises the value of the product and
ensuring a high quality product. I, however, take a two-sided market
approach underscoring that being open to third party developers can lead to
intensified competition for consumers. Hence, firms might prefer to restrict
third party application development despite that allowing it is free and
increases the value of the product to consumers.
(*) I am thankful for financial support from the Finnish Doctoral Programme in Economics and
the Research and Training Foundation of TeliaSonera Finland Oyj. I thank Jay Pil Choi,
Charlotta Grönqvist, Klaus Kultti, Andras Niedermayer, Tore Nilssen, Lars Sørgard, Rune
Stenbacka, and participants at the FDPE Microeconomics and IO Workshop in Helsinki and the
6th ZEW Conference on the Economics of ICT in Mannheim for insightful comments. This paper
is a shortened combination of the working papers “Open versus Closed Platforms” and
“Efficiency and the Provision of Open Platforms” and it is partly written within the Gustaf
Douglas Research Program on Entrepreneurship at the Research Institute of Industrial
Economics.
1The Economist, "Who holds the key?", Aug 15th 2008 from Economist.com.
W
Electronic copy available at: http://ssrn.com/abstract=1559094
96 No. 74, 2nd Q. 2009
The choice between allowing and banning third party application
developers is relevant in a number of markets. For example, operating
systems for modern personal computers are prime examples of products
that are open to third party application development. Apple's OS X,
Microsoft's Windows Vista and various versions of Linux all allow for and
even encourage application development. The same holds for video game
consoles. The three large consoles on the market (the Xbox 360, the
Playstation 3 and the Wii) have third parties developing games for them.
In some markets, the same firm provides products that both allow for and
restrict third party development. High-end phones often have an operating
system that allows for third party applications. The Nokia N95, for example,
comes with the S60 software permitting users to install software from third
party application developers. Yet, cheaper mobile phones such as the Nokia
1600 often restrict third party application development. Interestingly, when
Apple entered the mobile phone market in June 2007 with the iPhone, third
party application development was impossible for the phone. Apple,
however, later reversed this strategy by releasing a software development kit
for the iPhone in June 2008.
A related question is if firms allow third parties access to their products
when it is socially desirable? This has been a concern for antitrust
authorities. For example, in 1955, the FCC in the United States agreed with
the AT&T Bell System that an attachment to phones (the Hush-A-Phone)
that helped reduce noise could not be marketed and sold independently,
since it was a "foreign attachment" to the AT&T network. The FCC also
concluded that all telephone equipment should be sold by the network
operator. However, this decision was overturned on appeal by the D.C.
Circuit. In line with this appeal, the FCC later (in 1968) ruled that it should be
possible to use another attachment, the Carterfone, on the AT&T Bell
System network despite the fact that is was marketed by an independent
company.
This paper contributes to the literature on systems, aftermarkets and two-
sided markets by studying the decision to allow or restrict third party
application development. I start from a standard two-sided market model
from ARMSTRONG (2006) and I endogenize the choice of allowing one of
the sides (application developers) to interact with the other (consumers).
J. TÅG 97
Much of the early literature on two-sided markets focuses on solving the
problem of how much to charge each side 2. Related to comparing one and
two-sided markets, there has been some work on the difference between
operating as a merchant versus operating as a platform. According to
HAGIU (2007), the main difference is that a merchant takes full possession
of the content, whereas a platform leaves control over the sale to sellers and
simply intermediates the transaction.
There is also related work on exclusivity in two-sided markets by HAGIU
& LEE (2007). In their model, a content provider joins one or both platforms
depending on whether the content is exclusive or not. In contrast, I compare
the platforms' choice of whether to allow third parties 3. Finally, this paper is
also related to the two-sided market literature discussing pay-tv versus free-
to-air (see e.g. ANDERSON & COATE, 2005; PEITZ & VALLETTI, 2008;
KIND, NILSSEN & SORGARD, 2005). The main contribution to this literature
is that I consider platform competition with an endogeneous choice between
being one-sided (pay-tv) and being two-sided (partly or fully advertising
