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September  2021, 17(5): 2527-2555. doi: 10.3934/jimo.2020081

Bundling and pricing decisions for bricks-and-clicks firms with consideration of network externality

Yeu-Shiang Huang 1,, , Chih-Chiang Fang 2, , Pin-Chun Lin 3, and  Y. Chris Liao 4,

1. 

Department of Industrial and Information Management, Center for Innovative FinTech Business Models, National Cheng Kung University, Taiwan
2. 

School of Computer Science and Software, Zhaoqing University, Guangdong, China
3. 

Department of Industrial and Information Management, National Cheng Kung University, Taiwan
4. 

Department of Finance, National Sun Yat-sen University, Taiwan

* Corresponding author: Yeu-Shiang Huang

Received  July 2019 Revised  December 2019 Published  September 2021 Early access  April 2020

The development of the Internet has dramatically changed firms' business models. Companies can now use both virtual and physical channels to enhance their competitiveness and profitability. In addition, bundling is a commonly used promotion strategy, although managers should consider the characteristics of the candidate bundled products. This study proposes a two-stage game theoretic model, in which a manufacturer may start an online channel along with an existing physical one which is operated by a dealer, i.e., a bricks-and-clicks approach, to examine the bundling and pricing strategy when selling two products with different network externalities. In the first stage, the manufacturer offers the products to the dealer, who may sell the two products individually or in a bundle to customers. In the second stage, and with the aim of expanding market share, the manufacturer may consider starting an online channel to integrate with the existing physical channel. We consider four cases, in which the manufacturer and dealer may sell the two products either individually or bundled in the two channels, in order to obtain the corresponding optimal pricing strategies with the aim of maximizing their profits. We also perform a numerical analysis to investigate the effects that network externality has on the bundling strategies and profits of the two channels. The results indicate that the bricks-and-clicks business model benefits both the manufacturer and dealer, and their profits would increase as network externality increases. In particular, when the network externalities of the two products are both high, a mixed strategy, which sells the two products in a bundle in the online channel and individually in the physical channel, should be adopted.

Keywords: Pricing, Bricks-and-Clicks, Dual-Channel, Bundling, Network Externality.
Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.
Citation: Yeu-Shiang Huang, Chih-Chiang Fang, Pin-Chun Lin, Y. Chris Liao. Bundling and pricing decisions for bricks-and-clicks firms with consideration of network externality. Journal of Industrial and Management Optimization, 2021, 17 (5) : 2527-2555. doi: 10.3934/jimo.2020081
References:
[1]

A. Alexandrov and O. Bedre-Defolie, The equivalence of bundling and advance sales, Marketing Science, 33 (2014), 259-272.  doi: 10.1287/mksc.2013.0833.

[2]

M. Aoyagi, Bertrand competition under network externalities, J. Econom. Theory, 178 (2018), 517-550.  doi: 10.1016/j.jet.2018.10.006.

[3]

Y. Bakos and E. Brynjolfsson, Bundle and competition on the internet, Marketing Science, 19 (2000), 63-82.  doi: 10.1287/mksc.19.1.63.15182.

[4]

S. Balachander, B. Ghosh and A. Stock, Why bundle discounts can be a profitable alternative to competing on price promotions, Marketing Science, 29 (2010), 624-638.  doi: 10.1287/mksc.1090.0540.

[5]

M. Banciu, E. Gal-Or and P. Mirchandani, Bundling strategies when products are vertically differentiated and capacities are limited, Management Science, 56 (2010), 2207-2223.  doi: 10.1287/mnsc.1100.1242.

[6]

A. Basu, T. Mazumdar and S. P. Raj, Indirect network externality effects on product attributes, Marketing Science, 22 (2003), 209-221.  doi: 10.1287/mksc.22.2.209.16037.

[7]

E. Bendoly, D. Blocher, K. M. Bretthauer and M. A. Venkataramanan, Service and cost benefits through clicks-and-mortar integration: Implications for the centralization/decentralization debate, European J. Oper. Res., 180 (2007), 426-442.  doi: 10.1016/j.ejor.2006.03.043.

