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- ogy, 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 other (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 ↓ of 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: c vi = c + r vi (i=1,..,n) and 5

c di = c + r di (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 on their unit royalty rates – l v 1 , l v 2 , ..., l vn , l u 1 , l u 2 , .., l um � �If they form a patent pool, royalty rate l p . �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), di = sa − P X s c di Q ∗ = q ∗ (1) ( s + 1) b • If stage 2 eq-m is an interior solu- tion then c di = c + r di = c + P j l uj Now turn to stage 1 • Case 1: Absence of a Patent Pool: Individual upstream firm’ s (ui ∈ U) problem, l ui .Q ∗ ( l ui ) (2) max l ui • Then l ∗ ui = ( a − c ) / ( m +1) and r ∗ di = ui . m.l ∗ 7

• P ∗ = a − bQ ∗ = c + X 1 > 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, P = sa − s ( c + l p ) Q ∗ (3) ( s + 1) b Stage 1, upstream firms problem, l p .Q ∗ ( l p ) (4) max l p • l ∗ p = ( a − c ) / 2 p = a − bQ ∗ = c + X 2 > c + l ∗ p . • 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; � c vi = c + P j 6 = i l vj + P l uj , c di = c + P j 6 = i l vj + P l uj • Author shows 2nd stage Q ∗ (Cournot- Nash eq-m) is an interior eq-m � Q ∗ = n ( a − c ) − ( n − 1) P n l vj − n P m l uj ( 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, X π ∗ q ∗ (6) max vi ( l vi ) + l vi vj ( l vi ) l vi j 6 = i � ∂ P q ∗ vj X = ∂π ∗ ∂π vi j 6 = i vi q ∗ + vj + l vi = 0 ∂l vi ∂l vi ∂l vi j 6 = i (7) • ∂π ∗ ∂l vi > 0 , the firm ↑ l vi to get more vi 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 q ∗ vj ∂l vi < 0 , marginal upstream loss. j 6 = i • • At optimum marginal gain = mar- ginal loss. • Specialized upstream firm (m firms), l ui .Q ∗ (8) max l ui • FOC = Q ∗ + l ui .∂Q ∗ ∂π ui (9) = 0 ∂l ui ∂l ui • Solve for l ∗ ui and l ∗ vi from (7) and (9) = ⇒ get Q ∗ and P ∗ = c + X 3 • Straightforward to show P ∗ > c + vi and P ∗ < c + r ∗ 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 ( θ v 1 , ..., θ vn , θ u 1 , ..., θ um ) • θ ui > 0 , θ vi ≤ 1 , P θ vi + P θ ui = 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: π vi = ( a − bQ − c − l p ) q vi + θ vi l p Q (10) (11) π di = ( a − bQ − c − l p ) q di • At 1st stage upstream firm will choose to max. joint profit wr to l p , X X π ∗ π ∗ π pool = vi ( l p ) + ui ( l p ) n m (12) • Solving the above FOC for l ∗ p and p = c + X 4 . P ∗ > getting Q ∗ ⇒ P ∗ p = vi and P ∗ > c + r ∗ 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 θ vi = 1 . • P θ vi = 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) P p (0 , m, s ) = c + ( s + 2)( a − c ) 2( s + 1) (14) 14

• It can be shown that P p (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 ) for n > 1 v ( m, n ) (15) P p ( n, m, s ) = c + f ( θ vi , n, s ) ( a − c ) g ( θ vi , n, s ) 2 (16) • Not always P p ( 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