supported).
In taking the two-sided market route, my approach differs from the
aftermarket approach of KENDE (1998) in that I assume away the central
hold-up problem in the aftermarket literature. Instead, I focus on the ability of
firms to charge (or subsidize) third parties for the right to develop
applications for the platform. Adding this dimension, the firms can directly
profit from selling rights to develop for the platform. They also have the
ability to subsidize developers to encourage application development.
This paper differs from the components versus systems approach in
MATUTES & REGIBEAU (1988), CHURCH & GANDAL (1988) and ARORA
& BOKHARI (2007) by analyzing atomistic producers of secondary
components instead of two (or more) components produced by the same (or
different) firms. I place heavy emphasis on the existence of cross-group
externalities between consumers and application developers. Further, I
completely "black box" the pricing decision of application developers. My
approach has the advantage of emphasizing cross-group externalities and
2 See for example CAILLAUD & JULLIEN (2003), ROCHET & TIROLE (2003, 2006), HAGIU
(2006), and ARMSTRONG (2006).
3 One of the results in HAGIU & LEE (2007) is that firms might want to give up control rights
over pricing content in order to relax competition. This result is perhaps most closely related to
this paper as a firm here might want to give up all gains (from consumers and/or from third-
parties) in order to relax competition.
98 No. 74, 2nd Q. 2009
pricing to internalize them. The drawback is that I assume away potentially
important strategic interactions between the price of the product and the
price of applications set by application developers.
The model
I study a two-stage duopoly model of a two-sided market where firms
connect consumers with third party application providers. There are two
firms, {1, 2 }k, each with the same intrinsic value v. The value of any
applications developed in-house by the firm is also included in v. The
number of these applications is exogenous and independent of whether the
firm allows for or restricts third party development. For example, the same
basic set of applications (such as a calendar, a phone book, an alarm clock,
a simple game) bundled with high-end phones open to development are also
often available on low-end phones that do not allow development.
The firms can be open to third party development, in which case they are
platforms that connect consumers with application developers, or they can
be closed to development and simply sell the product of value v to
consumers. Firms can also set a fee (or subsidy) for the right to develop an
application.
The cost for allowing third party application development is zero. Fixed
costs are sunk and marginal costs zero. Consumers only buy one product or
platform, but application developers may develop for any or both of the
platforms that allow for development.
Consumers
Consumers are uniformly distributed on the unit interval ( [0,1]x) with
the firms, {1, 2 }k, located at the endpoints of the interval. The intrinsic
value of the products (or platforms), v, is sufficiently large for the market to
be completely covered.
In the eyes of consumers, the firms only differ in price and the number of
applications available. A consumer denoted by i receives utility
111
() ,
iia
u v tx bn p [1]
J. TÅG 99
if buying from firm 1 and utility
222
((1)) ,
iia
u v t x bn p [2]
if buying from firm 2. The number of applications available are given by 1a
n
and 2a
n. The parameter 0b! measures the marginal value to the
consumer of a third party application. Prices are 1
p
and 2
p
. The
transportation cost parameter, t, measures the intensity of competition
between firms. Finally, define by ck
n the number of consumers buying from
platform k.
Application developers
The application developers are independent monopolists. They are
treated as atomistic and are uniformly distributed on the unit interval,
[0,1]y. Developers are heterogeneous in terms of fixed costs for coming
up with a business idea, setting up shop and developing an application. An
application developer indexed by j
y
has fixed costs equal to j
f
y for
developing an application. Note that to keep the model tractable and
symmetric, application developers have no initial favored platform to develop
for and they view platforms as symmetric given the same number of
consumers using them and the same fee for application development.
Each application developer is able to extract an expected profit of 0a!
from each consumer purchasing the platform. These profits are generated
from sources such as selling advertising space or increased sales from
complementary products.
Application developers are allowed to multi-home. This means that they