[8]

F. Bernstein, J. S. Song and X. Zheng, "Bricks-and-mortar" vs. "clicks-and-mortar: An equilibrium analysis, European J. Oper. Res., 187 (2008), 671-690.  doi: 10.1016/j.ejor.2006.04.047.

[9]

H. K. Bhargava, Mixed bundling of two independently valued goods, Management Science, 59 (2013), 2170-2185.  doi: 10.1287/mnsc.1120.1663.

[10]

G. R. Bitran and J. C. Ferrer, On pricing and composition of bundles, Produc. Oper. Management, 16 (2007), 93-108.  doi: 10.1111/j.1937-5956.2007.tb00168.x.

[11]

K. Cattani, W. Gilland, H. S. Heese and J. Swaminathan, Pricing strategies for a manufacturer adding a direct channel that competes with the traditional channel, Produc. Oper. Management, 15 (2006), 40-56. 

[12]

Y. Chao and T. Derdenger, Mixed bundling in two-sided markets in the presence of installed base effects, Management Science, 59 (2013), 1904-1926.  doi: 10.1287/mnsc.1120.1688.

[13]

K. Y. Chen, M. Kaya and Ö. Özer, Dual sales channel management with service competition, Manufacturing Service Oper. Management, 10 (2008), 654-675.  doi: 10.1287/msom.1070.0177.

[14]

Y. Chen and J. Xie, Cross-market network effect with asymmetric customer loyalty: Implications for competitive advantage, Marketing Science, 26 (2007), 52-66.  doi: 10.1287/mksc.1060.0238.

[15]

H. K. Cheng and Q. C. Tang, Free trial or no free trial: Optimal software product design with network effects, European J. Oper. Res., 205 (2010), 437-447.  doi: 10.1016/j.ejor.2010.01.014.

[16]

W. K. Chiang, D. 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.

[17]

H. K. Chien and C. Y. C. Chu, Sale or lease? Durable-goods monopoly with network effects, Marketing Science, 27 (2008), 1012-1019.  doi: 10.1287/mksc.1070.0356.

[18]

S.-H. Chun and J.-C. Kim, Pricing strategies in B2C electronic commerce: Analytical and empirical approaches, Decision Support Systems, 40 (2005), 375-388. doi: 10.1016/j.dss.2004.04.012.

[19]

T. Derdenger and V. Kumar, The dynamic effects of bundling as a product strategy, Marketing Science, 32 (2013), 827-859.  doi: 10.1287/mksc.2013.0810.

[20]

A. Dumrongsiri, M. Fan, A. Jain and K. Moinzadeh, A supply chain model with direct and retail channels, European J. Oper. Res., 187 (2008), 691-718.  doi: 10.1016/j.ejor.2006.05.044.

[21]

N. Economides and E. Katsamakas, Two-sided competition of proprietary vs. open source technology platforms and the implications for the software industry, Management Science, 52 (2006), 1057-1071.  doi: 10.1287/mnsc.1060.0549.

[22]

X. J. Geng, M. B. Stinchcombe and A. B. Whinston, Bundling information goods of decreasing value, Management Science, 51 (2005), 662-667.  doi: 10.1287/mnsc.1040.0344.

[23]

L. M. Hitt and P.-Y. Chen, Bundling with customer self-selection: A simple approach to bundling low-marginal-cost goods, Management Science, 51 (2005), 1481-1493.  doi: 10.1287/mnsc.1050.0403.

[24]

L. Hsiao and Y. J. Chen, Strategic motive for introducing internet channels in a supply chain, Produc. Oper. Management, 23 (2014), 36-47.  doi: 10.1111/poms.12051.

[25]

G. Hua, S. Wang and T. C. E. Cheng, Price and lead time decisions in dual-channel supply chains, European J. Oper. Res., 205 (2010), 113-126.  doi: 10.1016/j.ejor.2009.12.012.

[26]

W. Hui, B. Yoo, V. Choudhary and K. Y. Tam, Sell by bundle or unit?: Pure bundling versus mixed bundling of information goods, Decision Support Systems, 53 (2012), 517-525.  doi: 10.1016/j.dss.2012.02.008.

[27]

R. Ibragimov and J. Walden, Optimal bundling strategies under heavy-tailed valuations, Management Science, 56 (2010), 1963-1976.  doi: 10.1287/mnsc.1100.1234.

