Strategy of duopolistic firms using targeted advertising with distinct targeting accuracy

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1 JOURNAL OF SYSTEMS ENGINEERING Vol.31 No.2 Apr. 2014,,, :..,., ;,,., ;,. : ; Nash ; ; : F270 : A : doi: /j.cnki.jse Strategy of duopolistic firms using targeted advertising with distinct targeting accuracy Zhao Jiang, Mei Shu e, Zhong Weijun School of Economics and Management, Southeast University, Nanjing , China Abstract: There is an important impact on market segmentation and accurate delivery of targeted advertising based on precise recognition of targeting customers. The optimized strategy model including the effect of targeting accuracy of targeted advertising on product price and firms equilibrium profit was established by game theory. The results indicate that the targeting accuracy plays a bidirectional role in the regulation of a firm s equilibrium profit. The targeting accuracy can increase a firm s profit in some parameter ranges. When the targeting accuracy is quite high, the competitive effect between duopolistic firms is greater than the advertising effect, leading to a decrease in each firm s profit. Only the firm with more loyal customers is likely to improve the targeting accuracy with a high coefficient, while both firms would like to improve the targeting accuracy with a low coefficient. Key words: targeting accuracy; Nash equilibrium; loyal customers; bidirectional regulation 1., ; [1]. : ; : : ; 2013 CXZZ

2 ,.,., , 9% 11%.,,, %, 7.6%, 49%.,., IP cookies, [2].,., Roy [3].,,.,,. Esteban [4]., Iyer [5],. Esteban [6],,. Galeotti [7],. Bergemann [8],,,.,.,. Johnson [9],.,. Anand [10],,. [11].,,,.,. Gal-Or [12].,,. Brahim [13] Hotelling,,,. Chen [14].,,. Chen [15],.,,.,,,,?,?,. cookies,.,.,,.,,,,.

3 2 : 157 2,. 2.1 :, i j i,j = 1,2. p i, π i., 0. : 1, 1, r. Varian [16] Narasimhan [17], h i,. s,, 1 2. h 1 + h 2 + s = 1. h 1 = h 2,. h 1 h 2,. s. s,. 2.2 :. Stahl [18],.,..,. : Stahl [18] Grossman [19], A i, [5], A i h i A i s. 2.3 :. Prk l l = L i,s;k = l i,s i i, l L i S k l i s i. l L i S, l L i S. α i = Prl i L i = Prs i S,i = 1,2, [0,1]. α i = 0 ; α i 0,1 ; α i = 1. : S L j, β i, Prl i S = Prl i L j = β i,i = 1,2., α i + β i 1, h i 1 α i = 1 h i β i, 1 h i i, h i 1 α i. 1 h i i, β i.,, γ i, Prs i L i = Prs i L j = γ i ,.,

4 [5],,,, ;,, Bertrand. i,i = 1,2,, : 1a i1 = h i Prl i L i, ; 2a i2 = s Prl i SPrl 3 i S ; 3a i3 = s Prl i SPrs 3 i S i, j ; 4h i Prl i L 3 i i j., i., i,i = 1,2 4 : 1b i1 = h i Prs i L i ; 2b i2 = s Prs i SPrl 3 i S i, j ; 3b i3 = s Prs i SPrs 3 i S ; 4h 3 i Prs i L 3 i i j., i,, i..,, 1, r,,. 0,, 0,. F j p i i j.,,. π i = p i h i α i + p i sα i 1 F j p i A i h i + s. 2, F j p i = 1, π i > 0,.. 1 α i,, α i r/a i,1], i = 1,2, r, π i = h iα i r A i. 1,,,,,. 2,. 1 α i, Nash. i Nash p i,p j,, p i p j. Nash, p i, p i p i, π il i p i,p j > π il i p i,p j. : 1 p i < p j,, i π ili p i,p j = p i hi Prl i L i + s Prl i S. 3 p i = p i + ε < p j, ε, 4, π ili p i,p j = p i + ε h i Prl i L i + s Prl i S > π ili p i,p j ; 4 2 p i = p j,, s Prl i S, j, i λ i, π ili p i,p j = p i hi Prl i L i + λ i s Prl i S. 5

