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 𝑥 ∈ 0,1 is given by
𝑣0 − 𝑝0 − 𝑡𝑡
:when he purchases from firm 0
𝑣1 − 𝑝1 − 𝑆 − 𝑡 1 − 𝑥 :when he purchases from firm 1
𝑣𝑖 : the value of products
𝑝𝑖 : price of the product
𝑆: cost of changing to different standard (switching cost).
𝑡: the per unit transportation cost
• We define the bench marks 𝑥�0 𝑝0 , 𝑥�1 𝑝1 and 𝑥� 𝑝0 , 𝑝1 by
𝑣0 − 𝑝0 − 𝑡𝑥�0 𝑝0 = 0
𝑣1 − 𝑝1 − 𝑆 − 𝑡 1 − 𝑥�1 𝑝1
=0
𝑣0 − 𝑝0 − 𝑡𝑥� 𝑝0 , 𝑝1 = 𝑣1 − 𝑝1 − 𝑆 − 𝑡 1 − 𝑥� 𝑝0 , 𝑝1
• We assume 𝑣𝑖 ≥ 2𝑡.
6
Hotelling Model
• Then
𝑣0 − 𝑝0
𝑣1 − 𝑝1
, 1 − 𝑥�1 𝑝1 =
,
𝑡
𝑡
𝑣0 − 𝑣1 − 𝑝0 + 𝑝1 + 𝑆 + 𝑡
𝑥� 𝑝0 , 𝑝1 =
2𝑡
𝑥�0 𝑝0 =
• By definition, it must be that either
or
7
Framework : Optimization in Market
• Firm 0 chooses 𝑝0 to maximize his profit
𝜋0 =
𝜋0𝐴 = 𝑝0 𝑥�0 =
𝜋0𝐵 = 𝑝0 𝑥� =
𝜋0𝐶 = 𝑝0
𝑝0 𝑣0 − 𝑝0
𝑡
𝑝0 𝑣0 − 𝑣1 − 𝑝0 + 𝑝1 + 𝑆 + 𝑡
𝑡
for
for
for
𝑣0 − 𝑝0 ≤ 𝑡 − 𝑣1 + 𝑆 + 𝑝1
𝑡 − 𝑣1 + 𝑆 + 𝑝1 < 𝑣0 − 𝑝0
≤ 𝑡 + 𝑣1 − 𝑆 − 𝑝1
𝑡 + 𝑣1 − 𝑆 − 𝑝1 < 𝑣0 − 𝑝0
• Firm 1 chooses 𝑝1 to maximize his profit
𝜋1 =
𝜋1𝐴 = 𝑝1 1 − 𝑥�1 =
𝜋1𝐵 = 𝑝1 1 − 𝑥� =
𝜋1𝐶 = 𝑝1
𝑝1 𝑣1 − 𝑆 − 𝑝1
𝑡
𝑝1 𝑡 − 𝑣0 + 𝑝0 + 𝑣1 − 𝑆 − 𝑝1
𝑡
for
for
for
𝑣1 − 𝑆 − 𝑝1 ≤ 𝑡 − 𝑣0 + 𝑝0
𝑡 − 𝑣0 + 𝑝0 < 𝑣1 − 𝑆 − 𝑝1
≤ 𝑡 + 𝑣0 − 𝑝0
𝑡 + 𝑣0 − 𝑝0 < 𝑣1 − 𝑆 − 𝑝1
8
Framework : Optimization in Market
• Firm 0’s best response correspondence 𝑝0 = 𝑅0 𝑝1
i.
If 3𝑡 < 𝑣0 , 𝑡𝑡𝑡𝑡
𝑅0 𝑝1 =
ii.
𝑣0 − 𝑣1 + 𝑆 + 𝑝1 − 𝑡
for
𝑣1 − 𝑆 − 𝑝1 ≤ 𝑣0 − 3𝑡
𝑣0 − 𝑣1 + 𝑆 + 𝑝1 + 𝑡
2
for
𝑣1 − 𝑆 − 𝑝1 ≥ 𝑣0 − 3𝑡
𝑣0 + 𝑣1 − 𝑆 − 𝑝1 − 𝑡
for
𝑣1 − 𝑆 − 𝑝1 ≤ 𝑡 −
𝑣0 − 𝑣1 + 𝑆 + 𝑝1 + 𝑡
2
for
𝑣1 − 𝑆 − 𝑝1 ≥ 𝑡 −
If 3𝑡 > 𝑣0 , 𝑡𝑡𝑡𝑡
𝑅0 𝑝1 =
iii. If 3𝑡 = 𝑣0 , 𝑡𝑡𝑡𝑡
𝑅0 𝑝1 =
𝑣0 − 𝑣1 + 𝑆 + 𝑝1 + 𝑡
2
for all
𝑣0
3
𝑣0
3
9
𝑣1 − 𝑆 − 𝑝1 ≥ 0
Framework : Optimization in Market
• Firm 1’s best response correspondence 𝑝1 = 𝑅1 𝑝0
i.
If 3𝑡 < 𝑣1 − 𝑆, 𝑡𝑡𝑡𝑡
𝑅1 𝑝0 =
ii.
