The optimal pricing and service strategies of a dual-channel retailer under free riding

Jinsen Guo; Yongwu Zhou; Baixun Li

doi:10.3934/jimo.2021056

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doi: 10.3934/jimo.2021056

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The optimal pricing and service strategies of a dual-channel retailer under free riding

Jinsen Guo ^1, , Yongwu Zhou ^2, and Baixun Li ^3,4,,

1.	Business School, Henan Normal University, Xinxiang 453007, China
2.	School of Business Administration, South China University of Technology, , Guangzhou 510640, China
3.	Business School, Shantou University, Shantou 515063, China
4.	Research Institute of Innovation Competitiveness of Guangdong, HongKong and Macao Bay Area, Guangdong University of Finance and Economics, Guangzhou 510320, China

^* Corresponding author: Baixun Li

Received March 2019 Revised December 2020 Early access March 2021

Fund Project: This research is supported by the National Natural Science Foundation of China with Grant Numbers 71902055, 71401042, 71701051

Free riding refers to that in a multi-channel market, consumers enjoy the presale service of a product at one channel but purchase the product at another channel. In this paper, we study the optimal pricing and service strategies for a dual-channel retailer, who sells a product through both a traditional retail channel and an online channel. We assume that the offline channel provides the presale service but the online channel does not. We investigate how the changes of the degree of free riding affect the pricing/service strategies and profits of the two channels under three different scenarios: Stackelberg competition, Bertrand competition and channel integration. Our analysis shows that when the dual-channel retailer operates the two channels separately, no matter under which competitive scenario, free riding has a negative effect on both channels. And it is much more beneficial for the dual-channel retailer to let one channel work as a leader and another channel as a follower than to let the two channels make their decision simultaneous. In contrast, when the dual-channel retailer runs the two channels jointly, i.e., employs the channel-integration scenario, free riding may be beneficial to the retailer. Finally, this paper proposes and analyzes a revenue-sharing contract to coordinate a decentralized dual-channel retailer to achieve beneficial outcomes for both channels.

Keywords: Game theory, or in marketing, free riding, channel conflict, channel integration.

Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

Citation: Jinsen Guo, Yongwu Zhou, Baixun Li. The optimal pricing and service strategies of a dual-channel retailer under free riding. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2021056

References:

[1]	K. D. Antia, M. Bergen and S. Dutta, Competing with gray markets, MIT Sloan Management Review, 46 (2004), 63-69. Google Scholar
[2]	S. V. Baal and C. Dach, Free riding and customer retention across retailers' channels, Journal of Interactive Marketing, 19 (2005), 75-85. Google Scholar
[3]	P. D. Berger, J. Lee and B. Weinberg, Optimal cooperative advertising integration strategy for organizations adding a direct online channel, Journal of the operational research society, 57 (2006), 920-927. Google Scholar
[4]	F. Bernstein, J.-S. Song and X. Zheng, Free riding in a multi-channel supply chain, Naval Res. Logist., 56 (2009), 745-765. doi: 10.1002/nav.20379. Google Scholar
[5]	D. W. Carlton and J. A. Chevalier, Free riding and sales strategies for the Internet, Journal of Industrial Economics, 49 (2001), 441-461. doi: 10.3386/w8067. Google Scholar
[6]	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
[7]	S. C. Choi, Price competition in a duopoly common retailer channel, Journal of retailing, 72 (1996), 117-134. Google Scholar
[8]	A. Cohen, When channel conflict is good, Sales and Marketing Management, 152 (2000), 13. Google Scholar
[9]	B. Dan, C. Liu, G. Y. Xu and X. M. Zhang, Pareto Improvement Strategy for Service-Based Free-Riding in a Dual-Channel Supply Chain, Asia-Pacific Journal of Operational Research, 31 (2014), 1-27. Google Scholar
[10]	R. Gulati and J. Garino, Get the right mix of bricks and clicks, Harvard Business Review, 78 (2000), 107-117. Google Scholar
[11]	L. W. Hann, E-Commerce can create unexpected challenges, Best's Review, 99 (1999), 75. Google Scholar
[12]	R. He, Y. 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
[13]	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
[14]	G. W. Hua, S. Y. Wang and T. C. E. Cheng, Price and lead time decisions in dual-channel supply chains, European Journal of Operational Research, 205 (2010), 113-126. Google Scholar
[15]	L. Huang, X. H. Lu and S. L. Ba, An empirical study of the cross-channel effects between web and mobile shopping channels, Information & Management, 53 (2016), 265-278. Google Scholar
[16]	S. Huang, C. Yang and H. Liu, Pricing and production decisions in a dual-channel supply chain when production costs are disrupted, Economic Modelling, 30 (2013), 521-538. Google Scholar
[17]	W. Huang and J. M. Swaminathan, Introduction of a second channel: Implications for pricing and profits, European Journal of Operational Research, 194 (2009), 258-279. doi: 10.1016/j.ejor.2007.11.041. Google Scholar
[18]	H. Ke and J. Liu, Dual-channel supply chain competition with channel preference and sales effort under uncertain environment, Journal of Ambient Intelligence and Humanized Computing, 8 (2017), 781-795. doi: 10.1007/s12652-017-0502-8. Google Scholar
[19]	S. U. Kucuk and R. C. Maddux, The role of the Internet on free-riding: An exploratory study of the wallpaper industry, Journal of Retailing and Consumer Services, 17 (2010), 313-320. Google Scholar
[20]	R. Lal and M. Sarvary, When and how is the internet likely to decrease price competition?, Marketing Science, 18 (1999), 485-610. doi: 10.1287/mksc.18.4.485. Google Scholar
[21]	Q.-H. Li and B. Li, Dual-channel supply chain equilibrium problems regarding retail services and fairness concerns, Appl. Math. Model., 40 (2016), 7349-7367. doi: 10.1016/j.apm.2016.03.010. Google Scholar
[22]	G. Li, L. Li and J. Sun, Pricing and service effort strategy in a dual-channel supply chain with showrooming effect, Transportation Research Part E, 126 (2019), 32-48. doi: 10.1016/j.tre.2019.03.019. Google Scholar
[23]	W.-H. Liu, D. Xie and X.-C. Xu, Quality supervision and coordination of logistic service supply chain under multi-period conditions, International Journal of Production Economics, 142 (2013), 353-361. doi: 10.1016/j.ijpe.2012.12.011. Google Scholar
[24]	L. Ma, F. Liu, S. Li and H. Yan, Channel bargaining with risk-averse retailer, International Journal of Production Economics, 139 (2012), 155-167. doi: 10.1016/j.ijpe.2010.08.016. Google Scholar
[25]	R. A. Mittelstaedt, Sasquatch, the abominable snowman, free riders and other elusive beings, Journal of Macromarketing, 6 (1986), 25-35. doi: 10.1177/027614678600600206. Google Scholar
[26]	Y. Moon, T. Yao and T. L. Friesz, Dynamic pricing and inventory policies: A strategic analysis of dual channel supply chain design, Service Science, 2 (2010), 136-215. doi: 10.1287/serv.2.3.196. Google Scholar
[27]	S. K. Mukhopadhyay, X. W. Zhu and X. H. Yue, Optimal contract Design for mixed channels under information asymmetry, Production and Operations Management, 17 (2008), 641-650. Google Scholar
[28]	X. Pu, L. Gong and X. Han, Consumer free riding: Coordinating sales effort in a dual-channel supply chain, Electronic Commerce Research & Applications, 22 (2017), 1-12. doi: 10.1016/j.elerap.2016.11.002. Google Scholar
