31 2 2016 4 JOURNAL OF SYSTEMS ENGINEERING Vol.31 No.2 Apr. 2014,,, 211189 :..,., ;,,., ;,. : ; Nash ; ; : F270 : A : 1000 5781201602 0155 11 doi: 10.13383/j.cnki.jse.2016.02.002 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 211189, 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]. : 2014 07 07; : 2015 03 30. : 71371050; 2013 CXZZ13 0137.
156 31.,.,., 2011 332.6, 9% 11%.,,,. 2011 2012 23.9%, 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,.,.,,.,,,,.
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. 3 3.1,.,
158 31 [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
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. 14 13 14, 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.
160 31 1 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. 15 11 12 15, c 11 c 12 p m F2 p m p n F2 p n a 11 b 11 p n p m. 16 11 12, 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
2 : 161 F i p n = 0 F i p n = Q. 10 11.,.,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, 20 20 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. 23 23 Q = h iα i h j α j, 24 h i α i p + sβ i β j p F j1 p =. 25 25 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. 27 27 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,?
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 20 22 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. 35 9 21 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,..
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,,,,., ;,,,.,,,.. 0. 6 0. 5 π1 π2 0. 4 π 0. 3 0. 2 0. 1 0 0. 2 0. 4 0. 6 0. 8 1 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
164 31, U 2 = 2ρα + Π i α = U 1 U 2 = 0, U 1 = hr + hrs1 h2 1 α 2 h1 h 2 α + sh 2 1 α 2, 45 2hα 2 rs1 h 2 h1 h 2 α + sh 2 1 α + hαrs1 h2 1 α 2 h1 h 2 2sh 2 1 α 2 h1 h2 α + sh 2 1 α 2 2. 46, α. α i α j, 2 Π i α i α j < 0, i,. I = ρα 2,., 0, Π i = 0, α i α j=1,,.. 5,,, ;. 4., ;., [20].,., ;. : [21] [22], ; [23], i j,. : [1] Bass F M, Krishnamoorthy A, Prasad A, et al. Generic and brand advertising strategies in a dynamic duopoly. Marketing Science, 2005, 244: 556 568. [2] Chandra A, Kaiser U. Targeted advertising in magazine markets and the advent of the internet. Management Science, 2014, 607: 1829 1843. [3] Roy S. Strategic segmentation of a market. International Journal of Industrial Organization, 2000, 188: 1279 1290. [4] Esteban L, Gil A, Hernández J M. Informative advertising and optimal targeting in a monopoly. The Journal of Industrial Economics, 2001, 492: 161 180. [5] Iyer G, Soberman D, Villas-Boas J M. The targeting of advertising. Marketing Science, 2005, 243: 461 476. [6] Esteban L, Hernández J M. Strategic targeted advertising and market fragmentation. Economics Bulletin, 2007, 1210: 1 12. [7] Galeotti A, Moraga-González J L. Segmentation, advertising and prices. International Journal of Industrial Organization, 2008, 265: 1106 1119. [8] Bergemann D, Bonatti A. Targeting in advertising markets: implications for offline versus online media. The RAND Journal of Economics, 2011, 423: 417 443. [9] Johnson J P. Targeted advertising and advertising avoidance. The RAND Journal of Economics, 2013, 441: 128 144. [10] Anand B N, Shachar R. Targeted advertising as a signal. Quantitative Marketing and Economics, 2009, 73: 237 266. [11],,.., 2014, 291: 30 40. Jiang L L, Mei S E, Zhong W J. The effect of ad-avoidance behaviors of consumers on media advertising strategies. Journal of Systems Engineering, 2014, 291: 30 40. in Chinese
2 : 165 [12] Gal-Or E, Gal-Or M, May J H, et al. Targeted advertising strategies on television. Management Science, 2006, 525: 713 725. [13] Ben Elhadj-Ben Brahim N, Lahmandi-Ayed R, Laussel D. Is targeted advertising always beneficial. International Journal of Industrial Organization, 2011, 296: 678 689. [14] Chen Y, Iyer G. Research note consumer addressability and customized pricing. Marketing Science, 2002, 212: 197 208. [15] Chen Y, Narasimhan C, Zhang Z J. Individual marketing with imperfect targetability. Marketing Science, 2001, 201: 23 41. [16] Varian H R. A model of sales. The American Economic Review, 1980, 704: 651 659. [17] Narasimhan C. Competitive promotional strategies. Journal of Business, 1988, 614: 427 449. [18] Stahl I I, Dale O. Oligopolistic pricing and advertising. Journal of Economic Theory, 1994, 641: 162 177. [19] Grossman G M, Shapiro C. Informative advertising with differentiated products. The Review of Economic Studies, 1984, 511: 63 81. [20] Boulding W, Staelin R, Ehret M, et al. A customer relationship management roadmap: What is known, potential pitfalls, and where to go. Journal of Marketing, 2005, 694: 155 166. [21],,.., 2013, 283: 307 315. Chen W, Xu X H, Peng H X. Rationing and price commitment in the presence of strategic consumers. Journal of Systems Engineering, 2013, 283: 307 315. in Chinese [22],,.., 2013, 283: 327 337. Lin H W, Shao P J, Yu B L. Two stage revenue pricing model for internet advertising with the risk-aversion. Journal of Systems Engineering, 2013, 283: 327 337. in Chinese [23],,.., 2013, 212: 66 75. Dan B, Tian L N, Dong S H. Research on advertising decision-making model between complementary goods enterprises considering spillover effect. Chinese Journal of Management Science, 2013, 212: 66 75. in Chinese : 1982,,,,, :,, Email: seuzhaojiang@163.com; 1968,,,,, :, Email: meishue@seu.edu.cn; 1962,,,,, :,, Email: zhongweijun@seu.edu.cn.