𝒗𝟏 − 𝑺
𝑜𝑜 𝑝0 − 𝑡 − 𝑣0 + 𝑣1 − 𝑆
𝟐
for
𝑡 − 𝑣0 + 𝑝0 + 𝑣1 − 𝑆
2
for
𝑝0 − 𝑡 − 𝑣0 + 𝑣1 − 𝑆
If 3𝑡 > 𝑣1 − 𝑆, 𝑡𝑡𝑡𝑡
𝒗𝟏 − 𝑺
𝟐
𝑅1 𝑝0 = 𝑣1 − 𝑆 − 𝑡 + 𝑣0 − 𝑝0
𝑡 − 𝑣0 + 𝑝0 + 𝑣1 − 𝑆
2
for
for
for
for
𝑣0 − 𝑝0 ≤ 𝑡 −
𝑡−
𝑣1 − 𝑆
2
𝑣1 − 𝑆
< 𝑣0 − 𝑝0 ≤ 𝑣1 − 𝑆 − 3𝑡
2
𝑣1 − 𝑆 − 3𝑡 < 𝑣0 − 𝑝0
𝑣0 − 𝑝0 ≤ 𝑡 −
𝑡−
𝑡−
𝑣1 − 𝑆
2
𝑣1 − 𝑆
𝑣1 − 𝑆
< 𝑣0 − 𝑝0 ≤ 𝑡 −
2
3
𝑣1 − 𝑆
< 𝑣0 − 𝑝0
3
10
Framework : Optimization in Market
• Firm 1’s best response correspondence 𝑝1 = 𝑅1 𝑝0
iii. If 3𝑡 = 𝑣0 , 𝑡𝑡𝑡𝑡
𝑅0 𝑝1 =
𝑡 − 𝑣0 + 𝑝0 + 𝑣1 − 𝑆
2
for all
𝑣0 − 𝑝0 ≥ 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
𝑣0 − 𝑣1 + 𝑆 + 3𝑡 ∗ 𝑣1 − 𝑣0 − 𝑆 + 3𝑡
, 𝑝1 =
3
3
2
1 𝑣0 − 𝑣1 + 𝑆 + 3𝑡
1 𝑣1 − 𝑣0 − 𝑆 + 3𝑡
𝜋0∗ =
, 𝜋1∗ =
2𝑡
2𝑡
3
3
𝑝0∗ =
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):
𝑝0∗
𝑣0 + 𝑣1 − 𝑆 < 3𝑡
3 − 𝛼 𝑣0
=
− 1−𝛼
3
p1
𝑣1 − 𝑆
𝑡−
3
p0 =
, 𝑝1∗ =
v0 − v1 + S + p1 + t
2
v1 − S + t + v0
R0
p1 =
𝑣0
2 + 𝛼 𝑣1 − 𝑆
−𝛼 𝑡−
3
3
where 𝛼 ∈ [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
𝑣1 − 𝑆 ≥ 2𝑡 , 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
𝑣0 = 𝑣̅ + Δ0 (Upgrade)
max 𝜋0 Δ0 , Δ1 , 𝑆 − 𝐶0 Δ0
Δ0
Firm 1 (Entrant) can invest in technology,Δ1
𝑣0 = 𝑣̅ + Δ1 (Replace)
max 𝜋1 Δ0 , Δ1 , 𝑆 − 𝐶1 Δ0
Δ1

Costs of investment are
𝐶0 Δ0
𝛿Δ20
𝛿Δ21
=
, 𝐶1 Δ1 =
2
2
17
Subgame
• For simplicity, we assume that 𝑣̅ > 3𝑡
• If there is no investment Δ0 = Δ1 = 0 , 𝑣0 = 𝑣1 = 𝑣̅
and regime (III) will transpire
• There are two possible regimes after Firm 0 has its
investment choice.
𝛥0 + 𝑆 > 3𝑡
ν1 − S
ν1 − S
Replacement
Regime II
3t
Regime III
Regime IV
0
𝑣̅ , 𝑣̅ − 𝑆
3t
𝛥0 + 𝑆 < 3𝑡
Replacement
Regime II
𝛥0
3t
Regime I
Upgrade
ν0
Regime III
Regime IV
0
𝛥0
𝑣̅ , 𝑣̅ − 𝑆
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 𝛿 ≤ 1/3𝑡 or 9𝑡 3𝑡𝑡 − 1 / 9𝑡𝑡 − 1 < 𝑆 ,
Δ∗0 + 𝑆 > 3𝑡 and Δ∗1 = 0
Final outcome is regime I (Upgrade)
if 𝛿 > 1/3𝑡 and 9𝑡 3𝑡𝑡 − 1 / 9𝑡𝑡 − 1 > 𝑆 ,
Δ∗0 + 𝑆 < 3𝑡 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 𝑣̅ > 3𝑡
• If there is no investment Δ0 = Δ1 = 𝑆 = 0 , 𝑣0 = 𝑣1 =
𝑣̅ and regime (III) will transpire
• There are two possible regimes after Firm 0 has its
investment choice.
𝛥0 + 𝑆 > 3𝑡
ν1 − S
ν1 − S
Replacement
Regime II
3t
0
Replacement
Regime II
Regime III
3t
Regime I
Upgrade
Regime IV
3t
𝛥0 + 𝑆 < 3𝑡
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 𝛿 ≤ 1/3𝑡,
if 𝛿 > 1/3𝑡,
Δ∗0 + 𝑆 ∗ ≡ Δ∗ > 3𝑡 and Δ∗1 = 0
Final outcome is regime I (Upgrade)
Δ∗0 + 𝑆 ∗ ≡ Δ∗ < 3𝑡 and Δ∗1 > 0
Final outcome is regime III (Co-existence)
24