[28]

P. I. Jeffers and B. R. Nault, Why competition from a multi-channel e-tailer does not always benefit consumers, Decision Sciences, 42 (2011), 69-91.  doi: 10.1111/j.1540-5915.2010.00302.x.

[29]

Y. Jiang, J. Shang, C. F. Kemerer and Y. Liu, Optimizing e-tailer profits and customer savings: Pricing multistage customized online bundles, Marketing Science, 30 (2011), 737-752.  doi: 10.1287/mksc.1100.0631.

[30]

Z. Katona, P. P. Zubcsek and M. Sarvary, Network effects and personal influences: The diffusion of an online social network, J. Marketing Res., 48 (2011), 425-443.  doi: 10.1509/jmkr.48.3.425.

[31]

M. Katz and C. Shapiro, Network externalities, competition, and compatibility, Amer. Economic Rev., 75 (1985), 424-440. 

[32]

L. J. Kornish, Technology choice and timing with positive network effects, European J. Oper. Res., 173 (2006), 268-282.  doi: 10.1016/j.ejor.2004.12.004.

[33]

M. Lai, H. Yang, E. Cao, D. Qiu and J. Qiu, Optimal decisions for a dual-channel supply chain under information asymmetry, J. Ind. Manag. Optim., 14 (2018), 1023-1040.  doi: 10.3934/jimo.2017088.

[34]

G. Li, J. Shao, D. Xu and W. Xu, The warehouse-retailer network design game, J. Ind. Manag. Optim., 11 (2015), 291-305.  doi: 10.3934/jimo.2015.11.291.

[35]

S. Li, M. Lai and W. Xue, Bundling strategy and channel competition in supply chains with complementary products, Procedia Computer Science, 126 (2018), 1730-1739.  doi: 10.1016/j.procs.2018.08.104.

[36]

H. Liu, X. Luo, W. Bi, Y. Man and K. L. Teo, Dynamic pricing of network goods in duopoly markets with boundedly rational consumers, J. Ind. Manag. Optim., 13 (2017), 427-445.  doi: 10.3934/jimo.2016025.

[37]

Y. Liu, S. Gupta and Z. J. Zhang, Note on self-restraint as an online entry-deterrence strategy, Management Science, 52 (2006), 1799-1809.  doi: 10.1287/mnsc.1050.0566.

[38]

X. Luo, M. Li, H. Feng and N. Feng, Intertemporal mixed bundling strategy of information products with network externality, Comput. Industrial Engineering, 113 (2017), 369-381.  doi: 10.1016/j.cie.2017.09.019.

[39]

K. F. McCardle, K. Rajaram and C. S. Tang, Bundling retail products: Models and analysis, European J. Oper. Res., 177 (2007), 1197-1217.  doi: 10.1016/j.ejor.2005.11.009.

[40]

E. Ofek, Z. Katona and M. Sarvary, "Bricks and clicks": The impact of product returns on the strategies of multichannel retailers, Marketing Science, 30 (2011), 42-60.  doi: 10.1287/mksc.1100.0588.

[41]

G. G. Parker and M. W. Van Alstyne, Two-sided network effects: A theory of information product design, Management Science, 51 (2005), 1494-1504.  doi: 10.1287/mnsc.1050.0400.

[42]

A. Prasad, R. Venkatesh and V. Mahajan, Optimal bundling of technological products with network externality, Management Science, 56 (2010), 2224-2236.  doi: 10.1287/mnsc.1100.1259.

[43]

S. Stremersch and G. J. Tellism, Strategic bundling of products and prices: A new synthesis for marketing, J. Marketing, 66 (2002), 55-72. doi: 10.1509/jmkg.66.1.55.18455.

[44]

S. Stremersch, G. J. Tellis, P. H. Franses and J. L. G. Binken, Indirect network effects in new product growth, J. Marketing, 71 (2007), 52-74. doi: 10.1509/jmkg.71.3.052.

[45]

B. Sun, J. Xie and H. H. Cao, Product strategy for innovators in markets with network effects, Marketing Science, 23 (2004), 243-254.  doi: 10.1287/mksc.1040.0058.

