doi: 10.3934/jimo.2022086
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Strategic service investment by retailers confronted by manufacturer encroachment

1. 

School of Management and Economics, University of Electronic Science and Technology of China, Chengdu Sichuan 611731, China

2. 

School of Management and Economics; Center for Digital Culture and Media Studies, University of Electronic Science and Technology of China, Chengdu Sichuan 611731, China

*Corresponding author: Junwu Chai

Received  July 2021 Revised  April 2022 Early access June 2022

Fund Project: The authors thank the National Natural Science Foundation of China (71872028) and the Digital Culture and Media Research Fund of Philosophy and Social Sciences Research Base in Sichuan Province (19CDCM03)

This study investigates the service strategies of retailers confronted by manufacturer encroachment and explores the influences of retail services on profitability under different channel structures. In contrast to previous studies, this paper differentiates between channel costs and considers retail service. First, it is demonstrated that retail services are profitable for supply chain members under certain circumstances, regardless of whether the retail service effort is endogenous or exogenous. In particular, when the service effort is endogenous, the retailer can optimize its service effort to influence sales and profit outcomes. Second, this study finds that a service strategy can cause harm to manufacturers while benefiting retailers, which can help retailers regain market dominance and make manufacturers less competitive. The findings also suggest that there can be a "lose-lose" outcome due to service inefficiencies and intense competition. Third, the results indicate that a retailer would prefer to improve their service effort if market competition is less intense or the retail channel has obvious cost advantages. As the service effort increases, a manufacturer has little incentive to encroach on the market. Finally, consumer surplus and service spillovers are discussed.

Citation: Hengyu Li, Junwu Chai. Strategic service investment by retailers confronted by manufacturer encroachment. Journal of Industrial and Management Optimization, doi: 10.3934/jimo.2022086
References:
[1]

A. AryaB. Mittendorf and D. E. M. Sappington, The bright side of supplier encroachment, Marketing Science, 26 (2007), 651-659. 

[2]

W. Y. 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. 

[3]

B. DanG. Xu and C. Liu, Pricing policies in a dual-channel supply chain with retail services, International Journal of Production Economics, 139 (2012), 312-320. 

[4]

A. HaX. Long and J. Nasiry, Quality in supply chain encroachment, Manufacturing & Service Operations Management, 18 (2016), 280-298. 

[5]

S. HuangX. G. Guan and Y. J. Chen, Retailer information sharing with supplier encroachment, Production and Operations Management, 27 (2018), 1089-1101. 

[6]

Y. LiuS. Gupta and Z. J. Zhang, Note on self-restraint as an online entry-deterrence strategy, Management Science, 52 (2006), 1799-1809. 

[7]

Z. LiS. M. Gilbert and G. Lai, Supplier encroachment under asymmetric information, Management Science, 60 (2014), 449-462. 

[8]

T. LiJ. Xie and X. Zhao, Supplier encroachment in competitive supply chains, International Journal of Production Economics, 165 (2015), 120-131. 

[9]

L. Luo and J. Sun, New product design under channel acceptance: Brick-and-mortar, online-exclusive, or brick-and-click, Production and Operation Management, 25 (2016), 2014-2034. 

[10]

Y. XiongW. Yan and K. Fernandes, 'Bricks vs. clicks': The impact of manufacturer encroachment with a dealer leasing and selling of durable goods, European Journal of Operational Research, 217 (2012), 75-83.  doi: 10.1016/j.ejor.2011.08.012.

[11]

R. Yan and Z. Pei, Retail services and firm profit in a dual-channel market, Journal of Retailing and Consumer Services, 16 (2009), 306-314. 

[12]

D.-H. Yoon, Supplier encroachment and investment spillovers, Production and Operations Management, 25 (2016), 1839-1854. 

[13]

S. ZhangJ. Zhang and G. Zhu, Retail service investing: an anti-encroachment strategy in a retailer-led supply chain, Omega, 84 (2016), 212-231. 

[14]

X. GuanB. LiuY. Chen and H. Wang, Inducing supply chain transparency through supplier encroachment, Production and Operations Management, 29 (2020), 725-749. 

[15]

S. Zheng and Y. Yu, Manufacturer encroachment with equal pricing strategy, Transportation Research Part E: Logistics and Transportation Review, 152 (2021), 102346. 

[16]

P. Hotkar and S. M. Gilbert, Supplier Encroachment in a Nonexclusive Reselling Channel, Management Science, 67 (2021), 5821-5837. 

[17]

J. ZhangQ. Cao and X. He, Manufacturer encroachment with advertising, Omega, 91 (2020), 102013. 

[18]

T. ZhangX. Feng and N. Wang, Manufacturer encroachment and product assortment under vertical differentiation, European Journal of Operational Research, 293 (2021), 120-132.  doi: 10.1016/j.ejor.2020.11.044.

[19]

X. Wu, J. Zhao and M. Wang, Managing cost reduction efforts in supplier encroachment, Mathematical Problems in Engineering, (2021), 1–6. doi: 10.1155/2021/6638830.

[20]

B. Liu, X. Guan and Y. Wang, Supplier encroachment with multiple retailers, Production and Operations Management, (2021). doi: 10.1111/poms.13447.

[21]

H. YangJ. Luo and Q. Zhang, Supplier encroachment under nonlinear pricing with imperfect substitutes: Bargaining power versus revenue-sharing, European Journal of Operational Research, 267 (2018), 1089-1101.  doi: 10.1016/j.ejor.2017.12.027.

[22]

K. Matsui, Optimal bargaining timing of a wholesale price for a manufacturer with a retailer in a dual-channel supply chain, European Journal of Operational Research, 287 (2020), 225-236.  doi: 10.1016/j.ejor.2020.05.004.

[23]

L. H. Zhang and C. Zhang, Manufacturer encroachment with capital-constrained competitive retailers, European Journal of Operational Research, 296 (2022), 1067-1083.  doi: 10.1016/j.ejor.2021.05.027.

[24]

S. Zhang, Y. Yao and J. Zhang, Consumer showrooming with supplier encroachment and omnichannel retail, Decision Sciences, (2021). doi: 10.1111/deci.12539.

[25]

J. LiL. YiV. Shi and X. Chen, Supplier encroachment strategy in the presence of retail strategic inventory: Centralization or decentralization?, Omega, 98 (2021), 102213. 

[26]

H. GuanH. GurnaniX. Geng and Y. Luo, Strategic inventory and supplier encroachment, Manufacturing & Service Operations Management, 21 (2019), 536-555. 

[27]

L. H. ZhangJ. Yao and L. Xu, Emission reduction and market encroachment: Whether the manufacturer opens a direct channel or not?, Journal of Cleaner Production, 269 (2020), 121932. 

[28]

J. Li, J. Liang, V. Shi and J. Zhu, The benefit of manufacturer encroachment considering consumer's environmental awareness and product competition, Annals of Operations Research, (2021), 1–21.

[29]

W. Hu and Y. Li, Retail service for mixed retail and E-tail channels, Annals of Operations Research, 192 (2012), 151-171.  doi: 10.1007/s10479-010-0818-7.