5 2 : 159 p i = p i ε < p j, i, ε, ε π ili p i,p j = p i ε h i Prl i L i + s Prl i S, 6 p i ε h i Prl i L i + s Prl i S > p i hi Prl i L i + λ i s Prl i S, 7 0 < ε < 1 λ i p i h i Prl i L i h i Prl i L i + s Prl i S, 8 ε π ili p i,p j > π il i p i,p j,.,. 2. Nash, α i,, i = 1,2, p il i p is. 1 : i π i = π ili + π is A i h i + s. 9 i j. F i1 p = Prp ili p, π ili = p ili ai1 + a i2 F3 i1 p ili + a i3 F3 i2 p ili = p ili ai1 + c i1 F3 i p ili, 10 c i1 = s Prl i S, F 3 i p ili = Prs 3 i S F 3 i2 p ili + Prl 3 i S F 3 i1 p ili., F i2 p = Prp is p, π is = p is bi1 + b i2 F3 i1 p is + b i3 F3 i2 p is = p is bi1 + c i2 F3 i p is, 11 c i2 = s Pr i s i S, F 3 i p is = Pr 3 i s 3 i S F 3 i2 p is + Pr 3 i l 3 i S F 3 i1 p is. Nash, p ili p is, π i = π il i A i h i +π is A i s. 10, α i > 0,, π ili A i h i p is.,π is A i s p ili., Nash, π il i p ili A i h i p ili, π is p is A i s p is ; 2 : i = 1 p m p n, p 1L1 p 1S. 4,, A 1 h 1. π 1L1 p m = π 1L1 p n, a11 + c 11 F2 p m p m = a 11 + c 11 F2 p n p n, 12, 11, π 1S p m = π 1S p n, p n F2 p n p m F2 p m = a 11 c 11 p m p n. 13 p n F2 p n p m F2 p m = b 11 c 11 p m p n , a 11 = b 11, α 2 i c 11 c = h i s 12 1 h i 1 s 1 α i 2 α i h i s 0,1, K =, K 0,1,.,.. 1 h i 1 s 3 Nash, α i, i = 1,2, p il i p is, p il i p is.

6 i = 1, α 1 = 1, p ili = r, p is r; 2 p ili p is, α 1 < 1,p 1L1 p 1S, p m,p o p 1L1, p o,p n p 1S1, p n p o = p o p m. p il i,p is = p m,p n, p m p n, p ili,p is = p n,p m., π 1L1 p m A 1 h 1 + π 1S p n A 1 s π 1L1 p n A 1 h 1 + π 1S p m A 1 s , c 11 c 12 p m F2 p m p n F2 p n a 11 b 11 p n p m , p n p o = p o p m π 1L1 p m = π 1L1 p o, π 1S p m = π 1S p o, p o F2 p o p n F2 p n = a 11 2c 11 p n p m, 17 p m F2 p m p o F2 p o = b 11 p n p m, 18 2c 12 a11 p m F2 p m p n F2 p n = + b 11 p n p m. 19 2c 11 2c 12 a11 + b 11 c 11 c 12 a 11 b 11, a 11,b 11,c 11,c 12, α 1 0,1.. 2c 11 2c 12,,,. Nash,,. 2 i j,,, [ ] p ili,r ;, [ ] p is 1 α i α j,.,,. i j p il i = Qr + 1 Qr h iα i ln 1 sβ iβ j sβ i β j h i α i p is = p js = p jl j = rh iα i ln 1 + sβ iβ j sβ i β j h i α i r1 α iα j h i α j ln, 1 1 α i α j, Q = h iα i h j α j. 1 α 1 = 0, 2 3, p 1L1 p 1S, π i p ili,p is = π i p m,p n = π i p n,p m,, p 1Li p 1S, p 1L1 p 1S. 0, ; 2 α i 0,1, p ki p 1L1 p ki,r, p 1S p n,p ki., F i1 p ki = 1, F i2 p n = 1, F i2 p ki = 0, F i1 r = Q i, Q i r, Q 1 Q 2 = 0. α i = 0,, Fi1 p = F i2 p = F i p, i