may develop applications for both platforms if they both allow for third party
application development. Then, application developers make the decision to
develop for one platform independently of the decision to develop for the
other platform. Thus, there is no direct competition between the firms for
developers. A firm can attract more developers by either reducing the price
of the platform, thereby selling to more consumers, or by reducing the fee or
increasing the subsidy for application development. Application developers
must pay the fixed development cost twice if they wish to supply an
application for both platforms.
100 No. 74, 2nd Q. 2009
Conditional on the number of consumers at each platform, an application
developer
j
has profits equal to
jk ck j k
an fy s
S
[3]
from platform {1, 2}k. The costs of developing applications are sufficiently
high to ensure that some developers always stay out of the market.
Parameter k
s denotes the fee or subsidy imposed or handed out by the
platform. If s is positive, it represents a fee that must be paid for the right to
develop an application. An example is a fee that must be paid for an
application development kit needed to create the application. If s is negative
it is a subsidy. It can then be any type of action by the firm operating the
platform that reduces the costs of developing an application, such as
training, subsidized conferences and free extensive documentation of
interfaces.
Figure 1 - Platforms can either be open or closed to third party application development
Timing
In stage 1, firms simultaneously decide whether to be open or closed to
third party development. Figure 1 illustrates possible outcomes.
In stage 2, firms observe the choice made by the rival. Then, they
simultaneously set prices to consumers. Firms allowing third party
application development also set the fee or subsidy to application
developers. Consumers and developers then observe prices and the fees or
J. TÅG 101
subsidies. They form rational expectations regarding participation of the
opposite group. Then, consumers buy the platform yielding the highest utility
and developers decide separately for each platform if they should develop
for the platform.
This timing captures the fact that the choice of being open or closed to
third party application development is more long term than the choice of
prices and fees (subsidies). It allows firms to commit to allowing
development or not before setting prices and fees. That consumers and
application developers make their adoption decisions simultaneously
captures the fact that they arrive in a sufficiently alternated fashion. I thus
abstract from situations in which one side clearly arrives before the other.
The assumption that consumers form rational expectations also implies that
adoption dynamics such as solving a chicken-and-egg problem (see e.g.
CAILLAUD & JULLIEN, 2003) are set aside.
In what follows, I solve this game by backwards induction. I look for pure
strategy sub-game perfect Nash equilibria. I start by analyzing pricing in the
second stage of the game. I consider separately all four sub-games outlined
in Figure 1. Then, I move back to the first stage of the game and analyze the
choice of being open or closed to third party application development.
Analysis
Stage 2: closed-closed
When both platforms are closed to development, the setup reduces to the
standard Hotelling model with firms at both endpoints of the unit interval. For
the consumer who is indifferent between purchasing from firm 1 or firm 2
12
(1 )
ii
vtx p v xt p [4]
holds. Then, demand for firm 1's product is 211
122
pp
ct
n
. Demand for firm
2's product is 21
1
cc
nn . The firms simultaneously set price to maximize
kCC k ck
p
n
S
resulting in equilibrium prices of kCC
t
, and profits of
2
t
kCC
S
.
102 No. 74, 2nd Q. 2009
Stage 2: open-open
The consumer indifferent between purchasing platform 1 and purchasing
platform 2 is located at the i
x
satisfying
11 2 2
(1 )
ai a i
vbn tx p vbn xt p [5]
Demand for firm 1's platform conditional on the number of applications at
each platform is then equal to 12 21
1
122 2
aa
bn bn pp
cond
ctt
n
. Demand for firm
2's platform conditional on the number of applications at each platform is
21
1
cond cond
cc
nn . The developer who is indifferent between developing and
not developing an application for platform k is located at ck k
an s
jf
y
.
Demand for developing applications for platform ck k
an s
jf
y
conditional on
the number of consumers purchasing each platform is then ck k
an s
cond
ak f
n
.
Simultaneously solve equations 11
cond
cc
nn ,22
cond
cc
nn ,11
cond
aa
nn and
22
cond
aa
nn to obtain demands as functions of prices on both sides of the
market:
21 21
11212
()( )
(, ,,) 2( )
c
bs a s f p p t
n ppss ft ab
  
