On the optimal timing of innovation and imitation · EBdV, RR, BV Innovation and imitation. Introduction The Model Innovation & Imitation Dynamics Social Welfare Optimum Extensions

IntroductionThe Model

Innovation & Imitation DynamicsSocial Welfare Optimum

ExtensionsConclusion

On the optimal timing of innovation and imitation

E. Billette de Villemeur, R. Ruble, B. Versaevel1

Ninth Annual Searle Center/USPTO Conference, Chicago 2016

1 Billette de Villemeur: Universite de Lille & LEM CNRS, France; Ruble andVersaevel: EMLYON Business School (primary affiliation) & GATE CNRS,France; corresponding author: [email protected]

EBdV, RR, BV Innovation and imitation




Research questions

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source: http://apps.who.int/globalatlas/DataQuery/default.asp





Research questions

Contrasting imitation conditions in drug vs. vaccine businesses:

Drugs: low cost of imitation by generic entrants

Vaccines: “there is technically no such thing as a generic vaccine”

→ How do conditions of imitation impact:

1) dynamics of innovation and imitation?2) economic welfare (industry and consumers)?3) incentives for innovator to change market access conditions?

(e.g., higher cost of reverse engineering; license agreement)





The Model





Structural assumptions

Two ex-ante symmetric firms

Growing market with uncertain future demand

Flow profit πM or πD scaled by a state variable Yt withGBM: dYt = αYtdt + σYtdZt , Y0 small, interest rate r > α

Endogenous fixed cost of discrete investmentI for innovator (= 1st investor)K for imitator (= 2nd investor)

A standard “real option game” except K 6= I





Timing

Firms i , j , j 6= i , non-cooperatively choose investment thresholds.

Two-stage game:

stage 1: firms choose initial investment thresholds (Yi ,Yj)that determine innovator and imitator roles;

stage 2: if a firm (i) innovates by investing first at Yi ≤ Yj ,the other firm (j) then imitates by investing at Y ∗F .

Solving the game backwards, we look for a NE in (Yi ,Yj).





Payoffs

Innovator (leader) payoff:

EYt

∫ τ∗F

τie−r (s−t)YsπMds − e−r (τi−t)I +

∫ ∞

τ∗F

e−r (s−t)YsπDds

Imitator (follower) payoff:

EYt

∫ ∞

τ∗F

e−r (s−t)YsπDds − e−r (τ∗F−t)K

with stopping times:τi ≡ mint ≥ 0 : Yt ≥ Yiτ∗F ≡ mint ≥ 0 : Yt ≥ Y ∗F





Payoffs (Dixit and Pindyck, 1994)

Innovator (leader) payoff:

LYt (Yi ,Y∗F ) =

(πM

r − αYi − I

)(Yt

Yi

)β

︸︷︷︸present value of monopoly profit flow

+πD − πM

r − αY ∗F

(Yt

Y ∗F

)β

︸︷︷︸effect of rival’s entry

Imitator (follower) payoff:

FYt (Yi ;K ) =

(πD

r − αYi −K

)(Yt

Yi

)β

︸︷︷︸present value of duopoly profit flow

where YF (K ) is the imitator value maximizing thresholdwith β (α, σ, r) > 1 decreasing in α, σ





Innovation & Imitation Dynamics





Nature of strategic competition driven by imitation cost K :

Proposition 1

The duopoly investment game has a unique symmetric equilibriumand there exists an imitation cost threshold K ≤ I such that:

(i) if K < K firms play a game of attrition. The randomizedinnovator investment threshold Yi is bounded below by YL; andthe imitator investment occurs at Y ∗F .

(ii) if K = K firms invest at standalone thresholds (YL,YF (K )).(iii) if K > K firms play a game of preemption. The innovator andimitator investment thresholds are YP < YL and YF (K ).

YP ≤ YL ≤ YF (K ) ≤ Y ∗F := supYF (K ), Yi





Nature of strategic competition driven by imitation cost K :

Proposition 1

The duopoly investment game has a unique symmetric equilibriumand there exists an imitation cost threshold K ≤ I such that:(i) if K < K firms play a game of attrition. The randomizedinnovator investment threshold Yi is bounded below by YL; andthe imitator investment occurs at Y ∗F .

(ii) if K = K firms invest at standalone thresholds (YL,YF (K )).(iii) if K > K firms play a game of preemption. The innovator andimitator investment thresholds are YP < YL and YF (K ).

YP ≤ YL ≤ YF (K ) ≤ Y ∗F := supYF (K ), Yi





Social Welfare Optimum





We study welfare as a function of K ≡ a policy instrument(e.g., strength of IP protection).

The industry perspective?

There is rent dissipation under both attrition and preemption:

E (Vi ) = min L (Y ∗L ,Y ∗F ) ,F (YF (K );K ) .

K increases ⇒ L (Y ∗L ,Y ∗F ) increases, F (YF (K );K ) decreases, so:

Proposition 2

Viewed as a function of imitation cost K , expected industry valueis initially constant (K < K ), single-peaked, and attains itsmaximum when neither attrition nor preemption occur (K = K ).





We study welfare as a function of K ≡ a policy instrument(e.g., strength of IP protection).

The industry perspective?

There is rent dissipation under both attrition and preemption:

E (Vi ) = min L (Y ∗L ,Y ∗F ) ,F (YF (K );K ) .

K increases ⇒ L (Y ∗L ,Y ∗F ) increases, F (YF (K );K ) decreases, so:

Proposition 2

Viewed as a function of imitation cost K , expected industry valueis initially constant (K < K ), single-peaked, and attains itsmaximum when neither attrition nor preemption occur (K = K ).





