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2 1 Lin, P. and Saggi, K. (2002) Product differentiation, process R&D, and the nature of market competition. European Economic Review 46(1), Manasakis, C., Petrakis, E., and Zikos, V. (2014) Downstream Research Joint Venture with upstream market power. Southern Economic Journal 80(3), Arya, A. and Mittendorf, B. (2006) Enhancing vertical efficiency through horizontal licensing. Journal of Regulatory Economics 29(3), Clark, D.J. and Riis, C. (1998). Contest success functions: an extension. Economic Theory 11(1),
3 3 20 3
4 2 (Schumpeter, 1975) Research Joint Venture 4
5 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
6 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
7 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
8 6 [1] 1 a i γa 2 i /2 i a i j sa i s 8
9 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
10 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
11 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
12 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
13 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
14 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
15 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
16 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
17 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
18 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
19 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
20 18 [2] 1 d i = di N d i = di N 20
21 (RJV)
22 19 Research Joint Venture (RJV) RJV Manasakis et al., 2014 RJV Manasakis et al. (2014, SEJ) 22
23
24 20 24
25 21 Arya and Mittendorf (2006, JRE) 25
26 22 Arya and Mittendorf (2006, JRE) [1] S F R 1 c 26
27 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
28 24 Arya and Mittendorf (2006) [3] 28
29 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
30 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
31 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
32 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
33 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 ) 33
34 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
35 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
37 32 contest 1 1 contest contest success functions (CSF) Clark and Riis (1998, ET) CSF 37
38 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
39 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
40 35 Clark and Riis (1998, ET) CSF 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
41 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
42 37 Lafay and Maximin (forthcoming) [2] CSF π L π F π O π L π F π O K i 42
43 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
45 39 [1] Arya, A. and Mittendorf, B. (2006) Enhancing vertical efficiency through horizontal licensing. Journal of Regulatory Economics 29(3), Clark, D.J. and Riis, C. (1998). Contest success functions: an extension. Economic Theory 11(1), Huck, S., Konrad, K.A., and Müller, W. (2001) Divisionalization in contests. Economics Letters 70(1), Lafay, T. and Maximin, C. (forthcoming) How R&D competition affects investment choices. Managerial and Decision Economics, DOI: /mde Lin, P. and Saggi, K. (2002) Product differentiation, process R&D, and the nature of market competition. European Economic Review 46(1), Manasakis, C., Petrakis, E., and Zikos, V. (2014) Downstream Research Joint Venture with upstream market power. Southern Economic Journal 80(3), Schumpeter, J., (1975) Capitalism, Socialism and Democracy, 5th ed., Harper: New York. 45
46 40 [1] Skaperdas, S. (1996) Contest success functions. Economic Theory 7(2),
1 Flores, D. (009) All you can drink: should we worry about quality? Journal of Regulatory Economics 35(1), Saggi, K., and Vettas, N. (00) On in
6 016 4 6 1 1 Flores, D. (009) All you can drink: should we worry about quality? Journal of Regulatory Economics 35(1), 1 18. Saggi, K., and Vettas, N. (00) On intrabrand and interbrand competition: The
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