[30]

G. LiL. Li and J. Sun, Pricing and service effort strategy in a dual-channel supply chain with showrooming effect, Transportation Research Part E: Logistics and Transportation Review, 126 (2019), 32-48. 

[31]

L. ZhaoJ. You and S. C. Fang, A dual-channel supply chain problem with resource-utilization penalty: Who can benefit from sales effort?, Journal of Industrial & Management Optimization, 17 (2021), 2837.  doi: 10.3934/jimo.2020097.

[32]

X. ChenX. Wang and X. Jiang, The impact of power structure on the retail service supply chain with an O2O mixed channel, Journal of the Operational Research Society, 67 (2016), 294-301. 

[33]

C. DongL. Yang and C. T. Ng, Quantity leadership for a dual-channel supply chain with retail service, Asia-Pacific Journal of Operational Research, 37 (2020), 2050005.  doi: 10.1142/S0217595920500050.

[34]

W. Zhao, C. Ye and X. Ding, Preferred service investment in the dual-channel supply chain: Leader-follower relationships and product characteristics, Mathematical Problems in Engineering, (2020). doi: 10.1155/2020/1656094.

[35]

Y. JiangL. Liu and A. Lim, Optimal pricing decisions for an omni-channel supply chain with retail service, International Transactions in Operational Research, 27 (2020), 2927-2948.  doi: 10.1111/itor.12784.

[36]

J. Guo, Y. Zhou and B. Li, The optimal pricing and service strategies of a dual-channel retailer under free riding, Journal of Industrial & Management Optimization, (2021). doi: 10.3934/jimo.2021056.

[37]

L. ChaiY. Duan and J. Huo, Pricing strategies for O2O business model considering service spillover and power structures, International Transactions in Operational Research, 28 (2021), 1978-2001.  doi: 10.1111/itor.12863.

[38]

J. Hamamura and Y. Zennyo, Retailer voluntary investment against a threat of manufacturer encroachment, Marketing Letters, (2021), 1–17.

[39]

N. Wang and Z. Li, Supplier encroachment with a dual-purpose retailer, Production and Operations Management, (2021). doi: 10.1111/poms.13400.

[40]

J. Nie, Q. Wang, C. Shi and Y. Zhou, The dark side of bilateral encroachment within a supply chain, Journal of the Operational Research Society, (2021), 1–11.

[41]

Z. ZhangH. SongX. GuV. Shi and J. Zhu, How to compete with a supply chain partner: Retailer's store brand vs. manufacturer's encroachment, Omega, 103 (2021), 102412. 

[42]

Z. Pei and R. Yan, Do channel members value supportive retail services? Why?, Journal of Business Research, 68 (2015), 1350-1358. 

[43]

J. Xia and W. Niu, Adding clicks to bricks: An analysis of supplier encroachment under service spillovers, Electronic Commerce Research and Applications, 37 (2019), 100876. 

[44]

Z. Cao and J. Min, Selection and impact of decision mode of encroachment and retail service in a dual-channel supply chain, Journal of Industrial & Management Optimization, (2020). doi: 10.3934/jimo.2020167.

[45]

S. FengJ. Liu and X. Hu, Presale strategy for a dual-channel retailer considering sales effort, IEEE Access, 9 (2021), 40318-40335. 

[46]

M. Tu, An exploratory study of internet of things (IoT) adoption intention in logistics and supply chain management: A mixed research approach, The International Journal of Logistics Management, 29 (2018), 131-151. 

[47]

K. Govindan, T. C. E. Cheng, N. Mishra and N. Shukla, Big data analytics and application for logistics and supply chain management, Transportation Research Part E: Logistics and Transportation Review, (2018), 343–349.

[48]

A. ReyE. PanettiR. Maglio and M. Ferretti, Determinants in adopting the internet of things in the transport and logistics industry, Journal of Business Research, 131 (2021), 584-590. 

[49]

J. SarkisL. M. Meade and S. Talluri, E-logistics and the natural environment, Supply Chain Management: An International Journal, 9 (2004), 303-312. 

[50]

S. P. Daly and L. X. Cui, E-logistics in China: Basic problems, manageable concerns and intractable solutions, Industrial Marketing Management, 32 (2003), 235-242. 

[51]

C. W. Hsu and C. C. Yeh, Understanding the factors affecting the adoption of the internet of things, Technology Analysis & Strategic Management, 29 (2017), 1089-1102. 

[52]

H. Zhou and W. C. Benton Jr, Supply chain practice and information sharing, Journal of Operations management, 25 (2007), 1348-1365. 

[53]

B. HuY. Mai and S. Pekec, Managing innovation spillover in outsourcing, Production and Operations Management, 29 (2020), 2252-2267. 

[54]

X. Zhang and W. Hou, The impacts of e-tailer's private label on the sales mode selection: From the perspectives of economic and environmental sustainability, European Journal of Operational Research, 296 (2022), 601-614.  doi: 10.1016/j.ejor.2021.04.009.

show all references

References:
[1]

A. AryaB. Mittendorf and D. E. M. Sappington, The bright side of supplier encroachment, Marketing Science, 26 (2007), 651-659. 

[2]

W. Y. 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. 

[3]

B. DanG. Xu and C. Liu, Pricing policies in a dual-channel supply chain with retail services, International Journal of Production Economics, 139 (2012), 312-320. 

[4]

A. HaX. Long and J. Nasiry, Quality in supply chain encroachment, Manufacturing & Service Operations Management, 18 (2016), 280-298. 

[5]

S. HuangX. G. Guan and Y. J. Chen, Retailer information sharing with supplier encroachment, Production and Operations Management, 27 (2018), 1089-1101. 

[6]

Y. LiuS. Gupta and Z. J. Zhang, Note on self-restraint as an online entry-deterrence strategy, Management Science, 52 (2006), 1799-1809. 

[7]

Z. LiS. M. Gilbert and G. Lai, Supplier encroachment under asymmetric information, Management Science, 60 (2014), 449-462. 

[8]

T. LiJ. Xie and X. Zhao, Supplier encroachment in competitive supply chains, International Journal of Production Economics, 165 (2015), 120-131. 

[9]

L. Luo and J. Sun, New product design under channel acceptance: Brick-and-mortar, online-exclusive, or brick-and-click, Production and Operation Management, 25 (2016), 2014-2034. 

[10]

Y. XiongW. Yan and K. Fernandes, 'Bricks vs. clicks': The impact of manufacturer encroachment with a dealer leasing and selling of durable goods, European Journal of Operational Research, 217 (2012), 75-83.  doi: 10.1016/j.ejor.2011.08.012.

[11]

R. Yan and Z. Pei, Retail services and firm profit in a dual-channel market, Journal of Retailing and Consumer Services, 16 (2009), 306-314. 

[12]

D.-H. Yoon, Supplier encroachment and investment spillovers, Production and Operations Management, 25 (2016), 1839-1854. 

[13]

S. ZhangJ. Zhang and G. Zhu, Retail service investing: an anti-encroachment strategy in a retailer-led supply chain, Omega, 84 (2016), 212-231. 

[14]

X. GuanB. LiuY. Chen and H. Wang, Inducing supply chain transparency through supplier encroachment, Production and Operations Management, 29 (2020), 725-749. 

