January 2018, 14(1): 105-134. doi: 10.3934/jimo.2017039

Advertising games on national brand and store brand in a dual-channel supply chain

1. 

School of Economics and Commerce, South China University of Technology, Guangzhou, Guangdong 510006, China

2. 

Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, Jiangsu 210016, China

* Corresponding author: Jingna Ji

Received  May 2015 Revised  February 2017 Published  April 2017

Fund Project: This research is partly supported by (ⅰ) the National Natural Science Foundation of China (71101054,71201083,71572058,71571100); (ⅱ) Jiangsu Province Science Foundation for Youths (BK2012379); and (ⅲ) the Fundamental Research Funds for the Central Universities (NS2015076)

This paper investigates a dual-channel supply chain, where one national brand manufacturer has both online and retail channels. The retailer is assumed to sell the national brand as well as his store brand to customers. The following five scenarios are considered: Centralized case, Stackelberg-manufacturer (SM) game, Stackelberg-retailer (SR) game, Nash-manufacturer (NM) game and Nash-retailer (NR) game. The paper derives the conditions under which the supply chain members would like to participate in cooperative advertising. The results show that in the Stackelberg games, the leader in Stackelberg game will reduce its investment in cooperative advertising when it gets a lower marginal profit from the cooperative advertising; In addition, the dual-channel supply chain can get a higher profit if it is dominated by the member whose marginal profit from cooperative advertising is higher. In the Nash games, in order to increase the whole supply chain's profit, the member who has a higher marginal profit in the cooperative advertising should give up the decision power on cost-sharing rate voluntarily. In addition, if there exists a leader in the supply chain, the cooperative advertising will be higher. Furthermore, the introduction of store brand will trigger the manufacturer's antipathy for the low profit.

Citation: Lei Yang, Jingna Ji, Kebing Chen. Advertising games on national brand and store brand in a dual-channel supply chain. Journal of Industrial & Management Optimization, 2018, 14 (1) : 105-134. doi: 10.3934/jimo.2017039
References:
[1]

A. Ahmadi-Javid and P. Hoseinpour, On a cooperative advertising model for a supply chain with one manufacturer and one retailer, European Journal of Operational Research, 219 (2012), 458-466. doi: 10.1016/j.ejor.2011.06.032.

[2]

N. AmroucheG. Martín-Herrán and G. Zaccour, Pricing and advertising of private and national brands in a dynamic marketing channel, Journal of Optimization Theory and Applications, 137 (2008), 465-483. doi: 10.1007/s10957-007-9340-8.

[3]

G. Aust and U. Buscher, Vertical cooperative advertising in a retailer duopoly, Computers & Industrial Engineering, 72 (2014), 247-254. doi: 10.1016/j.cie.2014.03.023.

[4]

G. Aust and U. Buscher, Vertical cooperative advertising and pricing decisions in a manufacturer-retailer supply chain: A game-theoretic approach, European Journal of Operational Research, 223 (2012), 473-482. doi: 10.1016/j.ejor.2012.06.042.

[5]

A. BurattoL. Grosset and B. Viscolani, Advertising coordination games of a manufacturer and a retailer while introducing a new product, TOP, 15 (2007), 307-321. doi: 10.1007/s11750-007-0019-y.

[6]

A. M. ChaabaneO. Sabri and B. Parguel, Competitive advertising within store flyers A win-win strategy, Journal of Retailing and Consumer Services, 17 (2010), 478-486. doi: 10.1016/j.jretconser.2010.08.001.

[7]

J. ChenH. Zhang and Y. Sun, Implementing coordination contracts in a manufacturer Stackelberg dual-channel supply chain, Omega, 40 (2012), 571-583. doi: 10.1016/j.omega.2011.11.005.

[8]

K. B. Chen and L. Yang, Random yield and coordination mechanisms of a supply chain with emergency backup sourcing, International Journal of Production Research, 52 (2014), 4747-4767. doi: 10.1080/00207543.2014.886790.

[9]

T. H. Chen, Effects of the pricing and cooperative advertising policies in a two-echelon dual-channel supply chain, Computers & Industrial Engineering, 87 (2015), 250-259. doi: 10.1016/j.cie.2015.05.013.

[10]

W. K. ChiangD. Chhajed and J. D. Hess, Direct marketing, indirect profits: A strategic analysis of dual-channel supply-chain design, Management Science, 49 (2003), 1-20. doi: 10.1287/mnsc.49.1.1.12749.

[11]

H. C. ChiuY. C. HsiehJ. RoanK. J. Tseng and J. K. Hsieh, The challenge for multichannel services: Cross-channel free-riding behavior, Electronic Commerce Research and Applications, 10 (2011), 268-277. doi: 10.1016/j.elerap.2010.07.002.

[12]

S. Y. ChouG. C. ShenH. C. Chiu and Y. T. Chou, Multichannel service providers' strategy: Understanding customers' switching and free-riding behavior, Journal of Business Research, 69 (2016), 2226-2232. doi: 10.1016/j.jbusres.2015.12.034.

[13]

K. J. Chung, The integrated inventory model with the transportation cost and two-level trade credit in supply chain management, Computers and Mathematics with Applications, 64 (2012), 2011-2033. doi: 10.1016/j.camwa.2012.03.102.

[14]

Y. DaiX. ChaoS. C. Fang and H. L. W. Nuttle, Game theoretic analysis of a distribution system with customer market search, Annals of Operations Research, 135 (2005), 223-238. doi: 10.1007/s10479-005-6243-7.