[29]	M. Radhi and G. Zhang, Pricing policies for a dual-channel retailer with cross-channel returns, Computers & Industrial Engineering, 119 (2018), 63-75. doi: 10.1016/j.cie.2018.03.020. Google Scholar
[30]	M. Setak, H. K. Ahar and S. Alaei, Coordination of information sharing and cooperative advertising in a decentralized supply chain with competing retailers considering free riding behavior, Journal of Industrial and Systems Engineering, 10 (2017), 151-168. Google Scholar
[31]	J. Shin, How does free riding on customer service affect competition?, Marketing Science, 26 (2007), 488-503. Google Scholar
[32]	R. B. Singley and M. R. Williams, Free riding in retail stores: An investigation of its perceived prevalence and costs, Journal of Marketing Theory and Practice, 2 (1995), 64-74. doi: 10.1080/10696679.1995.11501685. Google Scholar
[33]	F. Soleimani, A. Arshadi Khamseh and B. Naderi, Optimal decisions in a dual-channel supply chain under simultaneous demand and production cost disruptions, Ann. Oper. Res., 243 (2016), 301-321. doi: 10.1007/s10479-014-1675-6. Google Scholar
[34]	Y. L. Tan and J. E. Carrillo, Strategic analysis of the agency model for digital goods, Production and Operations Management, 26 (2017), 724-741. doi: 10.1111/poms.12595. Google Scholar
[35]	L. G. Telser, Why should manufactures want fair trade?, Journal of Law and Economics, 3 (1960), 86-105. Google Scholar
[36]	J. Tirole, The Theory of Industrial Organization, Contributions to nonlinear functional analysis, MIT Press, 1988. Google Scholar
[37]	A. A. Tsay and N. Agrawal, Channel dynamics under price and service competition, Manufacturing & Service Operations Management, 2 (2000), 372-391. doi: 10.1287/msom.2.4.372.12342. Google Scholar
[38]	P. C. Verhoef, S. A. Neslin and B. Vroomen, Multichannel customer management: Understanding the research-shopper phenomenon, International Journal of Research in Marketing, 24 (2007), 129-148. Google Scholar
[39]	J.-C. Wang, A.-M. Wang and Y.-Y. Wang, Markup pricing strategies between a dominant retailer and competitive manufacturers, Computers & Industrial Engineering, 64 (2013), 235-246. doi: 10.1016/j.cie.2012.09.009. Google Scholar
[40]	K. L. Webb and N. M. Didow, Understanding hybrid channel conflict: a conceptual model and propositions for research, Journal of Business-to-Business Marketing, 4 (1997), 39-78. doi: 10.1300/J033v04n01_02. Google Scholar
[41]	D. Wu, G. Ray, X. Geng and A. Whinston, Implications of reduced search cost and free riding in e-commerce, Marketing Science, 23 (2004), 173-274. doi: 10.1287/mksc.1040.0047. Google Scholar
[42]	Y. Xia and S. M. Gilbert, Strategic interactions between channel structure and demand enhancing services, European Journal of Operational Research, 181 (2007), 252-265. doi: 10.1016/j.ejor.2006.06.027. Google Scholar
[43]	D. H. Xing and T. M. Liu, Sales effort free riding and coordination with price match and channel rebate, European Journal of Operational Research, 219 (2012), 264-271. Google Scholar
[44]	R. Yan, Pricing strategy for companies with mixed online and traditional retailing distribution markets, Journal of Product & Brand Management, 17 (2008), 48-56. doi: 10.1108/10610420810856512. Google Scholar
[45]	R. Yan, Product brand differentiation and dual-channel store performances of a multi-channel retailer, European Journal of Marketing, 44 (2010), 672-692. doi: 10.1108/03090561011032324. Google Scholar
[46]	R. Yan and Z. Pei, The strategic value of cooperative advertising in the dual-channel competition, International Journal of Electronic Commerce, 19 (2015), 118-143. doi: 10.1080/10864415.2015.1000225. Google Scholar
[47]	J. Q. Yang, X. M. Zang, H. Y. Fu and C. Liu, Inventory competition in a dual-channel supply chain with delivery lead time consideration, Appl. Math. Model., 42 (2017), 675-692. doi: 10.1016/j.apm.2016.10.050. Google Scholar
[48]	W. S. Yoo and E. Lee, Internet channel entry: A strategic analysis of mixed channel structures, Marketing Science, 30 (2011), 2203-2211. doi: 10.1287/mksc.1100.0586. Google Scholar
[49]	L. Zhang and J. Wang, Coordination of the traditional and the online channels for a short-life-cycle product, European J. Oper. Res., 258 (2017), 639-651. doi: 10.1016/j.ejor.2016.09.020. Google Scholar
[50]	B. Zheng, C. Yang, J. Yang and M. Zhang, Dual-channel closed loop supply chains: Forward channel competition, power structures and coordination, International Journal of Production Research, 55 (2017), 3510-3527. doi: 10.1080/00207543.2017.1304662. Google Scholar
[51]	Y. Zhou, J. Guo and W. Zhou, Pricing/service strategies for a dual-channel supply chain with free riding and service-cost sharing, International Journal of Production Economics, 196 (2018), 198-210. doi: 10.1016/j.ijpe.2017.11.014. Google Scholar

