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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

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$
[1]

Mingyong Lai, Hongzhao Yang, Erbao Cao, Duo Qiu, Jing Qiu. Optimal decisions for a dual-channel supply chain under information asymmetry. Journal of Industrial & Management Optimization, 2018, 14 (3) : 1023-1040. doi: 10.3934/jimo.2017088

[2]

Lisha Wang, Huaming Song, Ding Zhang, Hui Yang. Pricing decisions for complementary products in a fuzzy dual-channel supply chain. Journal of Industrial & Management Optimization, 2019, 15 (1) : 343-364. doi: 10.3934/jimo.2018046

[3]

Hongxia Sun, Yao Wan, Yu Li, Linlin Zhang, Zhen Zhou. Competition in a dual-channel supply chain considering duopolistic retailers with different behaviours. Journal of Industrial & Management Optimization, 2017, 13 (5) : 0-0. doi: 10.3934/jimo.2019125

[4]

Ali Naimi Sadigh, S. Kamal Chaharsooghi, Majid Sheikhmohammady. A game theoretic approach to coordination of pricing, advertising, and inventory decisions in a competitive supply chain. Journal of Industrial & Management Optimization, 2016, 12 (1) : 337-355. doi: 10.3934/jimo.2016.12.337

[5]

Tinggui Chen, Yanhui Jiang. Research on operating mechanism for creative products supply chain based on game theory. Discrete & Continuous Dynamical Systems - S, 2015, 8 (6) : 1103-1112. doi: 10.3934/dcdss.2015.8.1103

[6]

Serap Ergün, Bariş Bülent Kırlar, Sırma Zeynep Alparslan Gök, Gerhard-Wilhelm Weber. An application of crypto cloud computing in social networks by cooperative game theory. Journal of Industrial & Management Optimization, 2017, 13 (5) : 1-15. doi: 10.3934/jimo.2019036

[7]

Jiahua Zhang, Shu-Cherng Fang, Yifan Xu, Ziteng Wang. A cooperative game with envy. Journal of Industrial & Management Optimization, 2017, 13 (4) : 2049-2066. doi: 10.3934/jimo.2017031

[8]

Jing Shi, Tiaojun Xiao. Store assistance and coordination of supply chains facing consumer's return. Journal of Industrial & Management Optimization, 2016, 12 (3) : 991-1007. doi: 10.3934/jimo.2016.12.991

[9]

Simon Hoof. Cooperative dynamic advertising via state-dependent payoff weights. Journal of Dynamics & Games, 2019, 6 (3) : 195-209. doi: 10.3934/jdg.2019014

[10]

Juliang Zhang, Jian Chen. Information sharing in a make-to-stock supply chain. Journal of Industrial & Management Optimization, 2014, 10 (4) : 1169-1189. doi: 10.3934/jimo.2014.10.1169

[11]

Yeong-Cheng Liou, Siegfried Schaible, Jen-Chih Yao. Supply chain inventory management via a Stackelberg equilibrium. Journal of Industrial & Management Optimization, 2006, 2 (1) : 81-94. doi: 10.3934/jimo.2006.2.81

[12]

Juliang Zhang. Coordination of supply chain with buyer's promotion. Journal of Industrial & Management Optimization, 2007, 3 (4) : 715-726. doi: 10.3934/jimo.2007.3.715

[13]

Na Song, Ximin Huang, Yue Xie, Wai-Ki Ching, Tak-Kuen Siu. Impact of reorder option in supply chain coordination. Journal of Industrial & Management Optimization, 2017, 13 (1) : 449-475. doi: 10.3934/jimo.2016026

[14]

Liping Zhang. A nonlinear complementarity model for supply chain network equilibrium. Journal of Industrial & Management Optimization, 2007, 3 (4) : 727-737. doi: 10.3934/jimo.2007.3.727

[15]

Joseph Geunes, Panos M. Pardalos. Introduction to the Special Issue on Supply Chain Optimization. Journal of Industrial & Management Optimization, 2007, 3 (1) : i-ii. doi: 10.3934/jimo.2007.3.1i

[16]

Jia Shu, Jie Sun. Designing the distribution network for an integrated supply chain. Journal of Industrial & Management Optimization, 2006, 2 (3) : 339-349. doi: 10.3934/jimo.2006.2.339

[17]

Jun Pei, Panos M. Pardalos, Xinbao Liu, Wenjuan Fan, Shanlin Yang, Ling Wang. Coordination of production and transportation in supply chain scheduling. Journal of Industrial & Management Optimization, 2015, 11 (2) : 399-419. doi: 10.3934/jimo.2015.11.399

[18]

Feimin Zhong, Wei Zeng, Zhongbao Zhou. Mechanism design in a supply chain with ambiguity in private information. Journal of Industrial & Management Optimization, 2020, 16 (1) : 261-287. doi: 10.3934/jimo.2018151

[19]

Claude Carlet, Sylvain Guilley. Complementary dual codes for counter-measures to side-channel attacks. Advances in Mathematics of Communications, 2016, 10 (1) : 131-150. doi: 10.3934/amc.2016.10.131

[20]

Eduardo Espinosa-Avila, Pablo Padilla Longoria, Francisco Hernández-Quiroz. Game theory and dynamic programming in alternate games. Journal of Dynamics & Games, 2017, 4 (3) : 205-216. doi: 10.3934/jdg.2017013

2018 Impact Factor: 1.025

Metrics

  • PDF downloads (144)
  • HTML views (1177)
  • Cited by (0)

Other articles
by authors

[Back to Top]