, [6]
12 12
21212
()( )
(, ,,) 2( )
c
bs a s f p p t
nppss ft ab
  
, [7]
2
12 2 1 1
11212
(( ) ( )) 2
(, ,,) 2( )
a
abs s f p p t ab fst
n ppss fft ab
  
, and [8]
2
12 1 2 2
21212
(( ) ( )) 2
(, ,,) 2( )
a
abs s f p p t ab fst
n ppss fft ab
  
[9]
Given these demand functions, firms simultaneously set prices, k
p
, to
consumers and the fees (subsidies) to application developers, k
s, to
maximize kOO k ck k ak
p
nsn
S
.
J. TÅG 103
Equilibrium prices are

( 3 ) / 4 and / 4,
kOO kOO
ptaabfs ab

and platform profits are 22
(1 / 2) ( 6 ) / 16
kOO ta abb f
S
. The
second-order conditions, 0
f
ft ab
,2
()
0
ft ab
fftab
, and 22
2
86
4( ) 0
ft a ab b
ab ft
 
!
are satisfied for 2
4( )0ft a b !. This is a technical condition required for
an equilibrium to exist, which can be rewritten as
2
0
2
ab
ft
§·
!!
¨¸
©¹
.
It says that the product of the transportation cost and the fixed entry cost
must be larger than the square of the average of the cross-group
externalities.
Firms balance the price to consumers with fees (or subsidies) to
application developers so as to best internalize cross-group externalities.
Application developers are subsidized if the valuation of applications by
consumers is sufficiently large in relation to developers' profits from reaching
an additional consumer (ba!).
As noted by ARMSTRONG (2006), profits from the multi-homing side
(the application developer side) are competed away on the single-homing
(consumer) side of the market. The reason is that the competition for
consumers is intensified when platforms are open to third party application
development and network effects are present. A cut in the price leads to
more consumers buying the platform. It also attracts more application
developers because more consumers have bought the platform. Both
platforms then have strong incentives to cut price. These incentives are
increasing in the size of cross-group externalities and decreasing in the
costs of developing applications (because it becomes easier to attract
developers). Hence, profits (and prices) are increasing in the costs of
developing applications and decreasing in the size of the cross-group
network externalities. Since profits are decreasing in the size of the cross-
group network externalities, firms would like to reduce them. This gives firms
an incentive to restrict third party application development in stage 1 as it
removes cross-group externalities.
104 No. 74, 2nd Q. 2009
Stage 2: open-closed and closed-open
Assume that firm 1 has the platform with third party application
development and firm 2 has restricted development and only sells a product.
The formulas for the reverse case can easily be obtained by renaming the
firms.
Conditional on the number of applications developed for platform 1, the
consumer who is indifferent between platforms is located at the i
x
that
satisfies
11 2
(1 )
ai i
vbn tx p v xt p . [10]
Demand for firm 1's platform conditional on the number of application
developers that develop for platform 1 is 121
1
122 2
a
bn pp
cond
ctt
n
. Demand for
firm 2's product conditional on the number of application developers that
develop for platform 1 is 21
1
cond cond
cc
nn . The developer who is indifferent
between developing for platform 1 and not developing is located at
11c
an s
jf
y
. Demand for developing applications for platform 1 conditional
on the number of consumers purchasing platform 1 is then 11
1
c
an s
cond
af
n
.
To obtain demands as functions of prices on both sides of the market,
simultaneously solve equations 11
cond
cc
nn ,22
cond
cc
nn and 11
cond
aa
nn .
This gives
112
1121
()
(, ,) 2
c
bs f p p t
n pps ab ft