[46]

H. Sun, Y. Wan, Y. Li, L. Zhang and Z. Zhou, Competition in a dual-channel supply chain considering duopolistic retailers with different behaviours, J. Ind. Manag. Optim., (2019). doi: 10.3934/jimo.2019125.

[47]

A. A. Taleizade, L. E. Cárdenas-Barrón and R. Sohani, Coordinating the supplier-retailer supply chain under noise effect with bundling and inventory strategies, J. Ind. Manag. Optim., 15 (2019), 1701-1727.  doi: 10.3934/jimo.2018118.

[48]

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

[49]

S. Viswanathan, Competing across technology-differentiated channels: The impact of network externalities and switching costs, Management Science, 51 (2005), 483-496.  doi: 10.1287/mnsc.1040.0338.

[50]

S. Wu, L. M. Hitt, P. Chen and G. Anandalingam, Customized bundle pricing for information goods: A nonlinear mixed-integer programming approach, Management Science, 54 (2008), 608-622.  doi: 10.1287/mnsc.1070.0812.

[51]

L. Xie, J. Ma and H. Han, Implications of stochastic demand and manufacturers' operational mode on retailer's mixed bundling strategy and its complexity analysis, Appl. Math. Model., 55 (2018), 484-501.  doi: 10.1016/j.apm.2017.06.005.

[52]

Y. Xiong, W. Yan, K. Fernandes, Z.-K. Xiong and N. Guo, "Bricks vs. clicks": The impact of manufacturer encroachment with a dealer leasing and selling of durable goods, European J. Oper. Res., 217 (2012), 75-83.  doi: 10.1016/j.ejor.2011.08.012.

[53]

L. Yang, J. Ji and K. Chen, Advertising games on national brand and store brand in a dual-channel supply chain, J. Ind. Manag. Optim., 14 (2018), 105-134.  doi: 10.3934/jimo.2017039.

[54]

D. Q. Yao and J. J. Liu, Competitive pricing of mixed retail and e-tail distribution channels, Omega, 33 (2005), 235-247.  doi: 10.1016/j.omega.2004.04.007.

[55]

Y. Yi and H. Yang, Wholesale pricing and evolutionary stable strategies of retailers under network externality, European J. Oper. Res., 259 (2017), 37-47.  doi: 10.1016/j.ejor.2016.09.014.

[56]

X. Zhang, Retailers' multichannel and price advertising strategies, Marketing Science, 28 (2009), 1080–1094. doi: 10.1287/mksc.1090.0499.

[57]

Z. Zhang, X. Luo, C. K. Kwong, J. Tang and Y. Yu, Impacts of service uncertainty in bundling strategies on heterogeneous consumers, Electronic Commerce Res. Appl., 28 (2018), 230-243.  doi: 10.1016/j.elerap.2018.02.003.

show all references

References:
[1]

A. Alexandrov and O. Bedre-Defolie, The equivalence of bundling and advance sales, Marketing Science, 33 (2014), 259-272.  doi: 10.1287/mksc.2013.0833.

[2]

M. Aoyagi, Bertrand competition under network externalities, J. Econom. Theory, 178 (2018), 517-550.  doi: 10.1016/j.jet.2018.10.006.

[3]

Y. Bakos and E. Brynjolfsson, Bundle and competition on the internet, Marketing Science, 19 (2000), 63-82.  doi: 10.1287/mksc.19.1.63.15182.

[4]

S. Balachander, B. Ghosh and A. Stock, Why bundle discounts can be a profitable alternative to competing on price promotions, Marketing Science, 29 (2010), 624-638.  doi: 10.1287/mksc.1090.0540.

[5]

M. Banciu, E. Gal-Or and P. Mirchandani, Bundling strategies when products are vertically differentiated and capacities are limited, Management Science, 56 (2010), 2207-2223.  doi: 10.1287/mnsc.1100.1242.

[6]

A. Basu, T. Mazumdar and S. P. Raj, Indirect network externality effects on product attributes, Marketing Science, 22 (2003), 209-221.  doi: 10.1287/mksc.22.2.209.16037.

[7]

E. Bendoly, D. Blocher, K. M. Bretthauer and M. A. Venkataramanan, Service and cost benefits through clicks-and-mortar integration: Implications for the centralization/decentralization debate, European J. Oper. Res., 180 (2007), 426-442.  doi: 10.1016/j.ejor.2006.03.043.