[15]

B. DanG. Y. Xu and C. Liu, Pricing policies in a dual-channel supply chain with retail services, International Journal of Production Economics, 139 (2012), 312-320. doi: 10.1016/j.ijpe.2012.05.014.

[16]

P. S. Desai, Multiple messages to retain retailers: signaling new product demand, Marketing Science, 19 (2000), 381-389. doi: 10.1287/mksc.19.4.381.11793.

[17]

X. FangS. Gavirnenib and V. R. Rao, Supply chains in the presence of store brands, European Journal of Operational Research, 224 (2013), 392-403. doi: 10.1016/j.ejor.2012.07.039.

[18]

R. HeY. Xiong and Z. Lin, Carbon emissions in a dual channel closed loop supply chain: The impact of consumer free riding behavior, Journal of Cleaner Production, 134 (2016), 384-394. doi: 10.1016/j.jclepro.2016.02.142.

[19]

S. Heitz-Spahn, Cross-channel free-riding consumer behavior in a multichannel environment: An investigation of shopping motives, sociodemographics and product categories, Journal of Retailing and Consumer Services, 20 (2013), 570-578. doi: 10.1016/j.jretconser.2013.07.006.

[20]

Z. HuangS. X. Li and V. Mahajan, An analysis of manufacturer-retailer supply chain coordination in cooperative advertising, Decision Sciences, 33 (2002), 469-494. doi: 10.1111/j.1540-5915.2002.tb01652.x.

[21]

J. JiZ. Zhang and L. Yang, Carbon emission reduction decisions in the retail-/dual-channel supply chain with consumers' preference, Journal of Cleaner Production, 141 (2017), 852-867. doi: 10.1016/j.jclepro.2016.09.135.

[22]

S. Jorgensen and G. Zaccour, A survey of game-theoretic models of cooperative advertising, European Journal of Operational Research, 237 (2014), 1-14. doi: 10.1016/j.ejor.2013.12.017.

[23]

A. KamaliS. M. T. Fatemi Ghomi and F. Jolai, A multi-objective quantity discount and joint optimization model for coordination of a single-buyer multi-vendor supply chain, Computers and Mathematics with Applications, 62 (2011), 3251-3269. doi: 10.1016/j.camwa.2011.08.040.

[24]

S. Karray and G. Martín-Herrán, A dynamic model for advertising and pricing competition between national and store brands, European Journal of Operational Research, 193 (2009), 451-467. doi: 10.1016/j.ejor.2007.11.043.

[25]

S. Karray and G. Zaccour, A differential game of advertising for national and store brands, Dynamic Games: Theory and Applications, 10 (2005), 213-229. doi: 10.1007/0-387-24602-9_11.

[26]

S. Karray and G. Zaccour, Could co-op advertising be a manufacturer's counterstrategy to store brands, Journal of Business Research, 59 (2006), 1008-1015. doi: 10.1016/j.jbusres.2006.05.002.

[27]

C. W. Kuo and S. Yang, The role of store brand positioning for appropriating supply chain profit under shelf space allocation, European Journal of Operational Research, 231 (2013), 88-97. doi: 10.1016/j.ejor.2013.05.018.

[28]

H. D. KurataQ. Yao and J. J. Liu, Pricing policies under direct vs. indirect channel competition and national vs. store brand competition, European Journal of Operational Research, 180 (2007), 262-281. doi: 10.1016/j.ejor.2006.04.002.

[29]

X. Li and Y. Li, Chain-to-chain competition on product sustainability, Journal of Cleaner Production, 112 (2016), 2058-2065. doi: 10.1016/j.jclepro.2014.09.027.

[30]

J. C. LuY. C. Tsao and C. Charoensiriwath, Competition under manufacturer service and retail price, Economic Modelling, 28 (2011), 1256-1264. doi: 10.1016/j.econmod.2011.01.008.

[31]

P. Mukherjee and B. J. Jansen, Performance analysis of keyword advertising campaign using gender-brand effect of search queries, Electronic Commerce Research and Applications, 13 (2014), 139-149. doi: 10.1016/j.elerap.2014.01.001.

[32]

S. SaymanS. J. Hoch and J. S. Raju, Positioning of store brands, Marketing Science, 21 (2002), 378-397. doi: 10.1287/mksc.21.4.378.134.

[33]

R. Sethuraman, Assessing the external validity of analytical results from national brand and store brand competition models, Marketing Science, 28 (2009), 759-781. doi: 10.1287/mksc.1080.0455.

[34]

W. Shang and L. Yang, Contract negotiation and risk preferences in dual-channel supply chain coordination, International Journal of Production Research, 53 (2015), 4837-4856. doi: 10.1080/00207543.2014.998785.

[35]

J. Shi and T. J. Xiao, Store assistance and coordination of supply chains facing consumer's return, Journal of Industrial and Management Optimization, 12 (2016), 991-1007. doi: 10.3934/jimo.2016.12.991.

[36]

D. W. Stewart and P. A. Pavlou, From consumer response to active consumer: Measuring the effectiveness of interactive media, Journal of the Academy of Marketing Science, 30 (2002), 376-396. doi: 10.1177/009207002236912.

[37]

A. A. Tsay and N. Agrawal, Channel conflict and coordination in the e-commerce age, Production and Operations Management, 13 (2004), 93-110. doi: 10.1111/j.1937-5956.2004.tb00147.x.