[15]

S. Zheng and Y. Yu, Manufacturer encroachment with equal pricing strategy, Transportation Research Part E: Logistics and Transportation Review, 152 (2021), 102346. 

[16]

P. Hotkar and S. M. Gilbert, Supplier Encroachment in a Nonexclusive Reselling Channel, Management Science, 67 (2021), 5821-5837. 

[17]

J. ZhangQ. Cao and X. He, Manufacturer encroachment with advertising, Omega, 91 (2020), 102013. 

[18]

T. ZhangX. Feng and N. Wang, Manufacturer encroachment and product assortment under vertical differentiation, European Journal of Operational Research, 293 (2021), 120-132.  doi: 10.1016/j.ejor.2020.11.044.

[19]

X. Wu, J. Zhao and M. Wang, Managing cost reduction efforts in supplier encroachment, Mathematical Problems in Engineering, (2021), 1–6. doi: 10.1155/2021/6638830.

[20]

B. Liu, X. Guan and Y. Wang, Supplier encroachment with multiple retailers, Production and Operations Management, (2021). doi: 10.1111/poms.13447.

[21]

H. YangJ. Luo and Q. Zhang, Supplier encroachment under nonlinear pricing with imperfect substitutes: Bargaining power versus revenue-sharing, European Journal of Operational Research, 267 (2018), 1089-1101.  doi: 10.1016/j.ejor.2017.12.027.

[22]

K. Matsui, Optimal bargaining timing of a wholesale price for a manufacturer with a retailer in a dual-channel supply chain, European Journal of Operational Research, 287 (2020), 225-236.  doi: 10.1016/j.ejor.2020.05.004.

[23]

L. H. Zhang and C. Zhang, Manufacturer encroachment with capital-constrained competitive retailers, European Journal of Operational Research, 296 (2022), 1067-1083.  doi: 10.1016/j.ejor.2021.05.027.

[24]

S. Zhang, Y. Yao and J. Zhang, Consumer showrooming with supplier encroachment and omnichannel retail, Decision Sciences, (2021). doi: 10.1111/deci.12539.

[25]

J. LiL. YiV. Shi and X. Chen, Supplier encroachment strategy in the presence of retail strategic inventory: Centralization or decentralization?, Omega, 98 (2021), 102213. 

[26]

H. GuanH. GurnaniX. Geng and Y. Luo, Strategic inventory and supplier encroachment, Manufacturing & Service Operations Management, 21 (2019), 536-555. 

[27]

L. H. ZhangJ. Yao and L. Xu, Emission reduction and market encroachment: Whether the manufacturer opens a direct channel or not?, Journal of Cleaner Production, 269 (2020), 121932. 

[28]

J. Li, J. Liang, V. Shi and J. Zhu, The benefit of manufacturer encroachment considering consumer's environmental awareness and product competition, Annals of Operations Research, (2021), 1–21.

[29]

W. Hu and Y. Li, Retail service for mixed retail and E-tail channels, Annals of Operations Research, 192 (2012), 151-171.  doi: 10.1007/s10479-010-0818-7.

[30]

G. LiL. Li and J. Sun, Pricing and service effort strategy in a dual-channel supply chain with showrooming effect, Transportation Research Part E: Logistics and Transportation Review, 126 (2019), 32-48. 

[31]

L. ZhaoJ. You and S. C. Fang, A dual-channel supply chain problem with resource-utilization penalty: Who can benefit from sales effort?, Journal of Industrial & Management Optimization, 17 (2021), 2837.  doi: 10.3934/jimo.2020097.

[32]

X. ChenX. Wang and X. Jiang, The impact of power structure on the retail service supply chain with an O2O mixed channel, Journal of the Operational Research Society, 67 (2016), 294-301. 

[33]

C. DongL. Yang and C. T. Ng, Quantity leadership for a dual-channel supply chain with retail service, Asia-Pacific Journal of Operational Research, 37 (2020), 2050005.  doi: 10.1142/S0217595920500050.

[34]

W. Zhao, C. Ye and X. Ding, Preferred service investment in the dual-channel supply chain: Leader-follower relationships and product characteristics, Mathematical Problems in Engineering, (2020). doi: 10.1155/2020/1656094.

[35]

Y. JiangL. Liu and A. Lim, Optimal pricing decisions for an omni-channel supply chain with retail service, International Transactions in Operational Research, 27 (2020), 2927-2948.  doi: 10.1111/itor.12784.

[36]

J. Guo, Y. Zhou and B. Li, The optimal pricing and service strategies of a dual-channel retailer under free riding, Journal of Industrial & Management Optimization, (2021). doi: 10.3934/jimo.2021056.

[37]

L. ChaiY. Duan and J. Huo, Pricing strategies for O2O business model considering service spillover and power structures, International Transactions in Operational Research, 28 (2021), 1978-2001.  doi: 10.1111/itor.12863.

[38]

J. Hamamura and Y. Zennyo, Retailer voluntary investment against a threat of manufacturer encroachment, Marketing Letters, (2021), 1–17.

[39]

N. Wang and Z. Li, Supplier encroachment with a dual-purpose retailer, Production and Operations Management, (2021). doi: 10.1111/poms.13400.

[40]

J. Nie, Q. Wang, C. Shi and Y. Zhou, The dark side of bilateral encroachment within a supply chain, Journal of the Operational Research Society, (2021), 1–11.

[41]

Z. ZhangH. SongX. GuV. Shi and J. Zhu, How to compete with a supply chain partner: Retailer's store brand vs. manufacturer's encroachment, Omega, 103 (2021), 102412. 

[42]

Z. Pei and R. Yan, Do channel members value supportive retail services? Why?, Journal of Business Research, 68 (2015), 1350-1358. 

[43]

J. Xia and W. Niu, Adding clicks to bricks: An analysis of supplier encroachment under service spillovers, Electronic Commerce Research and Applications, 37 (2019), 100876. 

[44]

Z. Cao and J. Min, Selection and impact of decision mode of encroachment and retail service in a dual-channel supply chain, Journal of Industrial & Management Optimization, (2020). doi: 10.3934/jimo.2020167.

[45]

S. FengJ. Liu and X. Hu, Presale strategy for a dual-channel retailer considering sales effort, IEEE Access, 9 (2021), 40318-40335. 

[46]

M. Tu, An exploratory study of internet of things (IoT) adoption intention in logistics and supply chain management: A mixed research approach, The International Journal of Logistics Management, 29 (2018), 131-151. 

[47]

K. Govindan, T. C. E. Cheng, N. Mishra and N. Shukla, Big data analytics and application for logistics and supply chain management, Transportation Research Part E: Logistics and Transportation Review, (2018), 343–349.

[48]

A. ReyE. PanettiR. Maglio and M. Ferretti, Determinants in adopting the internet of things in the transport and logistics industry, Journal of Business Research, 131 (2021), 584-590. 

[49]

J. SarkisL. M. Meade and S. Talluri, E-logistics and the natural environment, Supply Chain Management: An International Journal, 9 (2004), 303-312. 