show all references

References:

[1]	K. D. Antia, M. Bergen and S. Dutta, Competing with gray markets, MIT Sloan Management Review, 46 (2004), 63-69. Google Scholar
[2]	S. V. Baal and C. Dach, Free riding and customer retention across retailers' channels, Journal of Interactive Marketing, 19 (2005), 75-85. Google Scholar
[3]	P. D. Berger, J. Lee and B. Weinberg, Optimal cooperative advertising integration strategy for organizations adding a direct online channel, Journal of the operational research society, 57 (2006), 920-927. Google Scholar
[4]	F. Bernstein, J.-S. Song and X. Zheng, Free riding in a multi-channel supply chain, Naval Res. Logist., 56 (2009), 745-765. doi: 10.1002/nav.20379. Google Scholar
[5]	D. W. Carlton and J. A. Chevalier, Free riding and sales strategies for the Internet, Journal of Industrial Economics, 49 (2001), 441-461. doi: 10.3386/w8067. Google Scholar
[6]	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
[7]	S. C. Choi, Price competition in a duopoly common retailer channel, Journal of retailing, 72 (1996), 117-134. Google Scholar
[8]	A. Cohen, When channel conflict is good, Sales and Marketing Management, 152 (2000), 13. Google Scholar
[9]	B. Dan, C. Liu, G. Y. Xu and X. M. Zhang, Pareto Improvement Strategy for Service-Based Free-Riding in a Dual-Channel Supply Chain, Asia-Pacific Journal of Operational Research, 31 (2014), 1-27. Google Scholar
[10]	R. Gulati and J. Garino, Get the right mix of bricks and clicks, Harvard Business Review, 78 (2000), 107-117. Google Scholar
[11]	L. W. Hann, E-Commerce can create unexpected challenges, Best's Review, 99 (1999), 75. Google Scholar
[12]	R. He, Y. 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
[13]	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
[14]	G. W. Hua, S. Y. Wang and T. C. E. Cheng, Price and lead time decisions in dual-channel supply chains, European Journal of Operational Research, 205 (2010), 113-126. Google Scholar
[15]	L. Huang, X. H. Lu and S. L. Ba, An empirical study of the cross-channel effects between web and mobile shopping channels, Information & Management, 53 (2016), 265-278. Google Scholar
[16]	S. Huang, C. Yang and H. Liu, Pricing and production decisions in a dual-channel supply chain when production costs are disrupted, Economic Modelling, 30 (2013), 521-538. Google Scholar
[17]	W. Huang and J. M. Swaminathan, Introduction of a second channel: Implications for pricing and profits, European Journal of Operational Research, 194 (2009), 258-279. doi: 10.1016/j.ejor.2007.11.041. Google Scholar
[18]	H. Ke and J. Liu, Dual-channel supply chain competition with channel preference and sales effort under uncertain environment, Journal of Ambient Intelligence and Humanized Computing, 8 (2017), 781-795. doi: 10.1007/s12652-017-0502-8. Google Scholar
[19]	S. U. Kucuk and R. C. Maddux, The role of the Internet on free-riding: An exploratory study of the wallpaper industry, Journal of Retailing and Consumer Services, 17 (2010), 313-320. Google Scholar
[20]	R. Lal and M. Sarvary, When and how is the internet likely to decrease price competition?, Marketing Science, 18 (1999), 485-610. doi: 10.1287/mksc.18.4.485. Google Scholar
