Standards and Market Entry Reiko Aoki Yasuhiro Arai Kyushu University

advertisement
Standards and Market Entry
Reiko Aoki
Kyushu University
Yasuhiro Arai
Kochi University
1
Introduction
• Standards become beneficial when there are network effects
• Consumer Value
• Price of inputs
Standards are pro-innovation
• However, strategic use of standards is possible
• Switching cost
• Rival cost
Standards may be antiinnovation
What is the relationship between standards and innovation?
2
Standards and Innovation
• Relationship between standards and innovation
 Patent pools and innovation
Lampe and Moser (2012)
 Standards and innovation
Farrell & Saloner (1985), Cabral & Salant (2013)
• Entry Deterrence
 Entry Deterrence by Increasing standard inertia
Farrel and Saloner (1987)
 Entry Deterrence by Increasing switching cost
Klemperer (1987), Chen (1997)
3
Focus of this Paper
• There is a standard in place.
Incumbent
Investment
Standard
Inertia
Improve the
Technology
Entrant
Investment
Improve the
Technology
• • Incumbent
in two
things • Entrant
Incumbentcan
caninvest
improve
his technology
to deteronly
the invests
entry. to improve
1. Increase standard inertia
technology
 Investcan
in installed
baseto improve his technology to counter the
• Entrant
also invest
 Improve complementary technology
deterrence.
 Increase switching cost
2. Improve the standard (technology)
4
Framework: Timing
• Player
Firm 0 :incumbent
Firm 1 :new entrant
Consumers
• Timing of this game
1. Invest in technology (sequential)
I. Firm 0 invests in technology
II. Firm 1 invests in technology
2. Market competition (Bertrand competition)
• We examine how investments relate to second stage
subgame equilibria.
5
Framework: Consumer
• Consumers are located over unit interval ( Hotelling )
 The surplus of a consumer  ∈ 0,1 is given by
0 − 0 − 
:when he purchases from firm 0
1 − 1 −  −  1 −  :when he purchases from firm 1
 : the value of products
 : price of the product
: cost of changing to different standard (switching cost).
: the per unit transportation cost
• We define the bench marks �0 0 , �1 1 and � 0 , 1 by
0 − 0 − �0 0 = 0
1 − 1 −  −  1 − �1 1
=0
0 − 0 − � 0 , 1 = 1 − 1 −  −  1 − � 0 , 1
• We assume  ≥ 2.
6
Hotelling Model
• Then
0 − 0
1 − 1
, 1 − �1 1 =
,


0 − 1 − 0 + 1 +  + 
� 0 , 1 =
2
�0 0 =
• By definition, it must be that either
or
7
Framework : Optimization in Market
• Firm 0 chooses 0 to maximize his profit
0 =
0 = 0 �0 =
0 = 0 � =
0 = 0
0 0 − 0

0 0 − 1 − 0 + 1 +  + 

for
for
for
0 − 0 ≤  − 1 +  + 1
 − 1 +  + 1 < 0 − 0
≤  + 1 −  − 1
 + 1 −  − 1 < 0 − 0
• Firm 1 chooses 1 to maximize his profit
1 =
1 = 1 1 − �1 =
1 = 1 1 − � =
1 = 1
1 1 −  − 1

1  − 0 + 0 + 1 −  − 1

for
for
for
1 −  − 1 ≤  − 0 + 0
 − 0 + 0 < 1 −  − 1
≤  + 0 − 0
 + 0 − 0 < 1 −  − 1
8
Framework : Optimization in Market
• Firm 0’s best response correspondence 0 = 0 1
i.
If 3 < 0 , 
0 1 =
ii.
0 − 1 +  + 1 − 
for
1 −  − 1 ≤ 0 − 3
0 − 1 +  + 1 + 
2
for
1 −  − 1 ≥ 0 − 3
0 + 1 −  − 1 − 
for
1 −  − 1 ≤  −
0 − 1 +  + 1 + 
2
for
1 −  − 1 ≥  −
If 3 > 0 , 
0 1 =
iii. If 3 = 0 , 
0 1 =
0 − 1 +  + 1 + 
2
for all
0
3
0
3
9
1 −  − 1 ≥ 0
Framework : Optimization in Market
• Firm 1’s best response correspondence 1 = 1 0
i.
If 3 < 1 − , 
1 0 =
ii.
 − 
 0 −  − 0 + 1 − 