[38]

A. A. Tsay and N. Agrawal, Channel dynamics under price and service competition, Manufacturing and service operations management, 2 (2000), 372-391. doi: 10.1287/msom.2.4.372.12342.

[39]

S. Van Baal and C. Dach, Free riding and customer retention across retailers' channels, Journal of Interactive Marketing, 19 (2005), 75-85. doi: 10.1002/dir.20036.

[40]

F. J. WangQ. L. ZhangB. Li and W. Q. Liu, Optimal investment strategy on advertisement in duopoly, Journal of Industrial and Management Optimization, 12 (2016), 625-636. doi: 10.3934/jimo.2016.12.625.

[41]

Q. Wang and Z. Wu, An empirical study on the Lanchester model of combat for competitive advertising decisions, European Journal of Operational Research, 183 (2007), 1042-1054. doi: 10.1016/j.ejor.2006.02.031.

[42]

I. Wu and C. Chuang, Analyzing contextual antecedents for the stage-based diffusion of electronic supply chain management, Electronic Commerce Research and Applications, 8 (2009), 302-314. doi: 10.1016/j.elerap.2009.04.013.

[43]

J. Xie and S. Ai, A note on cooperative advertising, game theory and manufacturer-retailer supply chains, Omega, 34 (2006), 501-504. doi: 10.1016/j.omega.2005.01.009.

[44]

J. Xie and J. Wei, Coordinating advertising and pricing in a manufacturer-retailer channel, European Journal of Operational Research, 197 (2009), 785-791. doi: 10.1016/j.ejor.2008.07.014.

[45]

L. Yang, J. Ji and K. Chen, Game models on optimal strategies in a tourism dual channel supply chain, Discrete Dynamics in Nature and Society, 2016 (2016), Article ID 5760139, 15pp. doi: 10.1155/2016/5760139.

[46]

J. YueJ. AustinM. C. Wang and Z. Huang, Coordination of cooperative advertising in a two-level supply chain when manufacturer offers discount, European Journal of Operational Research, 168 (2006), 65-85. doi: 10.1016/j.ejor.2004.05.005.

[47]

J. ZhangQ. L. GouL. Liang and Z. Huang, Supply chain coordination through cooperative advertising with reference price effect, Omega, 41 (2013), 345-353. doi: 10.1016/j.omega.2012.03.009.

[48]

J. Zhang and J. Xie, Cooperative advertising with bilateral participation, Decision Sciences, 44 (2013), 193-203. doi: 10.1111/j.1540-5915.2012.00382.x.

[49]

S. ZhangS. Sun and H. Yang, Optimal convergence of discontinuous Galerkin methods for continuum modeling of supply chain networks, Computers and Mathematics with Applications, 68 (2014), 681-691. doi: 10.1016/j.camwa.2014.07.012.

[50]

W. ZhangS. LiD. Zhang and W. Hou, On the impact of advertising initiatives in supply chains, European Journal of Operational Research, 234 (2014), 99-107. doi: 10.1016/j.ejor.2013.10.069.

show all references

References:
[1]

A. Ahmadi-Javid and P. Hoseinpour, On a cooperative advertising model for a supply chain with one manufacturer and one retailer, European Journal of Operational Research, 219 (2012), 458-466. doi: 10.1016/j.ejor.2011.06.032.

[2]

N. AmroucheG. Martín-Herrán and G. Zaccour, Pricing and advertising of private and national brands in a dynamic marketing channel, Journal of Optimization Theory and Applications, 137 (2008), 465-483. doi: 10.1007/s10957-007-9340-8.

[3]

G. Aust and U. Buscher, Vertical cooperative advertising in a retailer duopoly, Computers & Industrial Engineering, 72 (2014), 247-254. doi: 10.1016/j.cie.2014.03.023.

[4]

G. Aust and U. Buscher, Vertical cooperative advertising and pricing decisions in a manufacturer-retailer supply chain: A game-theoretic approach, European Journal of Operational Research, 223 (2012), 473-482. doi: 10.1016/j.ejor.2012.06.042.

[5]

A. BurattoL. Grosset and B. Viscolani, Advertising coordination games of a manufacturer and a retailer while introducing a new product, TOP, 15 (2007), 307-321. doi: 10.1007/s11750-007-0019-y.

[6]

A. M. ChaabaneO. Sabri and B. Parguel, Competitive advertising within store flyers A win-win strategy, Journal of Retailing and Consumer Services, 17 (2010), 478-486. doi: 10.1016/j.jretconser.2010.08.001.

[7]

J. ChenH. Zhang and Y. Sun, Implementing coordination contracts in a manufacturer Stackelberg dual-channel supply chain, Omega, 40 (2012), 571-583. doi: 10.1016/j.omega.2011.11.005.

[8]

K. B. Chen and L. Yang, Random yield and coordination mechanisms of a supply chain with emergency backup sourcing, International Journal of Production Research, 52 (2014), 4747-4767. doi: 10.1080/00207543.2014.886790.

[9]

T. H. Chen, Effects of the pricing and cooperative advertising policies in a two-echelon dual-channel supply chain, Computers & Industrial Engineering, 87 (2015), 250-259. doi: 10.1016/j.cie.2015.05.013.

[10]

W. K. ChiangD. Chhajed and J. D. Hess, Direct marketing, indirect profits: A strategic analysis of dual-channel supply-chain design, Management Science, 49 (2003), 1-20. doi: 10.1287/mnsc.49.1.1.12749.