[8]

F. Bernstein, J. S. Song and X. Zheng, "Bricks-and-mortar" vs. "clicks-and-mortar: An equilibrium analysis, European J. Oper. Res., 187 (2008), 671-690.  doi: 10.1016/j.ejor.2006.04.047.

[9]

H. K. Bhargava, Mixed bundling of two independently valued goods, Management Science, 59 (2013), 2170-2185.  doi: 10.1287/mnsc.1120.1663.

[10]

G. R. Bitran and J. C. Ferrer, On pricing and composition of bundles, Produc. Oper. Management, 16 (2007), 93-108.  doi: 10.1111/j.1937-5956.2007.tb00168.x.

[11]

K. Cattani, W. Gilland, H. S. Heese and J. Swaminathan, Pricing strategies for a manufacturer adding a direct channel that competes with the traditional channel, Produc. Oper. Management, 15 (2006), 40-56. 

[12]

Y. Chao and T. Derdenger, Mixed bundling in two-sided markets in the presence of installed base effects, Management Science, 59 (2013), 1904-1926.  doi: 10.1287/mnsc.1120.1688.

[13]

K. Y. Chen, M. Kaya and Ö. Özer, Dual sales channel management with service competition, Manufacturing Service Oper. Management, 10 (2008), 654-675.  doi: 10.1287/msom.1070.0177.

[14]

Y. Chen and J. Xie, Cross-market network effect with asymmetric customer loyalty: Implications for competitive advantage, Marketing Science, 26 (2007), 52-66.  doi: 10.1287/mksc.1060.0238.

[15]

H. K. Cheng and Q. C. Tang, Free trial or no free trial: Optimal software product design with network effects, European J. Oper. Res., 205 (2010), 437-447.  doi: 10.1016/j.ejor.2010.01.014.

[16]

W. K. Chiang, D. 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.

[17]

H. K. Chien and C. Y. C. Chu, Sale or lease? Durable-goods monopoly with network effects, Marketing Science, 27 (2008), 1012-1019.  doi: 10.1287/mksc.1070.0356.

[18]

S.-H. Chun and J.-C. Kim, Pricing strategies in B2C electronic commerce: Analytical and empirical approaches, Decision Support Systems, 40 (2005), 375-388. doi: 10.1016/j.dss.2004.04.012.

[19]

T. Derdenger and V. Kumar, The dynamic effects of bundling as a product strategy, Marketing Science, 32 (2013), 827-859.  doi: 10.1287/mksc.2013.0810.

[20]

A. Dumrongsiri, M. Fan, A. Jain and K. Moinzadeh, A supply chain model with direct and retail channels, European J. Oper. Res., 187 (2008), 691-718.  doi: 10.1016/j.ejor.2006.05.044.

[21]

N. Economides and E. Katsamakas, Two-sided competition of proprietary vs. open source technology platforms and the implications for the software industry, Management Science, 52 (2006), 1057-1071.  doi: 10.1287/mnsc.1060.0549.

[22]

X. J. Geng, M. B. Stinchcombe and A. B. Whinston, Bundling information goods of decreasing value, Management Science, 51 (2005), 662-667.  doi: 10.1287/mnsc.1040.0344.

[23]

L. M. Hitt and P.-Y. Chen, Bundling with customer self-selection: A simple approach to bundling low-marginal-cost goods, Management Science, 51 (2005), 1481-1493.  doi: 10.1287/mnsc.1050.0403.

[24]

L. Hsiao and Y. J. Chen, Strategic motive for introducing internet channels in a supply chain, Produc. Oper. Management, 23 (2014), 36-47.  doi: 10.1111/poms.12051.

[25]

G. Hua, S. Wang and T. C. E. Cheng, Price and lead time decisions in dual-channel supply chains, European J. Oper. Res., 205 (2010), 113-126.  doi: 10.1016/j.ejor.2009.12.012.

[26]

W. Hui, B. Yoo, V. Choudhary and K. Y. Tam, Sell by bundle or unit?: Pure bundling versus mixed bundling of information goods, Decision Support Systems, 53 (2012), 517-525.  doi: 10.1016/j.dss.2012.02.008.

