V ertical Structure and Patent Pools by Sung-Hwan Kim. Review of - - PDF document

V ertical Structure and Patent Pools by Sung-Hwan Kim. Review of Industrial Organization, 25:231-250, 2004. 1

• Overlapping and fragmanted patent

rights, ’ ’ patent thickets’ ’(Heller and Eisenberg, 1998) ∗ to commercialize new technol-

• gy, obtain licences from multi-

ple patentees. Slows down com- mercialization of new tech. ∗ Transaction costs and complements problem where distinct firms sell complementary inputs (an exam- ple is due to Cournot (1838) for copper and zinc producers) to the downstream firm (Shapiro, 2001). ∗ The firms fail to internalize the effect of their royalty rates on

• ther (input) firms’demands (set

too high royalty rates) ∗ If they form a patent pool, roy- 2

alty rates decline, overcome com- plements pr. (↑ efficiency). ∗ Patent pool: set joint royalty rates to max. profits, overall price ↓

• f final product, efficiency gain.
• Shapiro (2001) shows a patent pool

enhances efficiency by eliminating complements problem.

• The author builds on by allowing for

vertical integration (in real life many examples like DVD patent pools, Sony, Phillips..etc) of upstream and down- stream firms, also assumes Cournot- Nash comp. for downstream indus- try.

• Suppliers produce distinct products,

producers only produce a single prod- 3

uct and all upstream firms have a patent over its product.

• 4 cases author considers,

Without a patent pool (integration vs no integration) ∗ Effect of integratedness on final product price is ambigous (↓ dou- ble marginalization (-), ↑ rivals’ costs (+)) With a patent pool (integration vs no integration) ∗ V ertical integration reduces prod- uct price (further) and ↑ the ef- ficiency gain of patent pools on welfare. 4

Model

• Patents in the pool are perfect com-

plements.

• Patent pool use linear pricing.
• No uncertainty.
• Downstream market: homogeneous

goods.

• Downstream firm buys licences of

patents.

• n vertically integrated firms V=–v1,v2,...,vn

, m only upstream segment firms U=–u1,u2,.., um , s only downstream segment firms D=–d1,d2,...,ds . In total m+n+s.

• P(Q)=a-bQ, mkt demand.
• Upstream cost of licensing=0, down-

stream: cvi = c + rvi (i=1,..,n) and 5

cdi = c + rdi (i=1,..,m). Also c < a.

• Firms engage in two-stage non-cooperative

game played once. 1st stage, upstream firms indepen- dently and simultaneously decide

• n their unit royalty rates –lv1, lv2, ..., lvn,

lu1, lu2, .., lum If they form a patent pool, royalty rate lp. 2nd stage, downstream firms ob- serve these rates (costs for them) and determine their quantities in- dependently and simultaneously.

• Licensing w/o VI firms (Benchmark

case)

• No VI (vertically integrated) firms,

n=0 and m, s > 1. 6

• Backwards induction, Cournot-Nash

Equilibrium for s downstream sup- pliers (assume all firms produce in eq-m), Q∗ = X q∗

di = sa − P s cdi

(s + 1)b (1)

• If stage 2 eq-m is an interior solu-

tion then cdi = c + rdi = c + P

j luj

Now turn to stage 1

• Case 1: Absence of a Patent Pool:

Individual upstream firm’ s (ui ∈ U) problem, max

lui

lui.Q∗(lui) (2)

• Then l∗

ui = (a−c)/(m+1) and r∗ di =

m.l∗

ui.

7

• P ∗ = a − bQ∗ = c + X1 > c + r∗

di.

Final good price is greater than MC, too high.

• ∂P ∗/∂m > 0 (complements prob-

lem), downstream firms compete for upstream’s surplus, as m↑ efficiency ↓ .

• Case 2: Presence of a Patent Pool
• 2nd stage industry supply,

Q∗

P = sa − s(c + lp)

(s + 1)b (3) Stage 1, upstream firms problem, max

lp

lp.Q∗(lp) (4)

• l∗

p = (a − c)/2

• P ∗

p = a − bQ∗ = c + X2 > c + l∗ p.