, [11]
112
2121
()
(, ,) 2
c
ab bs f p p t
n pps ab ft
 
, and [12]
12 1
1121
()2
(, ,) 2
a
ap p t st
n pps ab ft

. [13]
Firm 1 sets the price to consumers and the fee (or subsidy) to application
developers to maximize 11112111121
(, ,) (, ,).
OC c a
p
n pps sn pps
S
Firm 2
simultaneously sets the price to consumers to maximize
222121
(, ,).
OC c
p
npps
S
Equilibrium prices are
J. TÅG 105
122
(4 ( ))(3 )
(12 4 )
f
taab ftab
p
f
ft a ab b
 
  , [14]
122
()(3 )
12 4
ab ftab
s
f
ta abb

 , and [15]
2
222
(6 ( ) )(2 )
(12 4 )
f
tab ftab
p
f
ft a ab b
 
  . [16]
Figure 2 - The simultaneous move game played in stage 1
Platform profits are
22 22
12
222 222
(8 ( ) )( 3 ) (( ) 6 ) (2 )
, and
(4 12) (4 12)
OC OC
f
tab ab
f
tab
f
t
f
tab
f
aabb
f
t
f
aabb
f
t
SS

  
 
The second-order conditions - 2
20
f
ft ab
,4
20
t
ft ab
 and 2
2
8( )
(2) 0
ft a b
ab ft

! are
satisfied for 2
4( )0ft a b !.
By reversing the identities of the platforms, we can get profits under the
outcome Closed-Open instead of Open-Closed. These profits are
12CO OC
SS

and 21CO OC
SS

. Application developers are subsidized if
ba!. The size of cross-group network externalities and the costs of
developing applications can either increase or decrease profits. The reason
is that while cross-group externalities increase the value of the platform to
consumers, they also lead to intensified competition for consumers.
Stage 1: Open or Closed to Third Party Application Development?
The firms simultaneously decide if third-parties should be able to develop
for their platform. By solving the first stage, illustrated in Figure 2, we can
obtain the following proposition.
Proposition 1: For sufficiently large differences in cross-group network
externalities, both firms are open to third party application development.
106 No. 74, 2nd Q. 2009
They are trapped in a prisoner's dilemma. If the difference in cross-group
network externalities is sufficiently small, both firms restrict third party
application development in order to reduce network effects and relax
competition. For intermediate differences in cross-group network
externalities, one platform is open to third party application development and
the other is closed.
To see this, first assume that it is desirable for firm 1 to allow
development if firm 2 does not allow development. Then 11OC CC
SS

! or
22
222
(8 ( ) )( 3 )
2
(4 12)
ft a b ab ft t
fa abb ft
 
!. Simplifying, using 2
4( )0ft a b !, leads to the
following condition 22 2 2
2(6 )0ab a ab b ft  !. Note that this condition
holds if 22
60aabb! or equivalently, if 2
()4 0ab ab ! (there is a
sufficient difference in cross-group externalities). Assuming that
22
60aabb!, it is possible to show that 11OO CO
SS

! or that
22 22
222
86 (()6)(2)
16 (4 12)
ft a ab b a b ft ft ab
ffa abb ft
  

!. Then firm 1 has a dominant strategy to
allow for application development. This also holds for firm 2. Hence, the pure
strategy Nash equilibrium is for both firms to be open to third party
application development. The equilibrium is shown in area 1 in Figure 3.
Since 22
60aabb!, it must be that 11CC OO
SS

! and the game is a
prisoner's dilemma.
Second, now suppose that 22 2 2
2(6 )0ab a ab b ft  !, but that
22
60aabb (so
f
t is small). Then, 11OC CC
SS

! but it need not be
that 11OO CO
SS

!. If 11OO CO
SS

, the game has two pure strategy Nash
equilibria; either firm 1 is open to development and firm 2 is closed or the
reverse holds. Equilibria of this type must lie in area 3 in Figure 3, but area 3
also contains parameter combinations resulting in an equilibrium
characterized by both platforms allowing third party development.
Third, now assume that it is desirable for firm 1 to restrict application
development if firm 2 also does so. Then, 22 2 2
2(6 )0ab a ab b ft
 