for
 − 0 + 0 + 1 − 
2
for
0 −  − 0 + 1 − 
If 3 > 1 − , 
 − 

1 0 = 1 −  −  + 0 − 0
 − 0 + 0 + 1 − 
2
for
for
for
for
0 − 0 ≤  −
−
1 − 
2
1 − 
< 0 − 0 ≤ 1 −  − 3
2
1 −  − 3 < 0 − 0
0 − 0 ≤  −
−
−
1 − 
2
1 − 
1 − 
< 0 − 0 ≤  −
2
3
1 − 
< 0 − 0
3
10
Framework : Optimization in Market
• Firm 1’s best response correspondence 1 = 1 0
iii. If 3 = 0 , 
0 1 =
 − 0 + 0 + 1 − 
2
for all
0 − 0 ≥ 0
11
Market Equilibrium
I.
Only Firm 0 (Deter Entry):
All consumers purchase from firm 0
II. Only Firm 1 (Standard Replaced):
All consumers purchase from firm 1
12
III. Two firms co-exist in the market (unique equilibrium):
and
0 − 1 +  + 3 ∗ 1 − 0 −  + 3
, 1 =
3
3
2
1 0 − 1 +  + 3
1 1 − 0 −  + 3
0∗ =
, 1∗ =
2
2
3
3
0∗ =
p1
p0 =
v0 − v1 + S + p1 + t
2
R0
2
p0 = v0 − v1 + S + p1 − t
R1
p1 =
t − v0 + p0 + v1 − S
2
v1 − S + t − v0
13
p1 = p0 + v1 − S − t − v0
v1 − S − t − v0
0
p0
IV. Two firms co-exist in the market (multiple equilibria):
0∗
0 + 1 −  < 3
3 −  0
=
− 1−
3
p1
1 − 
−
3
p0 =
, 1∗ =
v0 − v1 + S + p1 + t
2
v1 − S + t + v0
R0
p1 =
0
2 +  1 − 
− −
3
3
where  ∈ [0,1]
t − v0 + p0 + v1 − S
2
t − v0 + v1 − S
2
R1
0
p0
If we also assume that the entrant is sufficiently efficient
1 −  ≥ 2 , then this regime never occurs.
Market Equilibrium
ν1 − S
Standard Replaced
Regime II
Only Firm 1
Co-existence (Unique equilibrium)
3t
Regime III
Regime I
Only Firm 0
Regime IV
Standard Upgraded
Co-existence
0
3t
ν0
15
Iso-consumer surplus curve
ν1 − S
ν1 − S
CS increases
Regime II
3t
Iso-social surplus curve
SW increases
Regime II
3t
Regime III
Regime III
Regime I
Regime I
0
Regime IV
3t
ν0
0
Regime IV
3t
ν0
Investment
• We examine how investments relate to second stage
subgame equilibria.


Firm 0 (Incumbent) can invest in technology, Δ0
0 = ̅ + Δ0 (Upgrade)
max 0 Δ0 , Δ1 ,  − 0 Δ0
Δ0
Firm 1 (Entrant) can invest in technology,Δ1
0 = ̅ + Δ1 (Replace)
max 1 Δ0 , Δ1 ,  − 1 Δ0
Δ1

Costs of investment are
0 Δ0
Δ20
Δ21
=
, 1 Δ1 =
2
2
17
Subgame
• For simplicity, we assume that ̅ > 3
• If there is no investment Δ0 = Δ1 = 0 , 0 = 1 = ̅
and regime (III) will transpire
• There are two possible regimes after Firm 0 has its
investment choice.
0 +  > 3
ν1 − S
ν1 − S
Replacement
Regime II
3t
Regime III
Regime IV
0
̅ , ̅ − 
3t
0 +  < 3
Replacement
Regime II
0
3t
Regime I
Upgrade
ν0
Regime III
Regime IV
0
0
̅ , ̅ − 
3t
Regime I
Upgrade
ν0
18
Subgame
• The final outcome depends on firm 1’s investment choice.
Next Proposition shows the equilibrium outcome of this
game.
Proposition 2
In equilibrium,
if  ≤ 1/3 or 9 3 − 1 / 9 − 1 <  ,
Δ∗0 +  > 3 and Δ∗1 = 0
Final outcome is regime I (Upgrade)
if  > 1/3 and 9 3 − 1 / 9 − 1 >  ,
Δ∗0 +  < 3 and Δ∗1 > 0
Final outcome is regime III (Co-existence)
19
Conclusion
• Policy (competition, standardization ) should be
technology life cycle dependent
• Incumbent improving technology (upgrade) always
makes consumer better-off
• Investment in installed base can reduce consumer
surplus
• When technology is in infancy, entry deterrence (upgrade,
switching cost) and persistence of single standard
• When technology matures, co-existence of new and old
standards
• There will never be replacement in equilibrium (entrant
never dominates)
20
Appendix:Dual Investment
• There is a standard in place.
Incumbent
Entrant
Investment
Investment
Increasing
Standard
Inertia
Improve the
Technology
Improve the
Technology
• Incumbent can invest in two things • Entrant only invests to improve
1. Increase standard inertia
technology
 Invest in installed base
 Improve complementary technology
 Increase switching cost
2. Improve the standard (technology)
21
Appendix:Dual Investment
• We examine how investments relate to second stage
subgame equilibria.



Firm 0 (Incumbent) can invest in
1. Technology improvement,
(Upgrade)
2. Installed base = increase switching cost
Firm 1 (Entrant) invests in technology,
(Replace)
Costs of investment are
22
Subgame
• For simplicity, we assume that ̅ > 3
• If there is no investment Δ0 = Δ1 =  = 0 , 0 = 1 =
̅ and regime (III) will transpire
• There are two possible regimes after Firm 0 has its
investment choice.
0 +  > 3
ν1 − S
ν1 − S
Replacement
Regime II
3t
0
Replacement
Regime II
Regime III
3t
Regime I
Upgrade
Regime IV
3t
0 +  < 3
ν0
Regime III
Regime I
Upgrade
Regime IV
0
3t
ν0
23
Subgame
• The final outcome depends on firm 1’s investment choice.
Next Proposition shows the equilibrium outcome of this
game.
Proposition 2
In equilibrium,
if  ≤ 1/3,
if  > 1/3,
Δ∗0 +  ∗ ≡ Δ∗ > 3 and Δ∗1 = 0
Final outcome is regime I (Upgrade)
Δ∗0 +  ∗ ≡ Δ∗ < 3 and Δ∗1 > 0
Final outcome is regime III (Co-existence)
24
Download
Related flashcards

Investment companies

42 cards

Insurance companies

35 cards

Lehman Brothers

18 cards

Create Flashcards