[50]

S. P. Daly and L. X. Cui, E-logistics in China: Basic problems, manageable concerns and intractable solutions, Industrial Marketing Management, 32 (2003), 235-242. 

[51]

C. W. Hsu and C. C. Yeh, Understanding the factors affecting the adoption of the internet of things, Technology Analysis & Strategic Management, 29 (2017), 1089-1102. 

[52]

H. Zhou and W. C. Benton Jr, Supply chain practice and information sharing, Journal of Operations management, 25 (2007), 1348-1365. 

[53]

B. HuY. Mai and S. Pekec, Managing innovation spillover in outsourcing, Production and Operations Management, 29 (2020), 2252-2267. 

[54]

X. Zhang and W. Hou, The impacts of e-tailer's private label on the sales mode selection: From the perspectives of economic and environmental sustainability, European Journal of Operational Research, 296 (2022), 601-614.  doi: 10.1016/j.ejor.2021.04.009.

Figure 1.  The supply chain structure
Figure 2.  The game theory flowchart
Figure 3.  Impact of encroachment without service ($ d = 0.5 $)
Figure 4.  Impact of encroachment with retail services ($ d = 0.5 $ $ s = 1 $ $ n = 1 $)
Figure 5.  The retailer's service strategy ($ d = 0.8 $ $ n = 1 $ $ c = 0.4 $)
Figure 6.  The impact of service on the manufacturer encroachment threshold ($ n = 1 $)
Figure 7.  Regions with the introduction of service ($ d = 0.8 $ $ n = 1 $ $ c = 0.4 $)
Figure 8.  Optimal service effort under different channel structure with variations in $ k $, $ d $, $ c $, $ n $
Figure 9.  The impact of endogenous service on retailer and total supply chain. ($ d = 0.8 $ $ n = 2 $)
Figure 10.  The impact of exogenous service on retailer and total supply chain. ($ b = 0.8 $ $ n = 1 $ $ c = 0.4 $)
Figure 11.  The impact of endogenous service on retailer and total supply chain. ($ b = 0.8 $ $ n = 2 $)
Table 1.  Recently published works
Literature Channel preference Retail cost Service cost Direct cost Situations Research issues
Chen et al. [32] No Yes No Yes Market share, pricing strategy Impact of power structure
Pei et al. [42] Yes No Yes No Product compatibility Impact of service
Xia et al. [43] Yes No Yes Yes Dominant power structure Impact of encroachment
Zhang et al. [13] Yes No Yes Yes Effect of information Impact of service
Cao et al. [44] No No Yes Yes Different decision sequences Encroachment and service
Wang et al. [39] No No No Yes Consumer surplus and profit Dual-purpose retailer on encroachment
Guo et al. [36] Yes No Yes No Degree of free riding Impact of free riding
Zhao et al. [31] Yes Yes Yes No Cost-sharing proportion resource-utilization and service impact
This study Yes Yes Yes Yes Extra channel and service cost Endogenous and exogenous service strategy
Literature Channel preference Retail cost Service cost Direct cost Situations Research issues
Chen et al. [32] No Yes No Yes Market share, pricing strategy Impact of power structure
Pei et al. [42] Yes No Yes No Product compatibility Impact of service
Xia et al. [43] Yes No Yes Yes Dominant power structure Impact of encroachment
Zhang et al. [13] Yes No Yes Yes Effect of information Impact of service
Cao et al. [44] No No Yes Yes Different decision sequences Encroachment and service
Wang et al. [39] No No No Yes Consumer surplus and profit Dual-purpose retailer on encroachment
Guo et al. [36] Yes No Yes No Degree of free riding Impact of free riding
Zhao et al. [31] Yes Yes Yes No Cost-sharing proportion resource-utilization and service impact
This study Yes Yes Yes Yes Extra channel and service cost Endogenous and exogenous service strategy
Table 2.  Description of notations
Indices Description
$ m, r $ Subscript, represents the manufacturer and the retailer.
$ i $ Superscript, represents Model N, S, E respectively.
Parameters
$ k $ Unit marginal cost to open the direct channel.
$ c $ Unit marginal cost to off-line retailing activity.
$ d $ The degree of consumer acceptance of direct channel.
$ n $ The cost-effectiveness of the retail service.
$ v $ The consumer utility on product.
$ U_m/U_r $ The consumer's willingness-to-pay through direct/retail channel.
Independent Variables
$ q_m^i /q_r^i $ Sales volume via the direct/tradition channel in Model $ i $.
$ s $ The service effort offered by the retailer.