[11]

H. C. ChiuY. C. HsiehJ. RoanK. J. Tseng and J. K. Hsieh, The challenge for multichannel services: Cross-channel free-riding behavior, Electronic Commerce Research and Applications, 10 (2011), 268-277. doi: 10.1016/j.elerap.2010.07.002.

[12]

S. Y. ChouG. C. ShenH. C. Chiu and Y. T. Chou, Multichannel service providers' strategy: Understanding customers' switching and free-riding behavior, Journal of Business Research, 69 (2016), 2226-2232. doi: 10.1016/j.jbusres.2015.12.034.

[13]

K. J. Chung, The integrated inventory model with the transportation cost and two-level trade credit in supply chain management, Computers and Mathematics with Applications, 64 (2012), 2011-2033. doi: 10.1016/j.camwa.2012.03.102.

[14]

Y. DaiX. ChaoS. C. Fang and H. L. W. Nuttle, Game theoretic analysis of a distribution system with customer market search, Annals of Operations Research, 135 (2005), 223-238. doi: 10.1007/s10479-005-6243-7.

[15]

B. DanG. Y. Xu and C. Liu, Pricing policies in a dual-channel supply chain with retail services, International Journal of Production Economics, 139 (2012), 312-320. doi: 10.1016/j.ijpe.2012.05.014.

[16]

P. S. Desai, Multiple messages to retain retailers: signaling new product demand, Marketing Science, 19 (2000), 381-389. doi: 10.1287/mksc.19.4.381.11793.

[17]

X. FangS. Gavirnenib and V. R. Rao, Supply chains in the presence of store brands, European Journal of Operational Research, 224 (2013), 392-403. doi: 10.1016/j.ejor.2012.07.039.

[18]

R. HeY. Xiong and Z. Lin, Carbon emissions in a dual channel closed loop supply chain: The impact of consumer free riding behavior, Journal of Cleaner Production, 134 (2016), 384-394. doi: 10.1016/j.jclepro.2016.02.142.

[19]

S. Heitz-Spahn, Cross-channel free-riding consumer behavior in a multichannel environment: An investigation of shopping motives, sociodemographics and product categories, Journal of Retailing and Consumer Services, 20 (2013), 570-578. doi: 10.1016/j.jretconser.2013.07.006.

[20]

Z. HuangS. X. Li and V. Mahajan, An analysis of manufacturer-retailer supply chain coordination in cooperative advertising, Decision Sciences, 33 (2002), 469-494. doi: 10.1111/j.1540-5915.2002.tb01652.x.

[21]

J. JiZ. Zhang and L. Yang, Carbon emission reduction decisions in the retail-/dual-channel supply chain with consumers' preference, Journal of Cleaner Production, 141 (2017), 852-867. doi: 10.1016/j.jclepro.2016.09.135.

[22]

S. Jorgensen and G. Zaccour, A survey of game-theoretic models of cooperative advertising, European Journal of Operational Research, 237 (2014), 1-14. doi: 10.1016/j.ejor.2013.12.017.

[23]

A. KamaliS. M. T. Fatemi Ghomi and F. Jolai, A multi-objective quantity discount and joint optimization model for coordination of a single-buyer multi-vendor supply chain, Computers and Mathematics with Applications, 62 (2011), 3251-3269. doi: 10.1016/j.camwa.2011.08.040.

[24]

S. Karray and G. Martín-Herrán, A dynamic model for advertising and pricing competition between national and store brands, European Journal of Operational Research, 193 (2009), 451-467. doi: 10.1016/j.ejor.2007.11.043.

[25]

S. Karray and G. Zaccour, A differential game of advertising for national and store brands, Dynamic Games: Theory and Applications, 10 (2005), 213-229. doi: 10.1007/0-387-24602-9_11.

[26]

S. Karray and G. Zaccour, Could co-op advertising be a manufacturer's counterstrategy to store brands, Journal of Business Research, 59 (2006), 1008-1015. doi: 10.1016/j.jbusres.2006.05.002.

[27]

C. W. Kuo and S. Yang, The role of store brand positioning for appropriating supply chain profit under shelf space allocation, European Journal of Operational Research, 231 (2013), 88-97. doi: 10.1016/j.ejor.2013.05.018.

[28]

H. D. KurataQ. Yao and J. J. Liu, Pricing policies under direct vs. indirect channel competition and national vs. store brand competition, European Journal of Operational Research, 180 (2007), 262-281. doi: 10.1016/j.ejor.2006.04.002.

[29]

X. Li and Y. Li, Chain-to-chain competition on product sustainability, Journal of Cleaner Production, 112 (2016), 2058-2065. doi: 10.1016/j.jclepro.2014.09.027.

[30]

J. C. LuY. C. Tsao and C. Charoensiriwath, Competition under manufacturer service and retail price, Economic Modelling, 28 (2011), 1256-1264. doi: 10.1016/j.econmod.2011.01.008.

[31]

P. Mukherjee and B. J. Jansen, Performance analysis of keyword advertising campaign using gender-brand effect of search queries, Electronic Commerce Research and Applications, 13 (2014), 139-149. doi: 10.1016/j.elerap.2014.01.001.

[32]

S. SaymanS. J. Hoch and J. S. Raju, Positioning of store brands, Marketing Science, 21 (2002), 378-397. doi: 10.1287/mksc.21.4.378.134.

[33]

R. Sethuraman, Assessing the external validity of analytical results from national brand and store brand competition models, Marketing Science, 28 (2009), 759-781. doi: 10.1287/mksc.1080.0455.