and it is possible to use this to show that 11CO OO
S
S
!. Firm 1 has a
dominant strategy to restrict development. This also holds for firm 2 and the
pure strategy Nash equilibrium is for both firms to restrict application
development (area 2 in Figure 3).
J. TÅG 107
Figure 3 - Equilibrium regions for 1
f
t
The line from (0,2) to (2,0) corresponds to 2
4( )0ft a b
, the line separating areas 1 and
3 to 2
()4 0ab ab
and the line separating areas 2 and 3 to the equation
22 2 2
2(6 )0ab a ab b ft
. Varying
f
or t scales the picture. Comparing with Figure 2,
Region 1 corresponds to the OO outcome, region 2 to the CC outcome and region 3 to the
outcomes OC, CO or OO.
The proposition underscores that firms may have a dominant strategy to
restrict third party application development; this takes place despite the fact
that allowing development is free and the product increases in value for
consumers. The reason is that competition is intensified when there are
network effects between consumers and application developers. All else
equal, a given price cut to consumers when development is possible attracts
more new consumers as compared to when development is restricted
because the price is lower and platform value higher.
To see this formally, we can examine the best response functions of
firm 1. The best response functions for price for firm 1 when it restricts
development are
2
12
() 2
CC
tp
pp , and [17]
108 No. 74, 2nd Q. 2009
22
122
()
(,) 22
CO
tp bas
pps
f

. [18]
When firm 1 provides an open platform, the best response functions are
21
11 2
()
(, ) 22
OC
tp abs
psp
f

, and [19]
212
11 2 2
() ( )
(, , ) 22 2
OO
tp abs bas
psps
f
f
 
. [20]
Studying these, we can see that because 2
()
20
ba s
f
! in equilibrium, firm 1
has incentives to price more aggressively if firm 2 is open to application
development 4. Hence, by restricting third party application development,
firms are able to reduce the intensity of competition for consumers by
removing network effects.
In equilibrium, the effect on profits from allowing third party development
depends on a balance between benefits from an increase in the value of the
platform and the possibility to profit from application developers and
intensified competition for consumers 5.
For a sufficiently similar to b, both firms have individual incentives to
restrict third party application development. Allowing development would
lead to lower profits due to intense competition for consumers. This case is
represented in area 2 in Figure 3. If a is much larger than b, acquiring
additional consumers is very profitable for the firm as the fee for the right to
develop applications can be substantially increased. Even though
competition for consumers is intensified with third party application
developers, the firm finds it profitable to be open to development because
4 Firm 1 is either more or less aggressive in pricing when allowing application development. If
ba!, so that 10s in equilibrium, firm 1 is less aggressive in pricing. If ba, so 10s! in
equilibrium, firm 1 is more aggressive in pricing.
5 There is a difference between a standard quality increase of the platform and a quality
increase induced by more application developers developing for the platform. The size of a
standard quality increase does not depend on price, whereas the quality increase due to more
application developers depends on prices on both sides of the market. Further, the total profits
of the platform are the sum of profits from consumers and profits from application developers,
so that increases in quality brought about through having more application developers have a
different effect on profits than standard quality increases.
J. TÅG 109
selling the rights to develop applications recoups losses from intensified
competition for consumers.
If b is much larger than a, the ability to subsidize application developers
so as to increase the value of the platform for consumers makes it profitable
to allow for development. The value increase in the platform becomes
sufficiently large so as to compensate for the effect of intensified
competition. These two cases are represented by area 1 in Figure 3. In both
cases, the firms are trapped in a prisoner's dilemma. They would have been
better off had they been able to collude in stage 1 on restricting application
development.
For intermediate differences in a and b, it may be that platforms prefer
to allow development if the rival restricts it and to restrict development if the
rival allows it. In these cases profit increases from allowing development are
enough to compensate for intensified competition only if the rival restricts
development. The reason is that competition is more intense when both
firms are open to development than if only one firm is open to development.
Area 3 in Figure 3 contains such parameter combinations, but area 3 also
contains parameter combinations where the equilibrium is for both firms to
allow for third party application development.
Finally, application development costs (
f
) and the intensity of
competition between platforms (t) also affect the choice of being open or
closed to third party application development. Increased development costs
for applications and decreases in the intensity of competition (increases in
t) tend to make restricting development more likely due to diminished
benefits from cross-group network externalities. This can be seen by noting
that if
f
t is large and the difference in cross-group externalities small, it is
more likely that 11OC CC
SS