$ w^i $ Manufacturer's unit wholesale price in Model $ i $.
Dependent Variables
$ p_m^i /p_r^i $ Unit market price from the direct/tradition channel in Model $ i $.
$ \pi _m^i /\pi _r^i $ Profit for the manufacturer/retailer in Model $ i $.
Indices Description
$ m, r $ Subscript, represents the manufacturer and the retailer.
$ i $ Superscript, represents Model N, S, E respectively.
Parameters
$ k $ Unit marginal cost to open the direct channel.
$ c $ Unit marginal cost to off-line retailing activity.
$ d $ The degree of consumer acceptance of direct channel.
$ n $ The cost-effectiveness of the retail service.
$ v $ The consumer utility on product.
$ U_m/U_r $ The consumer's willingness-to-pay through direct/retail channel.
Independent Variables
$ q_m^i /q_r^i $ Sales volume via the direct/tradition channel in Model $ i $.
$ s $ The service effort offered by the retailer.
$ w^i $ Manufacturer's unit wholesale price in Model $ i $.
Dependent Variables
$ p_m^i /p_r^i $ Unit market price from the direct/tradition channel in Model $ i $.
$ \pi _m^i /\pi _r^i $ Profit for the manufacturer/retailer in Model $ i $.
Table 3.  Equilibrium outcomes under no services
Strategy N
Direct channel
(NM) $k < k_m$
Dual channel
(ND) $k_m < k < k_r$
Retail channel
(NR) $k>k_r$
$ N/A $ $ w^{ND} = \frac{{8c + 4d - 4cd + dk - d^2 - 8}}{{6d - 16}} $ $ w^{NR} = \frac{1}{2} - \frac{c}{2} $
$ N/A $ $ q_r^{ND} = \frac{{2c + 2d - 2k - 2}}{{3d - 8}} $ $ q_r^{NR} = \frac{1}{4} - \frac{c}{4} $
$ q_m^{NM} = \frac{{d - k}}{{2d}} $ $ q_m^{ND} = \frac{{ - (6d - 8k + 2cd + dk - d^2 )}}{{2d(3d - 8)}} $ $ N/A $
$ \pi _m^{NM} = \frac{{(d - k)^2 }}{{4d}} $ $ \pi _m^{ND} = \frac{{4c^2 d + 8cd^2 - 8cdk - 8cd + d^3 - 2d^2 k + dk^2 - 8dk + 4d + 8k^2 }}{{ - 4d(3d - 8)}} $ $ \pi _m^{NR} = \frac{{(c - 1)^2 }}{8} $
$ N/A $ $ \pi _r^{ND} = \frac{{4(c + d - k - 1)^2 }}{{(3d - 8)^2 }} $ $ \pi _r^{NR} = \frac{{(c - 1)^2 }}{{16}} $
Strategy N
Direct channel
(NM) $k < k_m$
Dual channel
(ND) $k_m < k < k_r$
Retail channel
(NR) $k>k_r$
$ N/A $ $ w^{ND} = \frac{{8c + 4d - 4cd + dk - d^2 - 8}}{{6d - 16}} $ $ w^{NR} = \frac{1}{2} - \frac{c}{2} $
$ N/A $ $ q_r^{ND} = \frac{{2c + 2d - 2k - 2}}{{3d - 8}} $ $ q_r^{NR} = \frac{1}{4} - \frac{c}{4} $
$ q_m^{NM} = \frac{{d - k}}{{2d}} $ $ q_m^{ND} = \frac{{ - (6d - 8k + 2cd + dk - d^2 )}}{{2d(3d - 8)}} $ $ N/A $
$ \pi _m^{NM} = \frac{{(d - k)^2 }}{{4d}} $ $ \pi _m^{ND} = \frac{{4c^2 d + 8cd^2 - 8cdk - 8cd + d^3 - 2d^2 k + dk^2 - 8dk + 4d + 8k^2 }}{{ - 4d(3d - 8)}} $ $ \pi _m^{NR} = \frac{{(c - 1)^2 }}{8} $
$ N/A $ $ \pi _r^{ND} = \frac{{4(c + d - k - 1)^2 }}{{(3d - 8)^2 }} $ $ \pi _r^{NR} = \frac{{(c - 1)^2 }}{{16}} $
Table 4.  Equilibrium outcomes under retail services
Strategy S
Direct channel
(NM) $k < k_m$
Dual channel
(ND) $k_m < k < k_r$
Retail channel
(NR) $k>k_r$
$ N/A $ $ w^{SD} = \frac{{8c + 4d - 8s - 4cd + dk + 8cn + 4ds - d^2 - 4cdn - 8}}{{6d - 16}} $ $ w^{SR} = \frac{{1 + s}}{2} - \frac{{c(n + 1)}}{2} $
$ N/A $ $ q_r^{SD} = \frac{{2c + 2d - 2k - 2s + 2cn - 2}}{{3d - 8}} $ $ q_r^{SR} = \frac{{1 - c + s - cn}}{4} $
$ q_m^{SM} = \frac{{d - k}}{{2d}} $ $ q_m^{SD} = \frac{{2(3d - 4k + cd - ds + cdn) + dk - d^2 }}{{ - 2d(3d - 8)}} $ $ N/A $
$ \pi _m^{SM} = \frac{{(d - k)^2 }}{{4d}} $ $ \begin{array}{l} \pi _m^{SD} =\\ \frac{{\left[ \begin{array}{l} 4c^2 dn^2 + 8c^2 dn + 4c^2 d + 8cd^2 n + 8cd^2 \;\;\;\\ - 8cdkn - 8cdk - 8cdns - 8cdn - 8cds\;\;\;\\ - 8cd + d^3 - 2d^2 k - 8d^2 s + dk^2 + 8dks\;\;\;\\ - 8dk + 4ds^2 + 8ds + 4d + 8k^2\\ \end{array} \right]}}{{ - 4d(3d - 8)}}\\ \end{array} $ $ \pi _m^{SR} = \frac{{(c - s + cn - 1)^2 }}{8} $
$ N/A $ $ \pi _r^{SD} = \frac{{4(c + d - k - s + cn - 1)^2 }}{{(3d - 8)^2 }} $ $ \pi _r^{SR} = \frac{{(c - s + cn - 1)^2 }}{{16}} $
Strategy S
Direct channel
(NM) $k < k_m$
Dual channel
(ND) $k_m < k < k_r$
Retail channel
(NR) $k>k_r$
$ N/A $ $ w^{SD} = \frac{{8c + 4d - 8s - 4cd + dk + 8cn + 4ds - d^2 - 4cdn - 8}}{{6d - 16}} $ $ w^{SR} = \frac{{1 + s}}{2} - \frac{{c(n + 1)}}{2} $
$ N/A $ $ q_r^{SD} = \frac{{2c + 2d - 2k - 2s + 2cn - 2}}{{3d - 8}} $ $ q_r^{SR} = \frac{{1 - c + s - cn}}{4} $
$ q_m^{SM} = \frac{{d - k}}{{2d}} $ $ q_m^{SD} = \frac{{2(3d - 4k + cd - ds + cdn) + dk - d^2 }}{{ - 2d(3d - 8)}} $ $ N/A $