[21]	Q.-H. Li and B. Li, Dual-channel supply chain equilibrium problems regarding retail services and fairness concerns, Appl. Math. Model., 40 (2016), 7349-7367. doi: 10.1016/j.apm.2016.03.010. Google Scholar
[22]	G. Li, L. Li and J. Sun, Pricing and service effort strategy in a dual-channel supply chain with showrooming effect, Transportation Research Part E, 126 (2019), 32-48. doi: 10.1016/j.tre.2019.03.019. Google Scholar
[23]	W.-H. Liu, D. Xie and X.-C. Xu, Quality supervision and coordination of logistic service supply chain under multi-period conditions, International Journal of Production Economics, 142 (2013), 353-361. doi: 10.1016/j.ijpe.2012.12.011. Google Scholar
[24]	L. Ma, F. Liu, S. Li and H. Yan, Channel bargaining with risk-averse retailer, International Journal of Production Economics, 139 (2012), 155-167. doi: 10.1016/j.ijpe.2010.08.016. Google Scholar
[25]	R. A. Mittelstaedt, Sasquatch, the abominable snowman, free riders and other elusive beings, Journal of Macromarketing, 6 (1986), 25-35. doi: 10.1177/027614678600600206. Google Scholar
[26]	Y. Moon, T. Yao and T. L. Friesz, Dynamic pricing and inventory policies: A strategic analysis of dual channel supply chain design, Service Science, 2 (2010), 136-215. doi: 10.1287/serv.2.3.196. Google Scholar
[27]	S. K. Mukhopadhyay, X. W. Zhu and X. H. Yue, Optimal contract Design for mixed channels under information asymmetry, Production and Operations Management, 17 (2008), 641-650. Google Scholar
[28]	X. Pu, L. Gong and X. Han, Consumer free riding: Coordinating sales effort in a dual-channel supply chain, Electronic Commerce Research & Applications, 22 (2017), 1-12. doi: 10.1016/j.elerap.2016.11.002. Google Scholar
[29]	M. Radhi and G. Zhang, Pricing policies for a dual-channel retailer with cross-channel returns, Computers & Industrial Engineering, 119 (2018), 63-75. doi: 10.1016/j.cie.2018.03.020. Google Scholar
[30]	M. Setak, H. K. Ahar and S. Alaei, Coordination of information sharing and cooperative advertising in a decentralized supply chain with competing retailers considering free riding behavior, Journal of Industrial and Systems Engineering, 10 (2017), 151-168. Google Scholar
[31]	J. Shin, How does free riding on customer service affect competition?, Marketing Science, 26 (2007), 488-503. Google Scholar
[32]	R. B. Singley and M. R. Williams, Free riding in retail stores: An investigation of its perceived prevalence and costs, Journal of Marketing Theory and Practice, 2 (1995), 64-74. doi: 10.1080/10696679.1995.11501685. Google Scholar
[33]	F. Soleimani, A. Arshadi Khamseh and B. Naderi, Optimal decisions in a dual-channel supply chain under simultaneous demand and production cost disruptions, Ann. Oper. Res., 243 (2016), 301-321. doi: 10.1007/s10479-014-1675-6. Google Scholar
[34]	Y. L. Tan and J. E. Carrillo, Strategic analysis of the agency model for digital goods, Production and Operations Management, 26 (2017), 724-741. doi: 10.1111/poms.12595. Google Scholar
[35]	L. G. Telser, Why should manufactures want fair trade?, Journal of Law and Economics, 3 (1960), 86-105. Google Scholar
[36]	J. Tirole, The Theory of Industrial Organization, Contributions to nonlinear functional analysis, MIT Press, 1988. Google Scholar
