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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]
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Research questions
“Compared with the situation 50 years ago, the worldwideincidence of dengue has risen 30-fold.”(WHO, 2012)
0
10
20
30
40
50
60
1955 1965 1975 1985 1995 2005
number of countries reporting dengue cases
source: http://apps.who.int/globalatlas/DataQuery/default.asp
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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)
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The Model
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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
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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).
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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
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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
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Innovation & Imitation Dynamics
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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
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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
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Social Welfare Optimum
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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 ).
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IntroductionThe Model
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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 ).
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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.
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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
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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.
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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).
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Extensions
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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
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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
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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
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***
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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 ).
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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 .
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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 )
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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 )
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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 )
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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 )
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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