10 2016 5 16 1

1 Lin, P. and Saggi, K. (2002) Product differentiation, process R&D, and the nature of market competition. European Economic Review 46(1), 201 211. Manasakis, C., Petrakis, E., and Zikos, V. (2014) Downstream Research Joint Venture with upstream market power. Southern Economic Journal 80(3), 782 802. Arya, A. and Mittendorf, B. (2006) Enhancing vertical efficiency through horizontal licensing. Journal of Regulatory Economics 29(3), 333 342. Clark, D.J. and Riis, C. (1998). Contest success functions: an extension. Economic Theory 11(1), 201 204. 2

3 20 3

2 (Schumpeter, 1975) Research Joint Venture 4

3 1 2 q i c c i γc 2 i /2 c i sc i p = 1 q 1 q 2 π i = (1 q i q j )q i (c c i sc j )q i γ 2 c2 i. c i q i 5

4 FOC ( π i / q i = 0) max q i (1 q i q j )q i (c c i sc j )q i γ 2 c2 i. q i (c i, c j ) = 1 c + 2(c i + sc j ) (c j + sc i ). 3 max c i [ 1 q i (c i, c j ) q j (c i, c j ) ] q i (c i, c j ) (c c i sc j )q i (c i, c j ) γ 2 c2 i. FOC ( π i / c i = 0) c i = 2(1 c)(2 s) 9γ 4 2(1 s)s. 6

5 SOC ( 2 π i / c 2 i < 0) 2 π i c 2 i < 0, 8 8s + 2s2 9γ 9 < 0, 8 8s + 2s 2 9γ < 0. c i s SOC c i s = 2(1 c)(8 8s + 2s2 9γ) (4 + 2s 2s 2 9γ) 2 < 0, 7

6 [1] 1 a i γa 2 i /2 i a i j sa i s 8

7 [2] p i = 1 + a i + sa j q i q j i π i = (1 + a i + sa j q i q j )q i cq i γ 2 a2 i, = (1 q i q j )q i (c a i sa j )q i γ 2 a2 i. 9

8 2 q i (γ c i )q 2 i c i kc 2 i /2 p = 1 q i q j π i = (1 q i q j )q i (γ c i )q 2 i k 2 c2 i, = [ ] 1 (1 + γ c i )q i q j qi k 2 c2 i. 10

9 π i = (1 q i q j )q i (c c i )q i γ 2 c2 i. z i = c c i π i = (1 q i q j )q i z i q i γ 2 (c z i) 2, = (1 q i q j z i )q i γ 2 (c z i) 2. 11

10 Lin and Saggi (2002, EER) [1] R&D R&D R&D R&D 1 2 q i p i d i F(d i ) F (d i ) > 0 F (d i ) > 0 p i = a q i (s 0 d i d j )q j x i x 2 i /2 c 12

11 Lin and Saggi (2002) [2] π i = [ ] a q i (s 0 d i d j )q j qi (c x i )q i F(d i ) 1 2 x2 i. d i x i q i (x i = 0) 13

12 x i = 0 max q i [ a qi (s 0 d i d j )q j ] qi cq i F(d i ) (= π N i ). FOC ( π N i / q i = 0) π N i q i = 0, q N i (d i, d j ) = a c 2 + (s 0 d 1 d 2 ) = a c 2 + s, s = s 0 d i d j 14

13 q N i (d i, d j ) max d i [ a q N i (d i, d j ) (s 0 d i d j )q N j (d i, d j ) ] q N i (d i, d j ) cq N i (d i, d j ) F(d i ). FOC ( π N i / d i = 0) π N i d i = 0 2(a c)2 (2 + s N ) 3 F (d N i ) = 0. s N = s 0 d N i d N j 15

14 max q i [ a qi (s 0 d i d j )q j ] qi (c x i )q i F(d i ) 1 2 x2 i (= π I i ). FOC ( π I i / q i = 0) πi I = 0, qi I q (x i, x j, d i, d j ) = (a c)(2 s) + 2x i sx j, i (2 s)(2 + s) s = s 0 d i d j 16