$ \pi _m^{SM} = \frac{{(d - k)^2 }}{{4d}} $ $ \begin{array}{l} \pi _m^{SD} =\\ \frac{{\left[ \begin{array}{l} 4c^2 dn^2 + 8c^2 dn + 4c^2 d + 8cd^2 n + 8cd^2 \;\;\;\\ - 8cdkn - 8cdk - 8cdns - 8cdn - 8cds\;\;\;\\ - 8cd + d^3 - 2d^2 k - 8d^2 s + dk^2 + 8dks\;\;\;\\ - 8dk + 4ds^2 + 8ds + 4d + 8k^2\\ \end{array} \right]}}{{ - 4d(3d - 8)}}\\ \end{array} $ $ \pi _m^{SR} = \frac{{(c - s + cn - 1)^2 }}{8} $
$ N/A $ $ \pi _r^{SD} = \frac{{4(c + d - k - s + cn - 1)^2 }}{{(3d - 8)^2 }} $ $ \pi _r^{SR} = \frac{{(c - s + cn - 1)^2 }}{{16}} $
Table 5.  The retailer's service strategy
Strategy Service effectiveness Direct selling cost Region
No service $ 0<s<s_1 $ $ k_m(s)<k<k_{rs}(s) $ N
Services $ 0<s $ $ \max \{ 0, k_{ms} (s), k_{rs} (s)\}< k $ S
No retailer (direct channel) $ 0<s $ $ 0< k< \min \{ k_m (s), k_{ms} (s)\} $ M
Strategy Service effectiveness Direct selling cost Region
No service $ 0<s<s_1 $ $ k_m(s)<k<k_{rs}(s) $ N
Services $ 0<s $ $ \max \{ 0, k_{ms} (s), k_{rs} (s)\}< k $ S
No retailer (direct channel) $ 0<s $ $ 0< k< \min \{ k_m (s), k_{ms} (s)\} $ M
Table 6.  Impact of service on the retailer and manufacturer
Service effort Direct selling cost $ (\Delta \pi _r /\Delta \pi _m) $ Region
$ 0<s<s_1 $ $ k_m(s)<k<k_5(s) $ (-, -)(lose, lose) ND
$ 0<s<s_1 $ $ k_5(s)<k<k_r(s) $ (-, -)(lose, lose) NR
$ 0<s<s_1 $ $ k_r(s)<k<k_{rs}(s) $ (-, +)(lose, win) ND
$ s>s_1 $ $ \max \{ 0, k_{ms} (s)\}<k<k_{rs}(s) $ (+, +)(win, win) SD
$ s>0 $ $ k>k_{rs}(s) $ (+, +)(win, win) SR
$ 0<s<s_1 $ $ 0< k< \min \{ k_m (s), k_{ms} (s)\} $ N/A M
Service effort Direct selling cost $ (\Delta \pi _r /\Delta \pi _m) $ Region
$ 0<s<s_1 $ $ k_m(s)<k<k_5(s) $ (-, -)(lose, lose) ND
$ 0<s<s_1 $ $ k_5(s)<k<k_r(s) $ (-, -)(lose, lose) NR
$ 0<s<s_1 $ $ k_r(s)<k<k_{rs}(s) $ (-, +)(lose, win) ND
$ s>s_1 $ $ \max \{ 0, k_{ms} (s)\}<k<k_{rs}(s) $ (+, +)(win, win) SD
$ s>0 $ $ k>k_{rs}(s) $ (+, +)(win, win) SR
$ 0<s<s_1 $ $ 0< k< \min \{ k_m (s), k_{ms} (s)\} $ N/A M
Table 7.  Equilibrium outcomes when service effort is endogenous
Strategy E
Direct channel
(NM) $k < k_m$
Dual channel
(ND) $k_m < k < k_r$
Retail channel
(NR) $k>k_r$
$ N/A $ $ w^{ED} = \frac{{8c + 4d - 8s - 4cd + dk + 8cn + 4ds - d^2 - 4cdn - 8}}{{6d - 16}} $ $ w^{ER} = \frac{{4n(c + cn - 1)}}{{1 - 8n}} $
$ N/A $ $ s_d^{ED} = \frac{{8 - 8c - 8d + 8k - 8cn}}{{9nd^2 - 48nd + 64n - 8}} $ $ s_r^{ER} = \frac{{c + cn - 1}}{{1 - 8n}} $
$ N/A $ $ q_r^{ED} = \frac{{2n(3d - 8)(c + d - k + cn - 1)}}{{9nd^2 - 48nd + 64n - 8}} $ $ q_r^{ER} = \frac{{2n(c + cn - 1)}}{{1 - 8n}} $
$ q_m^{EM} = \frac{{d - k}}{{2d}} $ $ q_m^{ED} = \frac{{\left[ \begin{array}{l} 8d - 8k - 48dn + 64kn + 26d^2 n \\ - 3d^3 n + 6cd^2 n^2 - 16cdn - 32dkn \;\; \\ - 16cdn^2 + 6cd^2 n + 3d^2 kn \\ \end{array} \right]}}{{ - 2d(9nd^2 - 48nd + 64n - 8)}} $ $ N/A $
$ \pi _m^{EM} = \frac{{(d - k)^2 }}{{4d}} $ $ \pi _m^{ED} = $ shown in appendix proof $ \pi _m^{ER} = \frac{{8n^2 (c + cn - 1)^2 }}{{(8n - 1)^2 }} $
$ N/A $ $ \pi _r^{ED} = \frac{{4n(c + d - k + cn - 1)^2 }}{{9nd^2 - 48nd + 64n - 8}} $ $ \pi _r^{ER} = \frac{{n(c + cn - 1)^2 }}{{2(8n - 1)}} $
Strategy E
Direct channel
(NM) $k < k_m$
Dual channel
(ND) $k_m < k < k_r$
Retail channel
(NR) $k>k_r$
$ N/A $ $ w^{ED} = \frac{{8c + 4d - 8s - 4cd + dk + 8cn + 4ds - d^2 - 4cdn - 8}}{{6d - 16}} $ $ w^{ER} = \frac{{4n(c + cn - 1)}}{{1 - 8n}} $
$ N/A $ $ s_d^{ED} = \frac{{8 - 8c - 8d + 8k - 8cn}}{{9nd^2 - 48nd + 64n - 8}} $ $ s_r^{ER} = \frac{{c + cn - 1}}{{1 - 8n}} $
$ N/A $ $ q_r^{ED} = \frac{{2n(3d - 8)(c + d - k + cn - 1)}}{{9nd^2 - 48nd + 64n - 8}} $ $ q_r^{ER} = \frac{{2n(c + cn - 1)}}{{1 - 8n}} $
$ q_m^{EM} = \frac{{d - k}}{{2d}} $ $ q_m^{ED} = \frac{{\left[ \begin{array}{l} 8d - 8k - 48dn + 64kn + 26d^2 n \\ - 3d^3 n + 6cd^2 n^2 - 16cdn - 32dkn \;\; \\ - 16cdn^2 + 6cd^2 n + 3d^2 kn \\ \end{array} \right]}}{{ - 2d(9nd^2 - 48nd + 64n - 8)}} $ $ N/A $
$ \pi _m^{EM} = \frac{{(d - k)^2 }}{{4d}} $ $ \pi _m^{ED} = $ shown in appendix proof $ \pi _m^{ER} = \frac{{8n^2 (c + cn - 1)^2 }}{{(8n - 1)^2 }} $
$ N/A $ $ \pi _r^{ED} = \frac{{4n(c + d - k + cn - 1)^2 }}{{9nd^2 - 48nd + 64n - 8}} $ $ \pi _r^{ER} = \frac{{n(c + cn - 1)^2 }}{{2(8n - 1)}} $
Table A1.  results of comparison when $ c<c_1 $
Comparison of retailer's profit Comparison of manufacturer's profit