8

• It can be shown that P

m l∗ ui > l∗ p =

⇒ P ∗ > P ∗

p for m > 1. As m ↑ re-

duction in P (due to patent pool) ↑ (patent pool ↑ efficiency)

• Licensing w/ VI firms
• Case 1: Absence of a Patent Pool:

Asymmetric cost conditions for down- stream firms; cvi = c + P

j6=i lvj + P luj, cdi =

c + P

j6=i lvj + P luj

• Author shows 2nd stage Q∗ (Cournot-

Nash eq-m) is an interior eq-m

• Q∗ = n(a − c) − (n − 1) P

n lvj − n P m luj

(n + 1)b (5)

• Given Q∗ at 1st stage upstream firms

9

max their profits.

• Due to asymmetry, n of upstream firms

(VI) objective is, max

lvi

π∗

vi(lvi) + lvi

X

j6=i

q∗

vj(lvi)

(6)

• ∂πvi

∂lvi = ∂π∗

vi

∂lvi + X

j6=i

q∗

vj+lvi

∂ P

j6=i

q∗

vj

∂lvi = 0 (7)

• ∂π∗

vi

∂lvi > 0 , the firm ↑ lvi to get more

upstream profit. Highering the roy- alty makes firm more competitive in manufacturers market (keep rivals away from your innovation), this is raising rivals’costs. 10

• ∂P

j6=i

q∗

vj

∂lvi < 0, marginal upstream loss.

• At optimum marginal gain = mar-

ginal loss.

• Specialized upstream firm (m firms),

max

lui

lui.Q∗ (8)

• FOC

∂πui ∂lui = Q∗ + lui.∂Q∗ ∂lui = 0 (9)

• Solve for l∗

ui and l∗ vi from (7) and (9)=

⇒ get Q∗ and P ∗ = c + X3

• Straightforward to show P ∗ > c +

r∗

vi and P ∗ < c + r∗ di

• All specialized downstream produc-

ers (m firms) will be out (p < mc). 11

Theorem 1 Consider an industry with at least one vertically integrated firm and no patent pool. Then in a sub- game perfect equilibrium, all the spe- cialized manufacturers are excluded and only the vertically integrated firms are active downstream.

• Case 2: Presence of a Patent Pool
• Upstream patent pool members max.

joint profit and split it according to predetermined allocation rule (θv1, ..., θvn, θu1, ..., θum)

• θui > 0, θvi ≤ 1, P θvi+P θui = 1.
• Now at 2nd stage, a VI firm’s quan-

tity decision will affect pool’s profit, in turn, will affect their respective upstream profits according to the al- 12

location rule.

• Downstream firm’ s choices are vi

and di subject to objective functions: πvi = (a − bQ − c − lp)qvi + θvilpQ (10) πdi = (a − bQ − c − lp)qdi (11)

• At 1st stage upstream firm will choose

to max. joint profit wr to lp, πpool = X

n

π∗

vi(lp) +

X

m

π∗

ui(lp)

(12)

• Solving the above FOC for l∗

p and

getting Q∗

p =

⇒ P ∗

p = c + X4. P ∗ >

c + r∗

vi and P ∗ > c + r∗ di.

13

Theorem 2 Consider an industry with at least one vertically integrated firm and a patent pool. Then, in the unique subgame perfect equilibrium, there is no exclusion of downstream firms ex- cept when P θvi = 1.

• P θvi = 1 is when all pool profit is

shared among VI firms. As a summary,

• No VI, prices are given by;

P(0, m, s) = c+(ms + m + 1)(a − c) (m + 1)(s + 1) (13) Pp(0, m, s) = c + (s + 2)(a − c) 2(s + 1) (14) 14

• It can be shown that Pp(0, m, s) <

P(0, m, s) this holds always.

• Under VI, prices are given by,

P(n, m, s) = c+h(m, n)(a − c) v(m, n) for n > 1 (15) Pp(n, m, s) = c + f(θvi, n, s) g(θvi, n, s) (a − c) 2 (16)

• Not always Pp(n, m, s) < P(n, m, s).
• Due to two offsetting effects

Raising rivals’ costs (makes roy- alty costs ↑ because VI firm wants to ↑ cost of rival downstream prod, so P ↑ ) Reduced double marginalization (makes 15

royalty costs ↓ because a VI firm uses its own patent, P ↓)

• First effect dominates when there are

relatively few VI firms (low n).

• Second effect dominates when there

are sufficiently many VI firms (high n). As n ↑ P(n, m, s) ↓ . 16