long-run market conﬁgurations in a dynamic quality-ladder

Long-Run Market Configurations in a DynamicQuality-Ladder Model with Externalities

Mario Samano Marc SantuginiHEC Montreal University of Virginia

June 2, 2018

Introduction

• Motivation: A firm may decide to release its patents in order to increasethe overall market share of the industry by increasing the degree ofcompatibility among all competitors

• Ex.: Recently, this has been the strategy taken by Tesla Motors, themanufacturer of electric vehicles (EVs) [Tesla Motors, 2014]

• Ex.: NVIDIA has announced it will open source the accelerator technologyused in its next generation autonomous driving SOC, code-named “Xavier”[Forbes, 2017]

• More formally, this sharing process is implemented through Standard-settingOrganizations (SSOs)

• Is this a good business strategy?

Samano and Santugini Long-Run Market Configurations in a Dynamic Quality-Ladder Model with Externalities 1

Introduction


Introduction

• We study situations in which the leading firm causes a positiveexternality on the quality of the good produced by its competitors.

• Questions:• How the presence of this positive externality −due either to a firm’s unilateral

decision or to regulation− affects the leading firm and the industry overall?

• What is the effect of the heterogeneity in firms’ ability to invest in quality onlong-run market configurations?


What we do

• We model quality of a product as a function of its own innovation level+ the spillover

• This aggregate of innovation enters directly into the utility function tocapture higher compatibility among the products in the market

• We embed the associated maximization utility problem into a dynamicquality-ladder model (Ericson and Pakes (1995)) in which firms differ intheir return to investment and the intensity of the spillover

• We find the long-run market configurations under different parametervalues• We check for potential multiplicity of equilibria solving the game in

consecutive finite time horizons versions of the model a la Levhari andMirman (1980)

• Model can generate different long-run market configurations: marketcollapse, market dominance by either firm, duopoly, andcombinations of these cases


Previous evidence and our approach

• Empirical evidence on the existence of technological spillovers has beendocumented by Bloom et al. (2013).• They separate the technology spillovers from the product rivalry effect of

R&D

• Even in the absence of positive externalities on quality, firms havedifferent likelihoods of success of investment.• Goettler and Gordon (2011) find a parameter value for the likelihood of

success of investment of 0.0010 for Intel and 0.0019 for AMD


Model: Heterogeneity

• Innovation externality1 No externalities κ. = 0 No compatibility among different firms

⇒ a firm’s innovations affect only consumers’ valuation for this firm’s good

2 Externalities κ. > 0 Imperfect compatibility

⇒ e.g. many different apps can use the same video compressing algorithm

• Likelihood of success of investment. Technological ability to improvequality varies across firms

• i.e., some firms are more capable than others to turn investment into asuccessful upgrade in quality (parameter α.)


Demand and profits

• Innovation: ωj

• Demand:

D (pj , p3−j ;ωj , ω3−j ) = megj (ωj ,ω3−j )−λpj

1 + egj (ωj ,ω3−j )−λpj + eg3−j (ω3−j ,ωj )−λp3−j

where m > 0 is the size of the market and

gj (ωj , ω3−j ) =

−∞, ωj + κjω3−j ≤ 0ωj + κjω3−j , 1 ≤ ωj + κjω3−j < ω∗

ω∗ + log(2 − exp(ω∗ − ωj − κjω3−j ), ω∗ ≤ ωj + κjω3−j ≤ M

M is the max quality level

• Profits:

π (pj , p3−j ;ωj , ω3−j ) = D (pj , p3−j ;ωj , ω3−j ) (pj − c)


Investment

• Innovation is affected by a firm-specific shock τj ∈ {0, 1} and anindustry-wide depreciation shock η ∈ {−1, 0}

ω′j |ωj = min{max{ωj + τj + η, 0},M}

• Probability of success conditional on investing xj ≥ 0 is

Pr(τj = 1|xj ) =αjxj

1 + αjxj≡ φj (xj )

• Industry-wide depreciation has probability

Pr(η = −1) = δ ∈ [0, 1]


Value function

• Each firm (simultaneously) maximizes the sum of current profits minusthe investment plus the continuation value of net profits

vj (ωj , ω3−j ) =

maxxj≥0

{Π (ωj , ω3−j )− xj + βE[vj (ω

′j , ω′3−j )|ωj , ω3−j , xj , x3−j ]

}

• In what follows we use the parametrization αA = µ and αB = µ− ε

⇒ the larger ε is, the more asymmetry there is in the likelihood of success ofinvestment between the leader (A) and the laggard (B)


Value, policy, and probability of success functions

020

50

20

VA at mu = 1.7 epsilon = 1.2 depreciation = 0.1

ω A

10

ω B

100

100 0

020

50

20

VB at mu = 1.7 epsilon = 1.2 depreciation = 0.1

ω A

10

ω B

100

100 0

020

1

20

XA

ω A

10

ω B

2

100 0

020

1

20

XB

ω A

10

ω B

2

100 0

020

0.5

20

Prob. success invest. A

ω A

10

ω B

1

100 0

020

0.5

20

Prob. success invest. B

ω A

10

ω B

1

100 0

020

50

20

VA at mu = 1.7 epsilon = 1.2 depreciation = 0.1

ω A

10

ω B

100

100 0

020

50

20

VB at mu = 1.7 epsilon = 1.2 depreciation = 0.1

ω A

10

ω B

100

100 0

020

1

20

XA

ω A

10

ω B

2

100 0

020

1

20

XB

ω A

10

ω B

2

100 0

020

0.5

20

Prob. success invest. A

ω A

10

ω B

1

100 0

020

0.5

20

Prob. success invest. B

ω A

10

ω B

1

100 0

Figure: Notes: Left panel: asymmetric R&D capabilities and no externalities. Rightpanel: Asymmetric R&D capabilities with externalities κA = κB = 0.3. In both panelsλ = 1.7 and δ = 0.1.