[37]	A. A. Tsay and N. Agrawal, Channel dynamics under price and service competition, Manufacturing & Service Operations Management, 2 (2000), 372-391. doi: 10.1287/msom.2.4.372.12342. Google Scholar
[38]	P. C. Verhoef, S. A. Neslin and B. Vroomen, Multichannel customer management: Understanding the research-shopper phenomenon, International Journal of Research in Marketing, 24 (2007), 129-148. Google Scholar
[39]	J.-C. Wang, A.-M. Wang and Y.-Y. Wang, Markup pricing strategies between a dominant retailer and competitive manufacturers, Computers & Industrial Engineering, 64 (2013), 235-246. doi: 10.1016/j.cie.2012.09.009. Google Scholar
[40]	K. L. Webb and N. M. Didow, Understanding hybrid channel conflict: a conceptual model and propositions for research, Journal of Business-to-Business Marketing, 4 (1997), 39-78. doi: 10.1300/J033v04n01_02. Google Scholar
[41]	D. Wu, G. Ray, X. Geng and A. Whinston, Implications of reduced search cost and free riding in e-commerce, Marketing Science, 23 (2004), 173-274. doi: 10.1287/mksc.1040.0047. Google Scholar
[42]	Y. Xia and S. M. Gilbert, Strategic interactions between channel structure and demand enhancing services, European Journal of Operational Research, 181 (2007), 252-265. doi: 10.1016/j.ejor.2006.06.027. Google Scholar
[43]	D. H. Xing and T. M. Liu, Sales effort free riding and coordination with price match and channel rebate, European Journal of Operational Research, 219 (2012), 264-271. Google Scholar
[44]	R. Yan, Pricing strategy for companies with mixed online and traditional retailing distribution markets, Journal of Product & Brand Management, 17 (2008), 48-56. doi: 10.1108/10610420810856512. Google Scholar
[45]	R. Yan, Product brand differentiation and dual-channel store performances of a multi-channel retailer, European Journal of Marketing, 44 (2010), 672-692. doi: 10.1108/03090561011032324. Google Scholar
[46]	R. Yan and Z. Pei, The strategic value of cooperative advertising in the dual-channel competition, International Journal of Electronic Commerce, 19 (2015), 118-143. doi: 10.1080/10864415.2015.1000225. Google Scholar
[47]	J. Q. Yang, X. M. Zang, H. Y. Fu and C. Liu, Inventory competition in a dual-channel supply chain with delivery lead time consideration, Appl. Math. Model., 42 (2017), 675-692. doi: 10.1016/j.apm.2016.10.050. Google Scholar
[48]	W. S. Yoo and E. Lee, Internet channel entry: A strategic analysis of mixed channel structures, Marketing Science, 30 (2011), 2203-2211. doi: 10.1287/mksc.1100.0586. Google Scholar
[49]	L. Zhang and J. Wang, Coordination of the traditional and the online channels for a short-life-cycle product, European J. Oper. Res., 258 (2017), 639-651. doi: 10.1016/j.ejor.2016.09.020. Google Scholar
[50]	B. Zheng, C. Yang, J. Yang and M. Zhang, Dual-channel closed loop supply chains: Forward channel competition, power structures and coordination, International Journal of Production Research, 55 (2017), 3510-3527. doi: 10.1080/00207543.2017.1304662. Google Scholar
[51]	Y. Zhou, J. Guo and W. Zhou, Pricing/service strategies for a dual-channel supply chain with free riding and service-cost sharing, International Journal of Production Economics, 196 (2018), 198-210. doi: 10.1016/j.ijpe.2017.11.014. Google Scholar