and 11CO OO
SS

! since it is more likely that
22 2 2
2(6 )0ab a ab b ft  .
Welfare
Can restricting third party application development to relax competition
occur when it would be socially desirable that the platforms are open to third
party application development? To answer this question we need to
determine consumer surplus and application developer profits under each
possible outcome in stage 2.
110 No. 74, 2nd Q. 2009
Consumer surplus when both firms restrict application development is
15
12
4
0()((1))
in
in
xt
CC x
CS vtx pdx vt x pdx v
 

³³ . Third party
application providers' profits are zero since they cannot interact with
consumers. If both platforms allow for application development, consumer
surplus and application provider profits are
*
*
22
1
*** **
11 2 2
0
54
()((1))4
i
i
x
OO a a
x
f
ta abb
CS vbn tx pdx vbn t x pdx v f
 
³³
[21]
and
**
12
2
*** **
11 2 2
00
()
()()
16
jj
yy
OO c c
ab
an fx s dx an fx s dx
f
3 
³³ . [22]
Finally, under the asymmetric outcomes when one firm allows for
application development and the other restricts development consumer
surplus and third party developer profits are
*
*
1
*** *
11 2
0
222
222
22 22
22
()((1))
2( 3 )((( ) 5 )( 3 ) ( 4 12 ) )
(4 12)
(( ) 6 )((( ) 6 )(2 5 ) 2 ( 4 12 ) )
2( 4 12)
i
i
x
OC a OC OC OC
x
CS v bn tx p dx v t x p dx
ab ft a b ft ab ft f a ab b ft v
fa ab b ft
a b ft a b ft ab ft f a ab b ft v
fa ab b ft


   

³³
2
[23]
and
*
1
22
***
11 222
0
()(3)
()
2( 4 12)
j
y
OC c OC OC
ab ab ft
an fy s dy
f
aabb ft