Transient distributions

Figure: Transient distributions from same policy function at different time periods. Initialdistribution a0 is uniform.


Market structures: no externalities

0 0.5 1 1.4 1.9 2.3 2.8 3.2 3.7 4.1 4.6ϵ

0.1

0.6

1

1.5

1.9

2.4

2.8

3.3

3.7

4.2

4.6

µ

Market structure types for µ ∈ (0.1, 5.0) ϵ ∈ (0.0, 5.0) δ = 0.1

C

D

D, A, B

A, B

D, A

A

0 0.5 1 1.4 1.9 2.3 2.8 3.2 3.7 4.1 4.6ϵ

0.1

0.6

1

1.5

1.9

2.4

2.8

3.3

3.7

4.2

4.6

µ


C

C, A, B

C, A

D

D, A, B

A, B

D, A

A

Figure: αA = µ and αB = µ− ε. The letter A means that firm A dominates the market.The letter D refers to duopoly. The term A,B means that the limiting distribution forquality is bimodal, i.e., either firm may take over as a monopoly. Finally, the letter Cindicates that the market collapses. Left panel represents the outcomes λ = 1.2 andright panel when λ = 1.7.


Market structures: with externalities

0 0.5 1 1.4 1.9 2.3 2.8 3.2 3.7 4.1 4.6ϵ

0.1

0.6

1

1.5

1.9

2.4

2.8

3.3

3.7

4.2

4.6

µ


C

C, A, B

C, A

D

A, B

A

0 0.5 1 1.4 1.9 2.3 2.8 3.2 3.7 4.1 4.6ϵ

0.1

0.6

1

1.5

1.9

2.4

2.8

3.3

3.7

4.2

4.6

µ


C

C, B

C, A

C, D

C, A, D

D

D, A

B

A

Figure: αA = µ and αB = µ− ε. Left column represents the outcomes from thesymmetric externalities case (κA = 0.3 and κB = 0.3). Right column representsoutcomes when the externalities are not symmetric (κA = 0.3 and κB = 0.7). Both atλ = 1.7.


Observation 1: The quality ladder model with heterogeneity inthe likelihood of success of investment and externalities can exhibitdifferent long-run distributions over market structures depending onparameter values. Those different structures are: market collapse,market dominance by either firm, duopoly, and combinations ofthese structures.


Observation 2: Allowing for externalities, for instance throughan Standard-setting Organization (SSO), removes marketdominance by letting the lagging firm to benefit from the leadingfirm’s investment. Depending on parameter values, this may lead todominance by the laggard.


Expected market shares for different levels of theexternality

5 B0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1,A = ,B = 1.5, 5A = 0.0

outside goodAB

5 B0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1,A = ,B = 1.5, 5A = 0.3

outside goodAB

Figure: Notes: Each panel shows the stacked expected market shares at each level ofthe externality for firm B. αA = αB = 1.5 in both panels. κA = 0 in the first panel andκA = 0.3 in the second. Vertical axis represents market size.


When is it optimal to share knowledge?

vA(ωA, ωB) = maxxA≥0

{Π (ωA, ωB;κB = 0)− xA + βE[vA(ω

′A, ω

′B)|ωA, ωB, xA, xB],

Π (ωA, ωB;κB ≥ 0)− xA + βE[vA(ω′A, ω

′B)|ωA, ωB, xA, xB],

},A = 1.0, ,B = 1.0, 5A = 0.0, 5B = 0.1

" VB

1

1

1

11

2

2

22

3

33

3

4

44

4

5

5

5

6

6 6

7

5 10 15! B

2

4

6

8

10

12

14

16

18

! A

" VA

-12

-10

-10-10

-8-8

-8

-8

-6

-6-6

-6 -4

-4

-4

-4

-2

-2

-2

-2

-2

5 10 15! B

2

4

6

8

10

12

14

16

18

! A

Figure: Difference in discounted profits from patent disclosureSamano and Santugini Long-Run Market Configurations in a Dynamic Quality-Ladder Model with Externalities 17

Takeaways

• Usually, policy experiments consist of simulating a large number ofdifferent industries under some specific counterfactual scenario, eachindustry is simulated several time periods given the initial condition givenby the data

• Then different outcomes are provided: expected profits, consumer surplus,and investments

• It is unlikely but possible that the transient distribution over the quality spaceexhibits multiple modes: positive probability of different market structures

• In a patent release event, it is possible for the laggard to dominate themarket, in which case the patent release should have been avoided


long-run market conﬁgurations in a dynamic quality-ladder

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