Research on selecting the sale channel model of the information goods

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1 JOURNAL OF SYSTEMS ENGINEERING Vol.28 No. Feb. 203,2,, (., ; 2., 30034) :,,., Fixed-fee Per-copy.,.,,., Fixed-fee,, Per-copy.,,. : Stackelberg : F49 : A : (203) Research on selecting the sale channel model of the information goods Liu Zhiyong,2, Li Minqiang, Kou Jisong (. College of Management and Economics, Tianjin University, Tianjin , China; 2. Business School, Tianjin University of Commerce, Tianjin 30034, China ) Abstract: The information goods manufacturer can distribute their products through many kinds of channels, e.g. online direct sale and traditional retail marketing. The retailer pays a manufacturer based on two common payment schemes, the Fixed-fee policy and the Per-copy policy. Which channel and sell model is preferable for the manufacture? The product quality, the price, and the customer acceptance for direct channel are the decisive factors. Through analyzing the decision behaviors of the manufacture, retailer and consumer, the model of maximizing the manufacture s profit is presented in the presence of both direct and retail channel. Based on the comparison among different channels, the paper shows that when the valuation for the information goods has a uniform distribution, the manufacture prefers the Fixed-fee policy through the direct sale channel, whereas the Per-copy policy is preferable through dual-channel. The best sale channel strategy is to distribute the highquality version through the direct sale channel and the low-quality version through the retailing channel for the manufacturer. Key words: information goods; supply chain; Stackelberg game; dual-channel., : ; : : ( ).

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3 :.. 3,.,,. x, x X. p r x... Stackelberg, Stackelberg.,,.,,,.,,,..., (Brick & Mortor),.,,. (Click & Mortor) [0].,...,, x, p r.,,, c(x).. u(v)., u(v) = vx, u(v) = vx p, v,, x, p ( p r, p d ).,, f( ), F ( ). F ( ) = F ( ).,.,, q Pr{v p r x }, F { p r x }.,,. 4, Fixed-fee, R,,. Per-copy, x, rx. Chellappa,., Per-copy, Fixed-fee [].,, Per-copy Fixed-fee,. 4. Fixed-fee, Π m = Rx C, C,. : Π r = q r p r b r x 2 /2 Rx, q, b r x 2 /2, [7], b r,,.,,..

4 2 28 Per-copy, x 2, rx 2, Π m = q r2 rx 2 C. Π r = q r2 p r2 b r x 2 2/2 q r2 rx 2. Stackelberg,, Π r = 0, p r Π r = 0, Fixed-fee ( ()) Per-copy ( (2)) x. t t = F (t ) f(t ). 5 F (t 2 ) + f (t 2 ) t 2 t 2 = 3f(t 2 ) + f (t 2 ) 4.2 [ ] 2 F (t2) f(t 2) [ F (t2) f(t 2) Π m = t4 f 2 (t ) 4b r Π r = t4 f 2 (t ) 8b r R = t2 f(t ) 2 x = t2 f(t ) 2b r, Π m = F ( 3 (t 2 ) t 2 F ) (t 2 ) b r f(t 2 ) f(t 2 ) Π r = F 4 (t 2 ) 2b r f 2 (t 2 ) r = t 2 F (t 2 ) f(t 2 ) x 2 = F 2 (t 2 ) b r f(t 2 ), ].. θv, θ [2]. θ =,.,,,,. θ., u d = θvx p d, p d. b 2 dx d 2, b d. q d. q d =Pr{θvx p d 0}. (3). t 3 t 3 = F (t 3 ) f(t 3 ). 4.3 Π d m = θ2 t 4 3f 2 (t3) 2b d x 2 = θt2 3f(t 3 ) b d,, v [0, ]., () (2) (3)

5 : 3,. Table Direct sale vs. retail marketing Fixed-fee Per-copy θ 2 8b d r = 4 R = b 6b θ 9 4b d 64b 8b θ b d 2048b 64b 8 892b 28b,.,., Fixed-fee,., Per-copy., Fixed-fee,,, Per-copy,, 3/8., Fixed-fee., 2. 2, : ) =, x d >, p r = p d, Πm r = Πm d., ; 2) = x d, p r p d, Πm r Πm d,, ; 3), θ θ. 2bd b r. b d 5.,,., u d = θvx d p d, u r = v p r, v = p r p d,, v > v,, v < v, =, p r = p d ( v p r v p d, =, p r p d,, ).,. α, β, α + β =., >, p r > p d ( p r p d, (v p r ) (v p d ), ),, p r p d p d, p r > p d q d = 0,, q r = p r p d, p r > p d p r,.

6 4 28, <, p r < p d ( p r p d, (v p r ) (v p d ), ),, p r p d, p r < p d p r p d x q d = r θx p r, p r < p d d p q r = d,. 0,. θ,. (v 2 v ) ; (v v ) ; (v v v 2 ).. 5. Fixed-fee Fig. Segmentation of consumer Fixed-fee.,.. w, w, w. Fixed-fee, 2.. Table 2 2 Fixed-fee Solution of the dual-channel model based on Fixed-fee policy < > = (wθ) 2 (wθ ) 2 2(4wθ 3) 2 (b d w 2 +2b r) (w θ) 2 w 4 2(2w θ) 4 (b d w 2 +2b r) θ 2 32(b d +2b rθ 2 ) b r(wθ) 2 (wθ ) 2 n rw 6 (w θ) 2 b rθ 4 2(4wθ 3) 2 (b d w 2 +2b r) 2 2(2w θ) 4 (b d +2b rw 2 ) 2 32(b d +2b rθ 2 ) 2 wθ(wθ ) w(w θ)(4w+θ) θ 2 (4wθ 3)(2b r+b d w 2 ) 4(4w 3θ)(b d +2b rw 2 ) 4(b d +2b r) 2wθ 2 α 0 4wθ 3 2 wθ w β 4wθ 3 2w θ 2,,. b d = b r = b, 2, ,,,.,..,. ( = ),,,. 4,, <,,,.. 3/4. [ ]. 2wθ a) v 4wθ 3, ; 2 b d = b r, θ 2,. θ..