3  
³. [24]
Given these expressions, which of the four possible combinations of
being open or closed to third party development would maximize social
welfare? Suppose that social welfare is measured as the sum of consumer
surplus, firm profits and third party developer profits. Then, it is best for total
welfare to have both firms allow for development if
** * * ** *
12 1 12OO OO OO OO CC CC CC
CS CS
SS SS
3! , [25]
** * * ** * *
12 1 12OO OO OO OO OC OC OC OC
CS CS
SS SS
3! 3, and [26]
J. TÅG 111
** * * ** * *
12 1 12OO OO OO OO CO CO CO CO
CS CS
SS SS
3! 3
. [27]
The first condition always holds since the difference between the left-
hand and right-hand side is 2
1(( ) ) 0
fab!. The second and third
conditions are equivalent in this model. It is possible to show that they hold
for
f
t sufficiently large
6. Hence, for sufficiently large
f
t, it is socially
optimal that both platforms allow for third party application development.
If the firms privately choose between allowing and restricting third party
application development, each firm will have a dominant strategy to provide
an open platform if **
11OC CC
SS
!,**
22CO CC
SS
!,**
11OO CO
SS
!, and
**
22OO OC
SS
!. The first two and the second two conditions are equivalent.
The first two conditions hold for 22 2 2
2(6 )0ab a ab b ft  !, which is
positive for large
f
t only if 22
60aabb! or, equivalently, if
2
()4 0ab ab !. Hence, for large
f
t and sufficiently small difference in
cross group externalities, so that 2
()40ab ab  , firms would not have
any incentives to allow for third party application development even if it were
socially desirable.
Proposition 2: There exist cases where competing platforms restrict third
party application development in a sub-game perfect equilibrium when total
welfare would be higher if the firms allowed for third party application
development.
The reason for why firms do not have incentives to be open to third party
application development is that it makes the rival more aggressive in pricing.
Proposition 2 then suggests that there may be situations in which a policy of
supporting open platforms is warranted; particularly when firms seem to
restrict third party application development in order to reduce competition for
consumers.
6 The difference between the left-hand and right-hand side can be simplified to
43 22 34 243 2234 22
4(17 72 106 72 17 ) 3( ) ( 8 10 8 72 )aabababbftabaabababb ft   
which holds for sufficiently large
f
t.
112 No. 74, 2nd Q. 2009
Discussion on extensions
This stylized model can be extended in several directions. First, it was
assumed that the market was completely covered on the consumer side.
This implies that price cuts to consumers by the firms do not attract new
customers; neither do increases in quality from allowing third party
application development. Maintaining the assumption of a covered market
thus biases the results in favor of restricting application development. The
assumption does not, however, change the fact that competition between
firms with third party applications is more intense than competition between
firms that does not have third party applications.
Second, the current setup does not allow the firms to choose between in-
house application development and outsourcing the development of
applications to third-parties. I only consider the choice between allowing third
party application development or not. This is likely to bias the results in favor
of allowing third party development as this is the only way to increase the
quality of the product sold.
Third, it was assumed that there is no cost to the platform for allowing
third party application development. Introducing a fixed cost for developing
the capabilities for third party producers to develop applications is not likely
to change the nature of the results other than increasing the benefit to
platforms from restricting third party application development. It may also be
that unauthorized third party application development takes place. In that
case, opening the platform to third party application development may
involve cost savings, as costly measures to restrict unauthorized use and
development of applications no longer need to be undertaken. In this case
the results would change so that it would be more likely for the platforms to
be open to third party application development.
Fourth, it was assumed that third party application developers had to
incur the fixed cost of developing an application once for each platform.
Once an application has been developed, however, it is likely that porting it
to another platform is less expensive than rewriting it completely. Introducing
this aspect into the model potentially significantly complicates the analysis.
The reason is that in the current set up, each application developer decides
on developing for one platform independently of the decision to develop for
the other. As a consequence, the firms only compete directly for users and
not for application developers, as the choice to develop for one is
independent of the choice to develop for the other. If the costs for developing
an application are conditional on whether the application has previously
J. TÅG 113
been developed, development choice becomes interdependent. The likely
bias of this extension on the results is not clear and hence, is a good
direction for future research. Existing complementary work on the issue of
porting in two-sided markets include POLLOCK (2008).
Concluding remarks
Why are some platforms open to third party application development
while others are closed? In this paper, I take a two-sided market approach
and highlight that being open to third party development intensifies
competition for consumers. Hence, firms might prefer to commit to restricting
development despite the fact that applications are valuable to consumers
and allowing third party application development is free.
In a two-stage model of a two-sided market, I find three types of
equilibrium configurations: both firms allow development (and the firms are
trapped in a prisoner's dilemma); both firms restrict development; or one firm
allows development and the other restricts it. The outcome depends on the
relative difference in cross-group externalities, the intensity of competition for
consumers and the cost for developing applications.
The policy implications are that competing platforms may have incentives
to restrict third party application development even when it is desirable for
society that they are open to development. In particular, the model suggests
that private and social incentives to open the platforms diverge when
consumer transportation costs and application developer fixed costs are
large, and when there is a small difference in cross group externalities so
that it is not clear which side values the other more. Under these conditions -
and if firms provide closed platforms - a policy in support of open platforms
could be beneficial to society.
As regards to future research, the model is cast in the framework of
software and hardware platforms. It could also apply to other two-sided
markets where choosing between providing a one-sided product or a two-
sided platform is possible. In particular, as a firm can be open or closed to
advertisers, the analysis could be adapted to study how magazines and TV
stations are funded along the lines of KIND, NILSSEN & SORGARD (2005).
114 No. 74, 2nd Q. 2009
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