[34]

W. Shang and L. Yang, Contract negotiation and risk preferences in dual-channel supply chain coordination, International Journal of Production Research, 53 (2015), 4837-4856. doi: 10.1080/00207543.2014.998785.

[35]

J. Shi and T. J. Xiao, Store assistance and coordination of supply chains facing consumer's return, Journal of Industrial and Management Optimization, 12 (2016), 991-1007. doi: 10.3934/jimo.2016.12.991.

[36]

D. W. Stewart and P. A. Pavlou, From consumer response to active consumer: Measuring the effectiveness of interactive media, Journal of the Academy of Marketing Science, 30 (2002), 376-396. doi: 10.1177/009207002236912.

[37]

A. A. Tsay and N. Agrawal, Channel conflict and coordination in the e-commerce age, Production and Operations Management, 13 (2004), 93-110. doi: 10.1111/j.1937-5956.2004.tb00147.x.

[38]

A. A. Tsay and N. Agrawal, Channel dynamics under price and service competition, Manufacturing and service operations management, 2 (2000), 372-391. doi: 10.1287/msom.2.4.372.12342.

[39]

S. Van Baal and C. Dach, Free riding and customer retention across retailers' channels, Journal of Interactive Marketing, 19 (2005), 75-85. doi: 10.1002/dir.20036.

[40]

F. J. WangQ. L. ZhangB. Li and W. Q. Liu, Optimal investment strategy on advertisement in duopoly, Journal of Industrial and Management Optimization, 12 (2016), 625-636. doi: 10.3934/jimo.2016.12.625.

[41]

Q. Wang and Z. Wu, An empirical study on the Lanchester model of combat for competitive advertising decisions, European Journal of Operational Research, 183 (2007), 1042-1054. doi: 10.1016/j.ejor.2006.02.031.

[42]

I. Wu and C. Chuang, Analyzing contextual antecedents for the stage-based diffusion of electronic supply chain management, Electronic Commerce Research and Applications, 8 (2009), 302-314. doi: 10.1016/j.elerap.2009.04.013.

[43]

J. Xie and S. Ai, A note on cooperative advertising, game theory and manufacturer-retailer supply chains, Omega, 34 (2006), 501-504. doi: 10.1016/j.omega.2005.01.009.

[44]

J. Xie and J. Wei, Coordinating advertising and pricing in a manufacturer-retailer channel, European Journal of Operational Research, 197 (2009), 785-791. doi: 10.1016/j.ejor.2008.07.014.

[45]

L. Yang, J. Ji and K. Chen, Game models on optimal strategies in a tourism dual channel supply chain, Discrete Dynamics in Nature and Society, 2016 (2016), Article ID 5760139, 15pp. doi: 10.1155/2016/5760139.

[46]

J. YueJ. AustinM. C. Wang and Z. Huang, Coordination of cooperative advertising in a two-level supply chain when manufacturer offers discount, European Journal of Operational Research, 168 (2006), 65-85. doi: 10.1016/j.ejor.2004.05.005.

[47]

J. ZhangQ. L. GouL. Liang and Z. Huang, Supply chain coordination through cooperative advertising with reference price effect, Omega, 41 (2013), 345-353. doi: 10.1016/j.omega.2012.03.009.

[48]

J. Zhang and J. Xie, Cooperative advertising with bilateral participation, Decision Sciences, 44 (2013), 193-203. doi: 10.1111/j.1540-5915.2012.00382.x.

[49]

S. ZhangS. Sun and H. Yang, Optimal convergence of discontinuous Galerkin methods for continuum modeling of supply chain networks, Computers and Mathematics with Applications, 68 (2014), 681-691. doi: 10.1016/j.camwa.2014.07.012.

[50]

W. ZhangS. LiD. Zhang and W. Hou, On the impact of advertising initiatives in supply chains, European Journal of Operational Research, 234 (2014), 99-107. doi: 10.1016/j.ejor.2013.10.069.

