American Institute of Mathematical Sciences

Advanced
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  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 & Management Optimization, doi: 10.3934/jimo.2020081
References:
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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.  Google Scholar

[2]

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

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[6]

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[8]

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[13]

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[14]

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[15]

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[16]

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[17]

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[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[31]

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

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[43]

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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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