$ k<k_m $ $ N/A(only direct channel) $ $ N/A(only direct channel) $
$ k_m<k<k_{me} $ $ \pi _r^{EM} - \pi _r^{ND}< 0 $ $ \pi _m^{EM} - \pi _m^{ND}< 0 $
$ k_{me}<k<k_{re} $ $ \pi _r^{ED} - \pi _r^{ND}> 0 $ $ \pi _m^{ED} - \pi _m^{ND}> 0 $
$ k_{re}<k<k_{r} $ $ \pi _r^{ER} - \pi _r^{ND}< 0 $ $ \pi _m^{ER} - \pi _m^{ND}> 0 $
$ k>k_{r} $ if $c <c_3$, $\pi _r^{ER} - \pi _r^{NR} > 0$
if $c>c_3$, $\pi _r^{ER} - \pi _r^{NR} < 0$
$ \pi _m^{ER} - \pi _m^{NR}< 0 $
Comparison of retailer's profit Comparison of manufacturer's profit
$ k<k_m $ $ N/A(only direct channel) $ $ N/A(only direct channel) $
$ k_m<k<k_{me} $ $ \pi _r^{EM} - \pi _r^{ND}< 0 $ $ \pi _m^{EM} - \pi _m^{ND}< 0 $
$ k_{me}<k<k_{re} $ $ \pi _r^{ED} - \pi _r^{ND}> 0 $ $ \pi _m^{ED} - \pi _m^{ND}> 0 $
$ k_{re}<k<k_{r} $ $ \pi _r^{ER} - \pi _r^{ND}< 0 $ $ \pi _m^{ER} - \pi _m^{ND}> 0 $
$ k>k_{r} $ if $c <c_3$, $\pi _r^{ER} - \pi _r^{NR} > 0$
if $c>c_3$, $\pi _r^{ER} - \pi _r^{NR} < 0$
$ \pi _m^{ER} - \pi _m^{NR}< 0 $
Table A2.  results of comparison when $ c_1<c<c_2 $
Comparison of retailer's profit Comparison of manufacturer's profit
$ k<k_m $ $ N/A(only direct channel) $ $ N/A(only direct channel) $
$ k_m<k<k_{me} $ $ \pi _r^{EM} - \pi _r^{ND}< 0 $ $ \pi _m^{EM} - \pi _m^{ND}< 0 $
$ k_{me}<k<k_{r} $ $ \pi _r^{ED} - \pi _r^{ND}< 0 $ $ \pi _m^{ED} - \pi _m^{ND}< 0 $
$ k_{r}<k<k_{re} $ if $k <k_6$, $\pi _r^{ED} - \pi _r^{NR} <0$
if $k>k_6$, $\pi _r^{ED} - \pi _r^{NR} > 0$
$ \pi _m^{ED} - \pi _m^{NR}> 0 $
$ k>k_{re} $ $ \pi _r^{ER} - \pi _r^{NR}< 0 $ $ \pi _m^{ER} - \pi _m^{NR}< 0 $
Comparison of retailer's profit Comparison of manufacturer's profit
$ k<k_m $ $ N/A(only direct channel) $ $ N/A(only direct channel) $
$ k_m<k<k_{me} $ $ \pi _r^{EM} - \pi _r^{ND}< 0 $ $ \pi _m^{EM} - \pi _m^{ND}< 0 $
$ k_{me}<k<k_{r} $ $ \pi _r^{ED} - \pi _r^{ND}< 0 $ $ \pi _m^{ED} - \pi _m^{ND}< 0 $
$ k_{r}<k<k_{re} $ if $k <k_6$, $\pi _r^{ED} - \pi _r^{NR} <0$
if $k>k_6$, $\pi _r^{ED} - \pi _r^{NR} > 0$
$ \pi _m^{ED} - \pi _m^{NR}> 0 $
$ k>k_{re} $ $ \pi _r^{ER} - \pi _r^{NR}< 0 $ $ \pi _m^{ER} - \pi _m^{NR}< 0 $
Table A3.  results of comparison when $ c>c_2 $
Comparison of retailer's profit Comparison of manufacturer's profit
$ k<k_m $ $ N/A(only direct channel) $ $ N/A(only direct channel) $
$ k_m<k<k_{r} $ $ \pi _r^{EM} - \pi _r^{ND}< 0 $ $ \pi _m^{EM} - \pi _m^{ND}< 0 $
$ k_{r}<k<k_{me} $ $ \pi _r^{EM} - \pi _r^{NR}< 0 $ $ \pi _m^{EM} - \pi _m^{NR}< 0 $
$ k_{me}<k<k_{re} $ $ \pi _r^{ED} - \pi _r^{NR}< 0 $ $ \pi _m^{ED} - \pi _m^{NR}< 0 $
$ k>k_{re} $ $ \pi _r^{ER} - \pi _r^{NR}< 0 $ $ \pi _m^{ER} - \pi _m^{NR}< 0 $
Comparison of retailer's profit Comparison of manufacturer's profit
$ k<k_m $ $ N/A(only direct channel) $ $ N/A(only direct channel) $
$ k_m<k<k_{r} $ $ \pi _r^{EM} - \pi _r^{ND}< 0 $ $ \pi _m^{EM} - \pi _m^{ND}< 0 $
$ k_{r}<k<k_{me} $ $ \pi _r^{EM} - \pi _r^{NR}< 0 $ $ \pi _m^{EM} - \pi _m^{NR}< 0 $
$ k_{me}<k<k_{re} $ $ \pi _r^{ED} - \pi _r^{NR}< 0 $ $ \pi _m^{ED} - \pi _m^{NR}< 0 $
$ k>k_{re} $ $ \pi _r^{ER} - \pi _r^{NR}< 0 $ $ \pi _m^{ER} - \pi _m^{NR}< 0 $
Table A4.  Equilibrium outcomes when no service effort
Strategy N
Direct channel
(NM) $k<\frac{{c-1+b}}{{b}}$
Dual channel
(ND) $\frac{{c-1+b}}{{b}}<k <\frac{{2b-8-2cb+b^2}}{{b^2-8}}$
Retail channel
(NR) $k>\frac{{2b-8-2cb+b^2}}{{b^2-8}}$
$ N/A $ $ w^{ND} = \frac{{ - 8 + 8c + 4b^2 - 4cb^2 - b^3 + b^3 k}}{{2( - 8 + 3b^2 )}} $ $ w^{NR} = \frac{{1-c}}{{2}} $
$ N/A $ $ q_r^{ND} = \frac{{2n(3b - 8)(c + b - k + cn - 1)}}{{9nb^2 - 48nb + 64n - 8}} $ $ q_r^{NR} = \frac{{1-c}}{{4}} $
$ q_m^{NM} = \frac{{1 - k}}{{2}} $ $ q_m^{ND} = \frac{{8 - 2b + 2cb - b^2 - 8k + b^2 k}}{{2(8 - 3b^2 )}} $ $ N/A $
$ \pi _m^{NM} = \frac{{(k - 1)^2 }}{{4}} $ $ \pi _m^{ND} = \frac{{\left[ \begin{array}{l} 12 - 8c + 4c^2 - 8b + 8cd + b^2 - 16k \;\;\\ + 8bk - 8cbk - 2b^2 k + 8k^2 + b^2 k^2 \;\;\end{array} \right]}}{{4(8 - 3b^2 )}} $ $ \pi _m^{NR} = \frac{{(c - 1)^2 }}{{8}} $
$ N/A $ $ \pi _r^{ND} = \frac{{4(1 - c - b + bk)^2 }}{{( - 8 + 3b^2 )^2 }} $ $ \pi _r^{NR} = \frac{{(c - 1)^2}}{{16}} $
Strategy N
Direct channel
(NM) $k<\frac{{c-1+b}}{{b}}$
Dual channel
(ND) $\frac{{c-1+b}}{{b}}<k <\frac{{2b-8-2cb+b^2}}{{b^2-8}}$
Retail channel