[27]

R. Ibragimov and J. Walden, Optimal bundling strategies under heavy-tailed valuations, Management Science, 56 (2010), 1963-1976.  doi: 10.1287/mnsc.1100.1234.

[28]

P. I. Jeffers and B. R. Nault, Why competition from a multi-channel e-tailer does not always benefit consumers, Decision Sciences, 42 (2011), 69-91.  doi: 10.1111/j.1540-5915.2010.00302.x.

[29]

Y. Jiang, J. Shang, C. F. Kemerer and Y. Liu, Optimizing e-tailer profits and customer savings: Pricing multistage customized online bundles, Marketing Science, 30 (2011), 737-752.  doi: 10.1287/mksc.1100.0631.

[30]

Z. Katona, P. P. Zubcsek and M. Sarvary, Network effects and personal influences: The diffusion of an online social network, J. Marketing Res., 48 (2011), 425-443.  doi: 10.1509/jmkr.48.3.425.

[31]

M. Katz and C. Shapiro, Network externalities, competition, and compatibility, Amer. Economic Rev., 75 (1985), 424-440. 

[32]

L. J. Kornish, Technology choice and timing with positive network effects, European J. Oper. Res., 173 (2006), 268-282.  doi: 10.1016/j.ejor.2004.12.004.

[33]

M. Lai, H. Yang, E. Cao, D. Qiu and J. Qiu, Optimal decisions for a dual-channel supply chain under information asymmetry, J. Ind. Manag. Optim., 14 (2018), 1023-1040.  doi: 10.3934/jimo.2017088.

[34]

G. Li, J. Shao, D. Xu and W. Xu, The warehouse-retailer network design game, J. Ind. Manag. Optim., 11 (2015), 291-305.  doi: 10.3934/jimo.2015.11.291.

[35]

S. Li, M. Lai and W. Xue, Bundling strategy and channel competition in supply chains with complementary products, Procedia Computer Science, 126 (2018), 1730-1739.  doi: 10.1016/j.procs.2018.08.104.

[36]

H. Liu, X. Luo, W. Bi, Y. Man and K. L. Teo, Dynamic pricing of network goods in duopoly markets with boundedly rational consumers, J. Ind. Manag. Optim., 13 (2017), 427-445.  doi: 10.3934/jimo.2016025.

[37]

Y. Liu, S. Gupta and Z. J. Zhang, Note on self-restraint as an online entry-deterrence strategy, Management Science, 52 (2006), 1799-1809.  doi: 10.1287/mnsc.1050.0566.

[38]

X. Luo, M. Li, H. Feng and N. Feng, Intertemporal mixed bundling strategy of information products with network externality, Comput. Industrial Engineering, 113 (2017), 369-381.  doi: 10.1016/j.cie.2017.09.019.

[39]

K. F. McCardle, K. Rajaram and C. S. Tang, Bundling retail products: Models and analysis, European J. Oper. Res., 177 (2007), 1197-1217.  doi: 10.1016/j.ejor.2005.11.009.

[40]

E. Ofek, Z. Katona and M. Sarvary, "Bricks and clicks": The impact of product returns on the strategies of multichannel retailers, Marketing Science, 30 (2011), 42-60.  doi: 10.1287/mksc.1100.0588.

[41]

G. G. Parker and M. W. Van Alstyne, Two-sided network effects: A theory of information product design, Management Science, 51 (2005), 1494-1504.  doi: 10.1287/mnsc.1050.0400.

[42]

A. Prasad, R. Venkatesh and V. Mahajan, Optimal bundling of technological products with network externality, Management Science, 56 (2010), 2224-2236.  doi: 10.1287/mnsc.1100.1259.

[43]

S. Stremersch and G. J. Tellism, Strategic bundling of products and prices: A new synthesis for marketing, J. Marketing, 66 (2002), 55-72. doi: 10.1509/jmkg.66.1.55.18455.

[44]

S. Stremersch, G. J. Tellis, P. H. Franses and J. L. G. Binken, Indirect network effects in new product growth, J. Marketing, 71 (2007), 52-74. doi: 10.1509/jmkg.71.3.052.