Figure 1. Channel structures of dual-channel retailers

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Figure 2a-2b. The impact of $ \beta $ on the dual-channel retailer's profit under the four scenarios and his/her optimal decision under the channel-integration scenario.Channel structures of dual-channel retailers

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Figure 3a-3b. The impact of $ \eta $ on the dual-channel retailer's profit under the four scenarios and his/her optimal decision under the channel-integration scenario

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Figure 4a-4b. The impact of $ r $ on the dual-channel retailer's profit under the four scenarios and his/her optimal decision under the channel-integration scenario

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Figure 5 The impact of $ \lambda $ on the optimal decision and profit of the retailer's two channels under the TC-Stackelberg and RS-Stackelberg scenarios">Figure 1. Figure 5 The impact of $ \lambda $ on the optimal decision and profit of the retailer's two channels under the TC-Stackelberg and RS-Stackelberg scenarios

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Table 1. Notations used in the paper

$ p_{i} $	Retail price of channel $ i $
$ d_{i} $	Demand of the channel $ i $
$ a_{i} $	Market base or potential demand of channel $ i $
$ \theta_{i} $	Cross-price sensitivity for the two channels, where 0 < $ \theta_{i} $ < 1
$ S $	The pre-sales service level of the traditional channel
$ c_{s} $	The traditional channel's service cost incurred by providing service level $ S $
$ \beta $	The degree of free riding, where 0$ \le \beta \le r $
$ r $	Service sensitivity parameter
$ \lambda $	Revenue sharing rate of the online channel, where 0$ \le \lambda \le $1
$ \pi_{i} $	Profit of the channel $ i $
$ \pi $	The total profit of the dual-channel retailer Subscripts:
$ i= $1	represents the retailer's traditional channel and $ i= $2 the retailer's online channel

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$ p_{i} $	Retail price of channel $ i $
$ d_{i} $	Demand of the channel $ i $
$ a_{i} $	Market base or potential demand of channel $ i $
$ \theta_{i} $	Cross-price sensitivity for the two channels, where 0 < $ \theta_{i} $ < 1
$ S $	The pre-sales service level of the traditional channel
$ c_{s} $	The traditional channel's service cost incurred by providing service level $ S $
$ \beta $	The degree of free riding, where 0$ \le \beta \le r $
$ r $	Service sensitivity parameter
$ \lambda $	Revenue sharing rate of the online channel, where 0$ \le \lambda \le $1
$ \pi_{i} $	Profit of the channel $ i $
$ \pi $	The total profit of the dual-channel retailer Subscripts:
$ i= $1	represents the retailer's traditional channel and $ i= $2 the retailer's online channel

Table 2. The retailer's optimal pricing/service policies and profits of the two channels under different scenarios