15 q I i (x i, x j, d i, d j ) max x i [ a q I i (x i, x j, d i, d j ) (s 0 d i d j )q I j (x i, x j, d i, d j ) ] q I i (x i, x j, d i, d j ) FOC ( π I i / x i = 0) (c x i )q I i (x i, x j, d i, d j ) F(d i ) 1 2 x2 i. π I i x i = 0, x I i (d i, d j ) = 4(a c) (2 s)(2 + s) 2 4. x I i (d i, d j ) q I i (x i, x j, d i, d j ) q I i (d i, d j ) 17

16 x I i (d i, d j ) q I i (d i, d j ) max d i [ a q I i (d i, d j ) (s 0 d i d j )q I j (d i, d j ) ] q I i (d i, d j ) [ c x I i (d i, d j ) ] q I i (d i, d j ) F(d i ) 1 2 xi i (d i, d j ) 2 FOC ( π I i / d i = 0) π I i d i = 0, 2(a c)2 (2 + s I ) 2 [8(1 s I ) + (s I ) 3 (4 s I )] [(2 s I )(2 + s I ) 2 4] 3 F (d I i ) = 0 s I = s 0 d I i d I j 18

17 [1] 2(a c) 2 (2 + s N ) 3 F (d N i ) = 0, 2(a c) 2 (2 + s I ) 2 [8(1 s I ) + (s I ) 3 (4 s I )] [(2 s I )(2 + s I ) 2 4] 3 F (d I i ) = 0. FOC s I = s N d I i = d N i FOC 2(a c) 2 (2 + s N ) 2 [8(1 s N ) + (s N ) 3 (4 s N )] [(2 s N )(2 + s N ) 2 4] 3 F (d N i ) = 2(a c)2 (2 + s N ) 2 [8(1 s N ) + (s N ) 3 (4 s N )] [(2 s N )(2 + s N ) 2 4] 3 2(a c)2 (2 + s N ) 3 > 0. 0 s N 1 19

18 [2] 1 d i = di N d i = di N 20

(RJV) 21 22 21

19 Research Joint Venture (RJV) RJV Manasakis et al., 2014 RJV Manasakis et al. (2014, SEJ) 22

23 35 23

20 24

21 Arya and Mittendorf (2006, JRE) 25

22 Arya and Mittendorf (2006, JRE) [1] S F R 1 c 26

23 Arya and Mittendorf (2006) [2] q F q R p = a b(q F + q R ) CS = b(q F + q R ) 2 /2 t F t R 3 r f π S π F π R π F = [ ] a b(q F + q R ) t F qf + rq R + f, π R = [ ] a b(q F + q R ) t R qr rq R f, π S = (t F c)q F + (t R c)q R, 27

24 Arya and Mittendorf (2006) [3] 28

25 [1] q R = 0 r = f = 0 FOC ( π F / q F = 0) max q F [ a bqf t F ] qf (= π F ). π F q F = 0 q N F (t F) = a t F 2b. max t F (t F c)q N F (t F) (= π N S ). 29

26 [2] FOC ( π N S / t F = 0) πs N = 0 tf N t F = a + c 2. π N F = (a c)2 16b, πn S = (a c)2 8b, CS N = (a c)2 32b. 30

27 [1] max q F [ a b(qf + q R ) t F ] qf + rq R (= π F ), max q R [ a b(qf + q R ) t R ] qr rq R (= π R ). FOCs ( π F / q F = 0 and π R / q R = 0) q R F (t F, t R, r) = a 2t F + r + t R 3b, q R F (t F, t R, r) = a 2(r + t R) + t F 3b max t F,t R (t F c)q R F (t F, t R, r) + (t R c)q R R (t F, t R, r) (= π S ). FOCs ( π S / t F = 0 and π S / t R = 0) t R F = a + c 2, tr R (r) = a + c r. 2 31.