[45]

B. Sun, J. Xie and H. H. Cao, Product strategy for innovators in markets with network effects, Marketing Science, 23 (2004), 243-254.  doi: 10.1287/mksc.1040.0058.

[46]

H. Sun, Y. Wan, Y. Li, L. Zhang and Z. Zhou, Competition in a dual-channel supply chain considering duopolistic retailers with different behaviours, J. Ind. Manag. Optim., (2019). doi: 10.3934/jimo.2019125.

[47]

A. A. Taleizade, L. E. Cárdenas-Barrón and R. Sohani, Coordinating the supplier-retailer supply chain under noise effect with bundling and inventory strategies, J. Ind. Manag. Optim., 15 (2019), 1701-1727.  doi: 10.3934/jimo.2018118.

[48]

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

[49]

S. Viswanathan, Competing across technology-differentiated channels: The impact of network externalities and switching costs, Management Science, 51 (2005), 483-496.  doi: 10.1287/mnsc.1040.0338.

[50]

S. Wu, L. M. Hitt, P. Chen and G. Anandalingam, Customized bundle pricing for information goods: A nonlinear mixed-integer programming approach, Management Science, 54 (2008), 608-622.  doi: 10.1287/mnsc.1070.0812.

[51]

L. Xie, J. Ma and H. Han, Implications of stochastic demand and manufacturers' operational mode on retailer's mixed bundling strategy and its complexity analysis, Appl. Math. Model., 55 (2018), 484-501.  doi: 10.1016/j.apm.2017.06.005.

[52]

Y. Xiong, W. Yan, K. Fernandes, Z.-K. Xiong and N. Guo, "Bricks vs. clicks": The impact of manufacturer encroachment with a dealer leasing and selling of durable goods, European J. Oper. Res., 217 (2012), 75-83.  doi: 10.1016/j.ejor.2011.08.012.

[53]

L. Yang, J. Ji and K. Chen, Advertising games on national brand and store brand in a dual-channel supply chain, J. Ind. Manag. Optim., 14 (2018), 105-134.  doi: 10.3934/jimo.2017039.

[54]

D. Q. Yao and J. J. Liu, Competitive pricing of mixed retail and e-tail distribution channels, Omega, 33 (2005), 235-247.  doi: 10.1016/j.omega.2004.04.007.

[55]

Y. Yi and H. Yang, Wholesale pricing and evolutionary stable strategies of retailers under network externality, European J. Oper. Res., 259 (2017), 37-47.  doi: 10.1016/j.ejor.2016.09.014.

[56]

X. Zhang, Retailers' multichannel and price advertising strategies, Marketing Science, 28 (2009), 1080–1094. doi: 10.1287/mksc.1090.0499.

[57]

Z. Zhang, X. Luo, C. K. Kwong, J. Tang and Y. Yu, Impacts of service uncertainty in bundling strategies on heterogeneous consumers, Electronic Commerce Res. Appl., 28 (2018), 230-243.  doi: 10.1016/j.elerap.2018.02.003.