7 2 : 161 F i p n = 0 F i p n = Q ,.,α 1,α 2 0,1 h i Prl i L i h 3 i Prl 3 i L 3 i,i = 1,2, p k Ah i = Ah i, p k1 = p k2 = p k =, 21 p k s p k sα iα j A i s = p n s A i s, 22 Q r = h j α j r Q = h iα i h j α j, 24 h i α i p + sβ i β j p F j1 p = F j1 p = h iα i r p, 26 sβ i β j p h j α j p + sβ i β j p F i1 p = h j α j r + sβ i β j Qr F i1 p = h jα j r + sβ i β j Qr sβ i β j p F i2 p = F j2 p = 1 α iα j α i α j h jα j sβ i β j. 28 p 1. 29, i r Ep il i = pd F j1 p = p F j1 p r r Fj1 pdp, 30 p ki p ki p ki p il i = Qr + 1 Qr h iα i sβ i β j ln 1 sβ iβ j h i α i. 31 p jl j = rh iα i ln 1 + sβ iβ j, 32 sβ i β j h i α i p is = p js = r1 α iα j h i α j ln 1 1 α i α j. 33, 0,,,. α i 0,1,,,.. 2.,,. 3.2,?

8 162 31,,?. 3 j α i 0,1, i = 1,2, h i α i A i h j α j A j, i π i α 1,α 2 = π jα 1,α 2 = + s sα i α j A i h i + s, h j α j + sβ i β j + s sα i α j A j h j + s, π i α i,α j > 0, 2 πi α i,α j < 0,. α i α 2 i π ili = p k Ah i = Ah i, 34 π is = p n s A i s = p k1 α i α j s As π i α hi α i r1 α i α j 1,α 2 = A i + s A i π i α 1,α 2 = π jα 1,α 2 =, 36 + s sα i α j A i h i + s. 37 h j α j + sβ i β j + s sα i α j A j h j + s. 38 i 1 2 π i α i,α j > 0, 2 πi α i,α j < 0.. α i α 2 i 3,,., 1, 2 0,, 2,, h 1 = h 2 = h. 1, 2,. 4,, ;.,. α i,. α 2 = 0,α 1 > 0, β 1 = h 1 h 1 α 1,β 2 = h 1 h, 37 π hα 1 r i α 1,0 = hα 1 r A 1 + s A 1, 39 hα 1 + sβ 1 β 2 i 1 36 π i α 1,0 α 1 π 2α 1,0 = = hr + sr α 1 hα 1 hα 1 + sβ 1 β 2, 40 hα 1 r hα 1 + sβ 1 β 2 sβ 1 β 2 + s A 2 h + s. 41, α i,..

9 i 2 : 163 π 2α 1,0 = 0, h = 0.4,r = 1,A 1 = A 2 = 0.5,s = 0.2, MATLAB 7, α 1 α 1=α 1 1 2,, 1. 4,,,,., ;,,,.,,, π1 π π α 1 π i i = 1, 2 α Fig. 1 The relationship between firms profit π i i = 1, 2 and targeting accuracy α 3.3 Iyer [5].,,.,., α 1 = α 2 = α,,,.,. I = ρα 2 i. ρ,. 3, π i α,α = hαr hα + sβ 2hα + s + sβ2 sα 2 Ah + s, 42 Π i = Π i. hα ir hα i + sβ 2hα i + s + sβ 2 sα 2 i Ah + s ρα2 i. 43,. 5 Nash, α i 0,1, i = 1,2, ρ, ; ρ, ;,. 41, Π i α,α = hαr + hsαr1 h2 1 α 2 h1 h 2 α + sh 2 1 α 2 Ah + s ρα2. 44

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