Figure 1.  Dual-channel supply chain framework
Figure 2.  The profits of the manufacturer versus $\lambda$
Figure 3.  The profits of the retailer versus $\lambda$
Figure 4.  The profits of whole supply chain versus $\lambda$
Table 1.  Equilibrium advertising strategies under four games considering advertising competition in retail channel
Games${A_1^a}^*$${A_2^a}^*$
SM$\big[ \frac{2B_1+B_2}{4-4(\rho_1+\rho_2-\rho_3)\gamma} \big]^2$$\big[ \frac{\rho_3\varphi_2-\rho_2\varphi_1}{2-2(\rho_3-\rho_2)\gamma} \big]^2$
SR$\big[ \frac{B_1+2B_2}{4-4(\rho_1+\rho_2-\rho_3)\gamma} \big]^2$$\big[ \frac{\rho_3\varphi_2-\rho_2\varphi_1}{2-2(\rho_3-\rho_2)\gamma} \big]^2$
NM$\big[ \frac{B_2}{2-2(\rho_2-\rho_3)\gamma} \big]^2$$\big[ \frac{\rho_3\varphi_2-\rho_2\varphi_1}{2-2(\rho_3-\rho_2)\gamma} \big]^2$
NR$\big[ \frac{B_1}{2(1-\rho_1\gamma)} \big]^2$$\big[ \frac{\rho_3\varphi_2-\rho_2\varphi_1}{2-2(\rho_3-\rho_2)\gamma} \big]^2$
Games${A_1^a}^*$${A_2^a}^*$
SM$\big[ \frac{2B_1+B_2}{4-4(\rho_1+\rho_2-\rho_3)\gamma} \big]^2$$\big[ \frac{\rho_3\varphi_2-\rho_2\varphi_1}{2-2(\rho_3-\rho_2)\gamma} \big]^2$
SR$\big[ \frac{B_1+2B_2}{4-4(\rho_1+\rho_2-\rho_3)\gamma} \big]^2$$\big[ \frac{\rho_3\varphi_2-\rho_2\varphi_1}{2-2(\rho_3-\rho_2)\gamma} \big]^2$
NM$\big[ \frac{B_2}{2-2(\rho_2-\rho_3)\gamma} \big]^2$$\big[ \frac{\rho_3\varphi_2-\rho_2\varphi_1}{2-2(\rho_3-\rho_2)\gamma} \big]^2$
NR$\big[ \frac{B_1}{2(1-\rho_1\gamma)} \big]^2$$\big[ \frac{\rho_3\varphi_2-\rho_2\varphi_1}{2-2(\rho_3-\rho_2)\gamma} \big]^2$
Table 2.  Equilibrium solutions under four games without store brand
EquilibriaSM gameSR gameNM gameNR game
${A_1^b}^*$$\frac{(\rho_0\theta_0+\rho_1\theta_1)^2}{4}$$\frac{(\rho_0\theta_0+\rho_1\theta_1)^2}{4}$$\frac{(\rho_0\theta_0+\rho_1\theta_1)^2}{4}$$\frac{(\rho_0\theta_0+\rho_1\theta_1)^2}{4}$
${A_2^b}^*$$\frac{(2B_1+B_3)^2}{16}$$\frac{(2B_3+B_1)^2}{16}$$\frac{B_3^2}{4}$$\frac{B_1^2}{4}$
${t^b}^*$$ \left\{\begin{aligned}&\frac{2B_1-B_3}{2B_1+B_3}, &q_1>1/2\\&0, &q_1<1/2\end{aligned}\right.$$\frac{2B_1}{2B_3+B_1}$01
EquilibriaSM gameSR gameNM gameNR game
${A_1^b}^*$$\frac{(\rho_0\theta_0+\rho_1\theta_1)^2}{4}$$\frac{(\rho_0\theta_0+\rho_1\theta_1)^2}{4}$$\frac{(\rho_0\theta_0+\rho_1\theta_1)^2}{4}$$\frac{(\rho_0\theta_0+\rho_1\theta_1)^2}{4}$
${A_2^b}^*$$\frac{(2B_1+B_3)^2}{16}$$\frac{(2B_3+B_1)^2}{16}$$\frac{B_3^2}{4}$$\frac{B_1^2}{4}$
${t^b}^*$$ \left\{\begin{aligned}&\frac{2B_1-B_3}{2B_1+B_3}, &q_1>1/2\\&0, &q_1<1/2\end{aligned}\right.$$\frac{2B_1}{2B_3+B_1}$01
Table 3.  Effects of store brand's introduction on advertising decisions
Games$A_1$$t$${A_1}_m$${A_1}_r$
SM${A_1^{S_M}}^* \leq {A_1^{bS_M}}^*$${t^{S_M}}^* \geq {t^{bS_M}}^*$${A_{1m}^{S_M}}^* \geq {A_{1m}^{bS_M}}^*$${A_{1r}^{S_M}}^* \leq {A_{1r}^{bS_M}}^*$
SR${A_1^{S_R}}^* \leq {A_1^{bS_R}}^*$${t^{S_R}}^* \geq {t^{bS_R}}^*$${A_{1m}^{S_R}}^* \leq {A_{1m}^{bS_R}}^*$${A_{1r}^{S_R}}^* \leq {A_{1r}^{bS_R}}^*$
NM${A_1^{N_M}}^* \leq {A_1^{bN_M}}^*$${t^{N_M}}^* = {t^{bN_M}}^*$${A_{1m}^{N_M}}^* = {A_{1m}^{bN_M}}^*$${A_{1r}^{N_M}}^* \leq {A_{1r}^{bN_M}}^*$