What about consumers? For a consumer surplus CSM or CSD

scaled by Yt the expected welfare EYi ,YjW (K ) is

EYi ,Yj

[2V(Yi , Yj

)︸︷︷︸industry value

+CSM

r − α

(min

Yi , Yj

)−(β−1)Y

βt︸︷︷︸

consumer surplus from innovation

+(CSD −CSM)

r − αY∗−(β−1)F Y

βt︸︷︷︸

consumer surplus from imitation

Industry value (first term) is maximized at K .

A higher K accelerates innovation, but decelerates imitation.





A local social optimum KA ≤ K in attrition ?

K ≤ K : investment thresholds are minYi , Yj

,Y ∗F

attrition

⇒ ∃ KA in (K , K ).EBdV, RR, BV Innovation and imitation




A local social optimum KP ≥ K in preemption ?

K ≥ K : investment thresholds are YP ,YF (K )

preemption

⇒ ∃ KP finite if β < β0 (high volatility) and KP = +∞ otherwise.





The global social optimum K ∗?

(1) A social optimum can involve attrition (K < K ∗ = KA ≤ K )

(Suppose CSM = 0 < CSD : innovator perfectly price discriminates)

(2) A social optimum can involve preemption (K < K ∗ = KP)

(Suppose CSD − CSM = 0: product market collusion)

(3) More generally:

Corollary 4

Suppose the static private entry incentive is “socially excessive”(πD ≥ (CSD + 2πD)− (CSM + πM)). Then, preemption issocially optimal if CSM/πM ≥ Ω (β).

With a sufficiently high β the condition is satisfied for a givendemand specification (e.g., β ≥ 3.14 and P = a− bQ).





Extensions





Extension 2: licensing agreement (here with 2πD ≤ πM)

Redefine:

K := K0 +KI ; where KI relates to transferable part of technology,which is avoidable if license fee ϕ paid to the innovator

Stage 1”: both firms select initial entry thresholds (Yi ,Yj)

Stage 2”: if a single firm (i) innovates, it proposes a licensecontract involving lump sum transfer ϕ substituted for KI

Stage 3”: the remaining firm (j) decides whether or not toaccept the contract and selects its entry threshold





Extension 2: licensing agreement (here with 2πD ≤ πM)

Innovator allows entry at usual Y ∗F at maximum fee:

ϕ∗ = KI

⇒ Llic(Yi , ϕ∗) > L(Yi ,Y∗F ), F (Yi ;K0 + ϕ∗) = F (Yi ;K0 +KI )

In attrition: earlier innovation (stochastically), weakly earlierimitation (YF (K ) unchanged), higher equilibrium payoffs

In preemption: earlier innovation (deterministically, YP lower),same imitation threshold (YF (K )), unchanged equilibrium payoffs

→ Licensing increases social welfare





Conclusion

imitation cost (K ) implies either attrition or pre-emption

no “one size fits all” welfare recommendation (K ∗ = KA,KP)

there must be a non-zero cost to imitation (0 < KA ≤ KP)

usual demand specifications point to optimal pre-emption

a contract (licensing) is also welfare improving





***





Attrition: K < K (< K ≤ I )

YL

F (Yi ;K )

L(Yi ,YF ) M(Yi )

YF YS

E (Vi )

F (YF ;K )

L(YL,YF ) = M (YS ) at K = K ; firms mix over [YS , ∞), imitatorentry is immediate; rent equalization at E (Vi ) = M (YS ).





Attrition: K < K (< K ≤ I )

Each firm i ’s cumulative distribution of first entry thresholds Yi is

Ga (Yi ;K ) = 1− exp∫ Yi

YS

M ′(s)

F (s;K )−M(s)ds.

Substituting for the functions F and M and integrating gives

Ga (Yi ;K ) = 1−(Yi

YS

) βII−K

exp

− βI

I −K

(Yi

YS− 1

),

and the hazard rate is

ha (Yi ;K ) =βI

I −K

(1

YS− 1

Yi

),

so ∂h/∂K ≥ 0: first entry threshold decreases stochastically in K .





Attrition: K ≤ K < K (≤ I )

YL

F (Yi ;K )

L(Yi ,YF )

M(Yi )

YFYS ′ YS

F (YF ;K )

E (Vi )

L (YS ′ ,YF ) = M (YS ); firms mix over [YL,YS ′ ] ∪ [YS , ∞), imitatorentry at YF or Yi > YF , rent equalization at E (Vi ) = L (YL,YF )





Critical case: K = K

YL

E (Vi )

F (Yi ;K )L(Yi ,YF )

L(Yi ,Yi )

YF

L (YL,YF ) = F(YF ; K

), with K < I ; rent equalization at E (Vi )





Preemption: K ≤ K < I

YL

E (Vi ) F (Yi ;K )

L(Yi ,YF )

L(Yi ,Yi )

YFYP YP ′

L (YP ,YF ) = F (YF ;K ); rent equalization at E (Vi ) = F (YF ,K )





Preemption: I ≤ K (here with equality)

YL

E (Vi )F (Yi ;K )

L(YL,YF )

L(Yi ,YF )

YFYP

L (YP ,YF ) = F (YF ;K ); rent equalization at E (Vi ) = F (YF ,K )





Imitation cost thresholds

K : L(YL,YF (K )) = M (YS )

i.e., the imitation cost that equalizes the maxima

of payoff functions L and M

K : L(YL,YF (K )) = F (YF (K ); K )

i.e., the imitation cost that equalizes the maxima

of payoff functions L and F

KK IK

KK IKEBdV, RR, BV Innovation and imitation

Documents

On the optimal timing of innovation and imitation · EBdV, RR, BV Innovation and imitation. Introduction The Model Innovation & Imitation Dynamics Social Welfare Optimum Extensions