7 : 5 [ wθ b) v 4wθ 3, 2wθ ] ; [ 4wθ 3 c) v 0, wθ ]. 4wθ 3, Fixed-fee. 5,. θ,.,., θ =, 2, 3,,,,.,.0 2 Fixed-fee Fig. 2 The supplier s profit under the dual-channel model based on Fixed-fee policy0 3 Fixed-fee Fig. 3 The retailer s profit under the dual-channel model based on Fixed-fee Per-copy Per-copy Table 3 3 Per-copy Solution of the dual-channel model based on Per-copy policy < > = (θw) 2 32(4b r+b d w 2 ) b r(θw) 2 32(4b r+b d w 2 ) 2 wθ(wθ ) (4wθ 3)(2b r+b d w 2 ) 4b r(wθ )+b d (wθ )w 2 (8b r+2b d w 2 )(wθ ) br(wθ )(4br+b d w 2 ) (8b r+2b d w 2 )(wθ ) b rwθ 2 b r(wθ )(4b r+b d w 2 ) ( 28w 2 (b d +4b rw 2 ) 3 ) 2b d θw + 5b rθw 3 + 3b rw 4 + brw 4 (w θ)(4b d θ + b rw 2 (7θ + 9w)) ( 2b d θw b rθw 3 + 9b rw b rw 4 (w θ)(4b d θ + b rw 2 (7θ + 9w)) 4 3br(w θ)w+ br(w θ)(4b d θ + b rw 2 w 2 (7θ + 9w)) 52b r(w θ) 2 (b d +4b rw 2 ) 4 2b dθw b rθw 3 + 9b rw b rw 4 (w θ)(4b d θ + b rw 2 (7θ + 9w)) 6 27( α)b rθ ) 32(b 2 d ( α)+2b r(2 α)θ 2 ) 3 8( α) 2 3 b r θ 8 32(b d ( α)+2b r(2 α)θ 2 ) 4 9( α)b rθ 4 8(b d +4b rw 2 ) 2 4(b d ( α)+2b r(2 α)θ 2 ) 2 2b d(w θ)w + 5b r(w θ)w 3 br(w θ)w 4 (4b d θ + b rw 2 (7θ + 9w)) 4(w θ)w(b d +4b rw 2 ) 3br(w θ)w3 + br(w θ)w 4 (4b d θ + b rw 2 (7θ + 9w)) 4(w θ)w(b d +4b rw 2 ) 3αb rθ 2 2(b d ( α)+2b r(2 α)θ 2 ) 3βb rθ 2 2(b d ( α)+2b r(2 α)θ 2 )

8 Per-copy, b d = b r = b, ( 4 5), w.8,,.. 4 Fig. 4 The supplier s profit based on Per-copy policy0 5 Fig. 5 The retailer s profit based on Per-copy, Fixed-fee Per-copy,,,. 5.3 Fixed-fee Per-copy,,,,.,, Fixed-fee Per-copy, θ =. ( 6 7), < θx 3 d,, Per-copy Fixed-fee, Per-copy,. 4 6 w 4 + 6, Fixed-fee, Per-copy. 6 < x d Fig. 6 The supplier s profit (Fixed-fee vs. Per-copy) < x d Fig. 7 The retailer s profit (Fixed-fee vs. Per-copy) 65,, Per-copy,,,,. 3,,.

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10 Fixed-fee Fixed-fee,. ) < :Π m = q p d b d x 2 d /2 + R C :Π r = q 2 p r b rx 2 r /2 R q = pr p d p d x d pr < p d p d p r θx, q 2 = d 0 pr pr < p d. w = x d, w θ. t = p d, t 2 = p r., Π r / = 0, Π r / t 2 = x d 0, t 2 = t /(2θ), = 4Rθ + t 2 w 4Rθ 2 w. t 2,, t = 2θ(wθ ) 4wθ 3 2) > q = 4b r θ(wθ ), R = wθ(wθ )(b dw 2 + b r (5 4wθ)) (4wθ 3) 2, = (2b r + b d w 2 ) { pr p d p d 0 pr > p d, q 2 = { pr p d pr wθ(wθ ) (4wθ 3)(2b r + b d w 2 ). pr > p d = wx d, w θ. t = p d, t 2 = p r., Π r / = 0, Π r / t 2 = 0, x d t 2 = t θ + w, = t 2 + 2t (w θ) + (w θ)(θ + ( 4R)w) wθ θ2. q 0, t 2w 4b r θ(w θ) 2w θ. wθ θ2 t = k, 0 k., 2w θ R = (w θ)(b d((k )θ + 2w) 2 b r w 2 (( k 2 )θ 2 4( k 2 )wθ + 4w 2 )) 4(2w θ) 2. w(b d + 2b r w 2 ), k =. (w θ) 2 w 4 Π m = 2(2w θ) 4 (b d + 2b r w 2 ), Π b r w 6 (w θ) 2 r = 2(2w θ) 4 (b d + 2b r w 2 ) 2. 3) =,. p r = p d, t = p r. α, β, α + β =. Π m = b r θ 4 Π r = 32(b d + 2b r θ 2 ) 2. Fixed-fee. 2 Per-copy. θ 2 32(b d + 2b r θ 2 ), Per-copy., Stackelberg,,,,..