Figure 1.  The Decision Zone for the Pure Component Strategy
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Figure 2.  The Decision Zone for the Pure Bundling Strategy
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Figure 3.  The Decision Zone for Different Cases with Different Network Externalities
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Figure 4.  Effects of Network Externality and Consumers' Perceived Value on the Manufacturer's Profits
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Figure 5.  Effects of the Related Costs on the Manufacturer's Profits
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Figure 6.  The Effects of Transport Cost on Profits for the Manufacturer and Dealer
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Figure 7.  The Effects of the Wholesale Price and Network Externality on the Profits
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Figure 8.  The Effects of the Related Cost Factors on the Profit for the Manufacturer
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Figure 9.  The Effects of the Inconvenience Cost on the Profits for Manufacturer and Dealer
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Figure 10.  The Effects of the Inconvenience Cost on the Profits in the Four Cases
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Figure 11.  The Effects of the Network Externality on the Profits in the Four Cases
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Table 1.  The Bricks-and-Clicks Operation
The Online Channel
Pure component Pure Bundling
The Physical Channel Pure component Ⅰ Ⅲ
Pure Bundling Ⅳ Ⅱ
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The Online Channel
Pure component Pure Bundling
The Physical Channel Pure component Ⅰ Ⅲ
Pure Bundling Ⅳ Ⅱ
Table 2.  Parameter Settings
Parameters Values Parameters Values
$\delta _{1} $ 0.5 $\delta _{2} $ 0.3
$v_{1} $ 34 $v_{2} $ 20
$c_{1} $ 5 $c_{2} $ 3
$w_{1} $ 20 $w_{2} $ 12
$w_{B} $ 29 $s$ 16
$t$ 20 $F$ 1,200
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Parameters Values Parameters Values
$\delta _{1} $ 0.5 $\delta _{2} $ 0.3
$v_{1} $ 34 $v_{2} $ 20
$c_{1} $ 5 $c_{2} $ 3
$w_{1} $ 20 $w_{2} $ 12
$w_{B} $ 29 $s$ 16
$t$ 20 $F$ 1,200
Table 3.  The Optimal Selling Prices and Profits for the Manufacturer and Dealer
Strategy Selling Price Profit (＄000) Total Profit (＄000)
The Physical Channel (The First Stage) Pure Component $p_{r1} =27$ $\pi _{C}^{R} {\rm =4.8789}$ 15.4472
$p_{r2} =16$ $\pi _{C}^{M} {\rm =10.5684}$
Pure Bundling $p_{rB} =41.5$ $\pi _{B}^{R} {\rm =15.1536}$ 40.6116
$\pi _{B}^{M} {\rm =25.4580}$
Bricks-and-Clicks (The Second Stage) Case Ⅰ $p_{d1} ={\rm 30.875}$ $\pi _{1}^{R} {\rm =26.1846}$ 57.5858
$p_{d2} ={\rm 23.415}$
$p_{r1} ={\rm 33.0625}$ $\pi _{1}^{M} {\rm =31.4012}$
$p_{r2} ={\rm 25.5125}$
Case Ⅱ $p_{rB} ={\rm 41.2}$ $\pi _{2}^{R} {\rm =15.6491}$ 46.5392
$p_{dB} ={\rm 38.84}$ $\pi _{2}^{M} {\rm =30.8901}$
Case Ⅲ $p_{r1} ={\rm 27.67}$ $\pi _{3}^{R} {\rm =4.9547}$ 36.2380
$p_{dB} ={\rm 40.78}$ $\pi _{3}^{M} {\rm =31.2833}$
Case Ⅳ $p_{rB} ={\rm 47.0175}$ $\pi _{4}^{R} {\rm =32.8094}$ 58.6167
$p_{d1} ={\rm 29.785}$ $\pi _{4}^{M} {\rm =25.8073}$
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Strategy Selling Price Profit (＄000) Total Profit (＄000)
The Physical Channel (The First Stage) Pure Component $p_{r1} =27$ $\pi _{C}^{R} {\rm =4.8789}$ 15.4472
$p_{r2} =16$ $\pi _{C}^{M} {\rm =10.5684}$
Pure Bundling $p_{rB} =41.5$ $\pi _{B}^{R} {\rm =15.1536}$ 40.6116
$\pi _{B}^{M} {\rm =25.4580}$
Bricks-and-Clicks (The Second Stage) Case Ⅰ $p_{d1} ={\rm 30.875}$ $\pi _{1}^{R} {\rm =26.1846}$ 57.5858
$p_{d2} ={\rm 23.415}$
$p_{r1} ={\rm 33.0625}$ $\pi _{1}^{M} {\rm =31.4012}$
$p_{r2} ={\rm 25.5125}$
Case Ⅱ $p_{rB} ={\rm 41.2}$ $\pi _{2}^{R} {\rm =15.6491}$ 46.5392
$p_{dB} ={\rm 38.84}$ $\pi _{2}^{M} {\rm =30.8901}$
Case Ⅲ $p_{r1} ={\rm 27.67}$ $\pi _{3}^{R} {\rm =4.9547}$ 36.2380
$p_{dB} ={\rm 40.78}$ $\pi _{3}^{M} {\rm =31.2833}$
Case Ⅳ $p_{rB} ={\rm 47.0175}$ $\pi _{4}^{R} {\rm =32.8094}$ 58.6167
$p_{d1} ={\rm 29.785}$ $\pi _{4}^{M} {\rm =25.8073}$
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