NM${A_1^{N_R}}^* = {A_1^{bN_R}}^*$${t^{N_R}}^* = {t^{bN_R}}^*$${A_{1m}^{N_R}}^* = {A_{1m}^{bN_R}}^*$${A_{1r}^{N_R}}^* \leq {A_{1r}^{bN_R}}^*$
Games$A_1$$t$${A_1}_m$${A_1}_r$
SM${A_1^{S_M}}^* \leq {A_1^{bS_M}}^*$${t^{S_M}}^* \geq {t^{bS_M}}^*$${A_{1m}^{S_M}}^* \geq {A_{1m}^{bS_M}}^*$${A_{1r}^{S_M}}^* \leq {A_{1r}^{bS_M}}^*$
SR${A_1^{S_R}}^* \leq {A_1^{bS_R}}^*$${t^{S_R}}^* \geq {t^{bS_R}}^*$${A_{1m}^{S_R}}^* \leq {A_{1m}^{bS_R}}^*$${A_{1r}^{S_R}}^* \leq {A_{1r}^{bS_R}}^*$
NM${A_1^{N_M}}^* \leq {A_1^{bN_M}}^*$${t^{N_M}}^* = {t^{bN_M}}^*$${A_{1m}^{N_M}}^* = {A_{1m}^{bN_M}}^*$${A_{1r}^{N_M}}^* \leq {A_{1r}^{bN_M}}^*$
NM${A_1^{N_R}}^* = {A_1^{bN_R}}^*$${t^{N_R}}^* = {t^{bN_R}}^*$${A_{1m}^{N_R}}^* = {A_{1m}^{bN_R}}^*$${A_{1r}^{N_R}}^* \leq {A_{1r}^{bN_R}}^*$
Table 4.  Effects of store brand's introduction on profits
Games$\pi_m$$\pi_r$
ComparisonsConditions
SM${\pi_m^{S_M}}^* \leq {\pi_m^{bS_M}}^*$${\pi_r^{S_M}}^* < (\geq) {\pi_r^{bS_M}}^*$$a_2 < (\geq) C_1$
SR${\pi_m^{S_R}}^* \leq {\pi_m^{bS_R}}^*$${\pi_r^{S_R}}^* < (\geq) {\pi_r^{bS_R}}^*$$a_2 < (\geq) C_2$
NM${\pi_m^{N_M}}^* \leq {\pi_m^{bN_M}}^*$${\pi_r^{N_M}}^* < (\geq) {\pi_r^{bN_M}}^*$$a_2 < (\geq) C_3$
NM${\pi_m^{N_R}}^* \leq {\pi_m^{bN_R}}^*$${\pi_r^{N_R}}^* < (\geq) {\pi_r^{bN_R}}^*$$a_2 < (\geq) C_4$
Games$\pi_m$$\pi_r$
ComparisonsConditions
SM${\pi_m^{S_M}}^* \leq {\pi_m^{bS_M}}^*$${\pi_r^{S_M}}^* < (\geq) {\pi_r^{bS_M}}^*$$a_2 < (\geq) C_1$
SR${\pi_m^{S_R}}^* \leq {\pi_m^{bS_R}}^*$${\pi_r^{S_R}}^* < (\geq) {\pi_r^{bS_R}}^*$$a_2 < (\geq) C_2$
NM${\pi_m^{N_M}}^* \leq {\pi_m^{bN_M}}^*$${\pi_r^{N_M}}^* < (\geq) {\pi_r^{bN_M}}^*$$a_2 < (\geq) C_3$
NM${\pi_m^{N_R}}^* \leq {\pi_m^{bN_R}}^*$${\pi_r^{N_R}}^* < (\geq) {\pi_r^{bN_R}}^*$$a_2 < (\geq) C_4$
Table 5.  Equilibrium solutions under four games without direct channel
EquilibriaSM gameSR gameNM gameNR game
${A_0^c}^*$$\frac{(\rho_1\theta_1)^2}{4}$$\frac{(\rho_1\theta_1)^2}{4}$$\frac{(\rho_1\theta_1)^2}{4}$$\frac{(\rho_1\theta_1)^2}{4}$
${A_1^c}^*$$\frac{(2B_4+B_5)^2}{16}$$\frac{(2B_5+B_4)^2}{16}$$\frac{B_5^2}{4}$$\frac{B_4^2}{4}$
${A_2^c}^*$$\frac{(\rho_3\varphi_2-\rho_2\varphi_1)^2}{4}$$\frac{(\rho_3\varphi_2-\rho_2\varphi_1)^2}{4}$$\frac{(\rho_3\varphi_2-\rho_2\varphi_1)^2}{4}$$\frac{(\rho_3\varphi_2-\rho_2\varphi_1)^2}{4}$
${t^c}^*$$ \left\{\begin{aligned}&\frac{2B_4-B_5}{2B_4+B_5}, &q_1>1/2\\&0, &q_1<1/2\end{aligned}\right.$$\frac{2B_4}{2B_5+B_4}$01
EquilibriaSM gameSR gameNM gameNR game
${A_0^c}^*$$\frac{(\rho_1\theta_1)^2}{4}$$\frac{(\rho_1\theta_1)^2}{4}$$\frac{(\rho_1\theta_1)^2}{4}$$\frac{(\rho_1\theta_1)^2}{4}$
${A_1^c}^*$$\frac{(2B_4+B_5)^2}{16}$$\frac{(2B_5+B_4)^2}{16}$$\frac{B_5^2}{4}$$\frac{B_4^2}{4}$
${A_2^c}^*$$\frac{(\rho_3\varphi_2-\rho_2\varphi_1)^2}{4}$$\frac{(\rho_3\varphi_2-\rho_2\varphi_1)^2}{4}$$\frac{(\rho_3\varphi_2-\rho_2\varphi_1)^2}{4}$$\frac{(\rho_3\varphi_2-\rho_2\varphi_1)^2}{4}$
${t^c}^*$$ \left\{\begin{aligned}&\frac{2B_4-B_5}{2B_4+B_5}, &q_1>1/2\\&0, &q_1<1/2\end{aligned}\right.$$\frac{2B_4}{2B_5+B_4}$01