28 [2] q R F (t F, t R, r) q R F (t F, t R, r) q R F (r) q R R (r) max r ( a b [ q R F (r) + q R R (r)] t R F (r)) q R F (r) + rqr R (r) (= πr F ). FOC π R F r = 0, rr = 4(a c). 11 π R F = 3(a c)2 44b, π R R = (a c)2 484b, πr S = 31(a c)2 242b, CS R = 9(a c)2 242b. 32

29 π R F πn F (a c)2 = 176b CS R CS N = > 0, πr S 23(a c)2 3872b > 0. πn S = 3(a c)2 968b > 0, (Proposition 1 and 2, pp.338 339) 33

30 (r = 0) tf R(0), tr R (0) q R F (0), qr R (0) π R F (0) = ( a b [ q R F (0) + qr R (0)] tf R (0)) q R F (0) + 0 (a qr c)2 R (0) + f = 36b π R R (0) = ( a b [ q R F (0) + qr R (0)] tf R (0)) q R R (0) 0 (a qr c)2 R (0) f = 36b f F = (a c) 2 /(36b) + f, f. π F F = (a c)2 36b + (a c)2 36b = (a c)2 18b. 34

31 π F F πn F π F F πn F = (a c)2 144b < 0. (Proposition 3. (i), p.340) (Proposition 3. (ii), p.340) 35

36 43 36

32 contest 1 1 contest contest success functions (CSF) Clark and Riis (1998, ET) CSF 37

33 Clark and Riis (1998, ET) CSF [1] Clark and Riis (1998) Skaperdas (1996, ET) Contest Success Function n y = (y 1,..., y n ) p i (y) (CSF) 1 i, 0 p i (y) < 1, n k=1 p k(y) = 1 and y i > 0, p i (y) > 0. 2 i, p i (y)/ y i > 0 and j i, p i (y)/ y j 0. 1 2 38

34 Clark and Riis (1998) CSF [2] 4 i, k i, p i (y 1,..., y k 1, 0, y k+1,..., y n ) = p i (y)/[1 p k (y)]. 6 i, λ > 0, p i (y) = p i (λy). 4 6 λ 6 CSF Skaperdas (1996, ET) 39

35 Clark and Riis (1998, ET) CSF 1 2 4 6 CSF (Clark and Riis, 1998, Theorem on p.202) p i (y) = r α i, α k α i y r i n k=1 α ky r, k CSF r = α i = α k = 1 p i (y) = y i n k=1 y. k 0 y 0 p 0 (y) = y 0 y 0 + n k=1 y. k 40

36 Lafay and Maximin (forthcoming, MDE) [1] Lafay and Maximin (forthcoming, MDE) CSF n K i i p i i p i p 0 CSF p i = K i K 0 + n j=1 K j, p i = l i K l K 0 + n j=1 K j, p 0 = K 0 K 0 + n j=1 K j. CSF K 0 K 0 41

37 Lafay and Maximin (forthcoming) [2] CSF π L π F π O π L π F π O K i 42

38 Lafay and Maximin (forthcoming) [3] K i max K i K i K 0 + n j=1 K j π L + l i K l K 0 + n j=1 K j π F + K 0 K 0 + n j=1 K j π O K i. Nash Huck et al. (2001, EL) CSF Divisionalization CSF 43

44 46 44

39 [1] Arya, A. and Mittendorf, B. (2006) Enhancing vertical efficiency through horizontal licensing. Journal of Regulatory Economics 29(3), 333 342. Clark, D.J. and Riis, C. (1998). Contest success functions: an extension. Economic Theory 11(1), 201 204. Huck, S., Konrad, K.A., and Müller, W. (2001) Divisionalization in contests. Economics Letters 70(1), 89 93. Lafay, T. and Maximin, C. (forthcoming) How R&D competition affects investment choices. Managerial and Decision Economics, DOI:10.1002/mde.2745. Lin, P. and Saggi, K. (2002) Product differentiation, process R&D, and the nature of market competition. European Economic Review 46(1), 201 211. Manasakis, C., Petrakis, E., and Zikos, V. (2014) Downstream Research Joint Venture with upstream market power. Southern Economic Journal 80(3), 782 802. Schumpeter, J., (1975) Capitalism, Socialism and Democracy, 5th ed., Harper: New York. 45

40 [1] Skaperdas, S. (1996) Contest success functions. Economic Theory 7(2), 283 290. 46