$ a$	$\Omega $	Channel integration					TC-Stackelberg						OC-Stackelberg						Bertrand
		$p_{1}^{I^{\ast} }$	$S^{I^{\ast} }$	$p_{2}^{I^{\ast} }$	$\pi^{I\ast }$ (× 10$^{4})$	Sales mode	$p_{1}^{TC}$	$S^{TC}$	$p_{2}^{TC}$	$\pi_{1}^{TC}$ (× 10$^{4})$	$\pi_{2}^{TC}$ (× 10$^{4})$	$\pi^{\, TC}$ (× 10$^{4})$	$p_{1}^{OC}$	$S^{OC}$	$p_{2}^{OC}$	$\pi_{1}^{OC}$ (× 10$^{4})$	$\pi_{2}^{OC}$ (× 10$^{4})$	$\pi^{\, OC}$ (× 10$^{4})$	$p_{1}^{B}$	$S^{B}$	$p_{2}^{B}$	$\pi_{1}^{\, B}$ (× 10$^{4})$	$\pi_{2}^{\, B}$ (× 10$^{4})$	$\pi^{\, B}$ (× 10$^{4})$
40	65.5	—-	107.4	289	7.0234	Single-channel	284	58.7	136	1.1585	1.8385	2.9970	232	50	121	1.1393	1.3513	2.4907	231	50	116	1.1179	1.3490	2.4669
70	65.5 and $\Psi $ < 0	—-	112.5	326	8.9311	Single-channel	304	58.7	155	1.5977	2.3871	3.9849	251	50	141	1.5788	1.8229	3.4017	249	50	135	1.5495	1.8197	3.3692
500	65.5 and $\Psi $ > 0	—-	161.8	802	54.017	Single-channel	584	58.7	426	15.633	18.113	33.746	522	50	421	15.740	16.321	32.062	518	50	404	15.463	16.293	31.756
3500	65.5 and $\Psi $ > 0	3879	139.0	3248	1146.6	Dual-channel	2541	58.7	2317	516.20	536.80	1053.0	2413	50	2378	523.51	520.13	1043.6	2393	50	2279	514.49	519.22	1033.7
5000	65.5 and $\Psi $ > 0	5140	140.1	4500	2258.0	Dual-channel	3519	58.7	3263	1030.6	1064.4	2095.0	3359	50	3356	1045.7	1036.2	2081.8	3331	50	3216	1027.7	1034.4	2062.0

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$ a$	$\Omega $	Channel integration					TC-Stackelberg						OC-Stackelberg						Bertrand
		$p_{1}^{I^{\ast} }$	$S^{I^{\ast} }$	$p_{2}^{I^{\ast} }$	$\pi^{I\ast }$ (× 10$^{4})$	Sales mode	$p_{1}^{TC}$	$S^{TC}$	$p_{2}^{TC}$	$\pi_{1}^{TC}$ (× 10$^{4})$	$\pi_{2}^{TC}$ (× 10$^{4})$	$\pi^{\, TC}$ (× 10$^{4})$	$p_{1}^{OC}$	$S^{OC}$	$p_{2}^{OC}$	$\pi_{1}^{OC}$ (× 10$^{4})$	$\pi_{2}^{OC}$ (× 10$^{4})$	$\pi^{\, OC}$ (× 10$^{4})$	$p_{1}^{B}$	$S^{B}$	$p_{2}^{B}$	$\pi_{1}^{\, B}$ (× 10$^{4})$	$\pi_{2}^{\, B}$ (× 10$^{4})$	$\pi^{\, B}$ (× 10$^{4})$
40	65.5	—-	107.4	289	7.0234	Single-channel	284	58.7	136	1.1585	1.8385	2.9970	232	50	121	1.1393	1.3513	2.4907	231	50	116	1.1179	1.3490	2.4669
70	65.5 and $\Psi $ < 0	—-	112.5	326	8.9311	Single-channel	304	58.7	155	1.5977	2.3871	3.9849	251	50	141	1.5788	1.8229	3.4017	249	50	135	1.5495	1.8197	3.3692
500	65.5 and $\Psi $ > 0	—-	161.8	802	54.017	Single-channel	584	58.7	426	15.633	18.113	33.746	522	50	421	15.740	16.321	32.062	518	50	404	15.463	16.293	31.756
3500	65.5 and $\Psi $ > 0	3879	139.0	3248	1146.6	Dual-channel	2541	58.7	2317	516.20	536.80	1053.0	2413	50	2378	523.51	520.13	1043.6	2393	50	2279	514.49	519.22	1033.7
5000	65.5 and $\Psi $ > 0	5140	140.1	4500	2258.0	Dual-channel	3519	58.7	3263	1030.6	1064.4	2095.0	3359	50	3356	1045.7	1036.2	2081.8	3331	50	3216	1027.7	1034.4	2062.0

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The optimal pricing and service strategies of a dual-channel retailer under free riding

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