Table 6.  Effects of direct channel's introduction on advertising decisions
Game typeCooperative advertising
ComparisonsConditions
SM${A_1^{S_M}}^* < {A_1^{cS_M}}^*$$C_5\lambda < \rho_0\beta_0$
${A_1^{S_M}}^* \geq {A_1^{cS_M}}^*$$C_5\lambda \geq \rho_0\beta_0$
SR${A_1^{S_R}}^* < {A_1^{cS_R}}^*$$C_6\lambda < \rho_0\beta_0$
${A_1^{S_R}}^* \geq {A_1^{cS_R}}^*$$C_6\lambda \geq \rho_0\beta_0$
NM${A_1^{N_M}}^* \leq {A_1^{cN_M}}^*$-
--
NR${A_1^{N_R}}^* < {A_1^{cN_R}}^*$$C_7\lambda < \rho_0\beta_0$
${A_1^{N_R}}^* \geq {A_1^{cN_R}}^*$$C_7\lambda \geq \rho_0\beta_0$
Game typeCooperative advertising
ComparisonsConditions
SM${A_1^{S_M}}^* < {A_1^{cS_M}}^*$$C_5\lambda < \rho_0\beta_0$
${A_1^{S_M}}^* \geq {A_1^{cS_M}}^*$$C_5\lambda \geq \rho_0\beta_0$
SR${A_1^{S_R}}^* < {A_1^{cS_R}}^*$$C_6\lambda < \rho_0\beta_0$
${A_1^{S_R}}^* \geq {A_1^{cS_R}}^*$$C_6\lambda \geq \rho_0\beta_0$
NM${A_1^{N_M}}^* \leq {A_1^{cN_M}}^*$-
--
NR${A_1^{N_R}}^* < {A_1^{cN_R}}^*$$C_7\lambda < \rho_0\beta_0$
${A_1^{N_R}}^* \geq {A_1^{cN_R}}^*$$C_7\lambda \geq \rho_0\beta_0$
Table 7.  Effects of direct channel's introduction on profits
Game typeManufacturer's profitsRetailer's Profits
ComparisonsConditionsComparisonsConditions
SM${\pi_m^{S_M}}^* < {\pi_m^{cS_M}}^*$$0 \leq a_0 < C_8$${\pi_r^{S_M}}^* < {\pi_r^{cS_M}}^*$$Z_1 < 0$
${\pi_m^{S_M}}^* \geq {\pi_m^{cS_M}}^*$$ a_0 \geq C_8$${\pi_r^{S_M}}^* \geq {\pi_r^{cS_M}}^*$$Z_1 \geq 0$
SR${\pi_m^{S_R}}^* < {\pi_m^{cS_R}}^*$$0 \leq a_0 < C_9$${\pi_r^{S_R}}^* < {\pi_r^{cS_R}}^*$$Z_2 < 0$
${\pi_m^{S_R}}^* \geq {\pi_m^{cS_R}}^*$$ a_0 \geq C_9$${\pi_r^{S_R}}^* \geq {\pi_r^{cS_R}}^*$$Z_2 \geq 0$
NM${\pi_m^{N_M}}^* < {\pi_m^{cN_M}}^*$$0 \leq a_0 < C_{10}$${\pi_r^{N_M}}^* < {\pi_r^{cN_M}}^*$$Z_3 < 0$
${\pi_m^{N_M}}^* \geq {\pi_m^{cN_M}}^*$$ a_0 \geq C_{10}$${\pi_r^{N_M}}^* \geq {\pi_r^{cN_M}}^*$$Z_3 \geq 0$
NR${\pi_m^{N_R}}^* < {\pi_m^{cN_R}}^*$$0 \leq a_0 < C_{11}$${\pi_r^{N_R}}^* < {\pi_r^{cN_R}}^*$$Z_4 < 0$
${\pi_m^{N_R}}^* \geq {\pi_m^{cN_R}}^*$$ a_0 \geq C_{11}$${\pi_r^{N_R}}^* \geq {\pi_r^{cN_R}}^*$$Z_4 \geq 0$
Game typeManufacturer's profitsRetailer's Profits
ComparisonsConditionsComparisonsConditions
SM${\pi_m^{S_M}}^* < {\pi_m^{cS_M}}^*$$0 \leq a_0 < C_8$${\pi_r^{S_M}}^* < {\pi_r^{cS_M}}^*$$Z_1 < 0$
${\pi_m^{S_M}}^* \geq {\pi_m^{cS_M}}^*$$ a_0 \geq C_8$${\pi_r^{S_M}}^* \geq {\pi_r^{cS_M}}^*$$Z_1 \geq 0$
SR${\pi_m^{S_R}}^* < {\pi_m^{cS_R}}^*$$0 \leq a_0 < C_9$${\pi_r^{S_R}}^* < {\pi_r^{cS_R}}^*$$Z_2 < 0$
${\pi_m^{S_R}}^* \geq {\pi_m^{cS_R}}^*$$ a_0 \geq C_9$${\pi_r^{S_R}}^* \geq {\pi_r^{cS_R}}^*$$Z_2 \geq 0$
NM${\pi_m^{N_M}}^* < {\pi_m^{cN_M}}^*$$0 \leq a_0 < C_{10}$${\pi_r^{N_M}}^* < {\pi_r^{cN_M}}^*$$Z_3 < 0$
${\pi_m^{N_M}}^* \geq {\pi_m^{cN_M}}^*$$ a_0 \geq C_{10}$${\pi_r^{N_M}}^* \geq {\pi_r^{cN_M}}^*$$Z_3 \geq 0$
NR${\pi_m^{N_R}}^* < {\pi_m^{cN_R}}^*$$0 \leq a_0 < C_{11}$${\pi_r^{N_R}}^* < {\pi_r^{cN_R}}^*$$Z_4 < 0$
${\pi_m^{N_R}}^* \geq {\pi_m^{cN_R}}^*$$ a_0 \geq C_{11}$${\pi_r^{N_R}}^* \geq {\pi_r^{cN_R}}^*$$Z_4 \geq 0$
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