(NR) $k>\frac{{2b-8-2cb+b^2}}{{b^2-8}}$
$ N/A $ $ w^{ND} = \frac{{ - 8 + 8c + 4b^2 - 4cb^2 - b^3 + b^3 k}}{{2( - 8 + 3b^2 )}} $ $ w^{NR} = \frac{{1-c}}{{2}} $
$ N/A $ $ q_r^{ND} = \frac{{2n(3b - 8)(c + b - k + cn - 1)}}{{9nb^2 - 48nb + 64n - 8}} $ $ q_r^{NR} = \frac{{1-c}}{{4}} $
$ q_m^{NM} = \frac{{1 - k}}{{2}} $ $ q_m^{ND} = \frac{{8 - 2b + 2cb - b^2 - 8k + b^2 k}}{{2(8 - 3b^2 )}} $ $ N/A $
$ \pi _m^{NM} = \frac{{(k - 1)^2 }}{{4}} $ $ \pi _m^{ND} = \frac{{\left[ \begin{array}{l} 12 - 8c + 4c^2 - 8b + 8cd + b^2 - 16k \;\;\\ + 8bk - 8cbk - 2b^2 k + 8k^2 + b^2 k^2 \;\;\end{array} \right]}}{{4(8 - 3b^2 )}} $ $ \pi _m^{NR} = \frac{{(c - 1)^2 }}{{8}} $
$ N/A $ $ \pi _r^{ND} = \frac{{4(1 - c - b + bk)^2 }}{{( - 8 + 3b^2 )^2 }} $ $ \pi _r^{NR} = \frac{{(c - 1)^2}}{{16}} $
Table A5.  Equilibrium outcomes when service effort is exogenous
Strategy S
Direct channel
(SM) $k<k_1^S$
Dual channel
(SD) $k_1^S <k<k_2^S$
Retail channel
(SR) $k>k_2^S$
$ N/A $ $ w^{SD} = \frac{{ - 8 + 8c + 4b^2 - 4cb^2 - b^3 + b^3 k + 8cn - 4cb^2 n - 8s + 4b^2 s}}{{2(3b^2 - 8)}} $ $ w^{SR} = \frac{{1-c-cn+s}}{{2}} $
$ N/A $ $ q_r^{SD} = \frac{{2(1 - c - b + bk - cn + s)}}{{8 - 3b^2 }} $ $ q_r^{SR} = \frac{{1-c-cn+s}}{{4}} $
$ q_m^{SM} = \frac{{1 - k}}{{2}} $ $ q_m^{SD} = \frac{{8 - 2b + 2cb - b^2 - 8k + b^2 k + 2cbn - 2bs}}{{2(8 - 3b^2 )}} $ $ N/A $
$ \pi _m^{SM} = \frac{{(k - 1)^2 }}{{4}} $ $ \pi _m^{SD} = \frac{{\left[ \begin{array}{l} 12 - 8c + 4c^2 - 8b + 8cb + b^2 - 16k \\ + 8bk - 8cbk - 2b^2 k + 8k^2 + b^2 k^2 - \\ 8cn + 8c^2 n + 8cbn - 8cbkn + 4c^2 n^2 + \;\;\\ 8s - 8cs - 8bs + 8bks - 8cns + 4s^2 \end{array} \right]}}{{4(3b^2 - 8)}} $ $ \pi _m^{SR} = \frac{{(c + cn - s - 1)^2 }}{{8}} $
$ N/A $ $ \pi _r^{SD} = \frac{{4(1 - c - b + bk - cn +s)^2 }}{{( - 8 + 3b^2 )^2 }} $ $ \pi _r^{SR} = \frac{{(c + cn - s - 1)^2}}{{16}} $
Strategy S
Direct channel
(SM) $k<k_1^S$
Dual channel
(SD) $k_1^S <k<k_2^S$
Retail channel
(SR) $k>k_2^S$
$ N/A $ $ w^{SD} = \frac{{ - 8 + 8c + 4b^2 - 4cb^2 - b^3 + b^3 k + 8cn - 4cb^2 n - 8s + 4b^2 s}}{{2(3b^2 - 8)}} $ $ w^{SR} = \frac{{1-c-cn+s}}{{2}} $
$ N/A $ $ q_r^{SD} = \frac{{2(1 - c - b + bk - cn + s)}}{{8 - 3b^2 }} $ $ q_r^{SR} = \frac{{1-c-cn+s}}{{4}} $
$ q_m^{SM} = \frac{{1 - k}}{{2}} $ $ q_m^{SD} = \frac{{8 - 2b + 2cb - b^2 - 8k + b^2 k + 2cbn - 2bs}}{{2(8 - 3b^2 )}} $ $ N/A $
$ \pi _m^{SM} = \frac{{(k - 1)^2 }}{{4}} $ $ \pi _m^{SD} = \frac{{\left[ \begin{array}{l} 12 - 8c + 4c^2 - 8b + 8cb + b^2 - 16k \\ + 8bk - 8cbk - 2b^2 k + 8k^2 + b^2 k^2 - \\ 8cn + 8c^2 n + 8cbn - 8cbkn + 4c^2 n^2 + \;\;\\ 8s - 8cs - 8bs + 8bks - 8cns + 4s^2 \end{array} \right]}}{{4(3b^2 - 8)}} $ $ \pi _m^{SR} = \frac{{(c + cn - s - 1)^2 }}{{8}} $
$ N/A $ $ \pi _r^{SD} = \frac{{4(1 - c - b + bk - cn +s)^2 }}{{( - 8 + 3b^2 )^2 }} $ $ \pi _r^{SR} = \frac{{(c + cn - s - 1)^2}}{{16}} $
Table A6.  Equilibrium outcomes when service effort is endogenous
Strategy E
Direct channel
(EM) $k <k_1^E$
Dual channel
(ED) $k_1^E<k<k_2^E$
Retail channel
(ER) $k>k_2^E$
$ N/A $ $ w^{ED} = $ shown in below $ w^{ER} = \frac{{1-c-cn+s}}{{2}} $
$ N/A $ $ q_r^{ED} = \frac{{2n(3b^2 - 8)(c + b - bk + cn - 1)}}{{9nb^4 - 48nb^2 + 64n - 8}} $ $ q_r^{ER} = \frac{{1-c-cn+s}}{{4}} $
$ q_m^{EM} = \frac{{1 - k}}{{2}} $ $ q_m^{ED} = $ shown in below $ N/A $
$ \pi _m^{EM} = \frac{{(k - 1)^2 }}{{4}} $ $ \pi _m^{ED} = $ shown in below $ \pi _m^{ER} = \frac{{(c + cn - s - 1)^2 }}{{8}} $
$ N/A $ $ \pi _r^{ED} = \frac{{4n(c + b - bk + cn -1)^2 }}{{(9nb^4 - 48nb^2 + 64n - 8)}} $ $ \pi _r^{ER} = \frac{{(c + cn - s - 1)^2}}{{16}} $
Strategy E
Direct channel
(EM) $k <k_1^E$
Dual channel
(ED) $k_1^E<k<k_2^E$
Retail channel
(ER) $k>k_2^E$
$ N/A $ $ w^{ED} = $ shown in below $ w^{ER} = \frac{{1-c-cn+s}}{{2}} $
$ N/A $ $ q_r^{ED} = \frac{{2n(3b^2 - 8)(c + b - bk + cn - 1)}}{{9nb^4 - 48nb^2 + 64n - 8}} $ $ q_r^{ER} = \frac{{1-c-cn+s}}{{4}} $
$ q_m^{EM} = \frac{{1 - k}}{{2}} $ $ q_m^{ED} = $ shown in below $ N/A $
$ \pi _m^{EM} = \frac{{(k - 1)^2 }}{{4}} $ $ \pi _m^{ED} = $ shown in below $ \pi _m^{ER} = \frac{{(c + cn - s - 1)^2 }}{{8}} $
$ N/A $ $ \pi _r^{ED} = \frac{{4n(c + b - bk + cn -1)^2 }}{{(9nb^4 - 48nb^2 + 64n - 8)}} $ $ \pi _r^{ER} = \frac{{(c + cn - s - 1)^2}}{{16}} $
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