# American Institute of Mathematical Sciences

doi: 10.3934/jimo.2020081

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

 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.

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:

show all references

##### References:
The Decision Zone for the Pure Component Strategy
The Decision Zone for the Pure Bundling Strategy
The Decision Zone for Different Cases with Different Network Externalities
Effects of Network Externality and Consumers' Perceived Value on the Manufacturer's Profits
Effects of the Related Costs on the Manufacturer's Profits
The Effects of Transport Cost on Profits for the Manufacturer and Dealer
The Effects of the Wholesale Price and Network Externality on the Profits
The Effects of the Related Cost Factors on the Profit for the Manufacturer
The Effects of the Inconvenience Cost on the Profits for Manufacturer and Dealer
The Effects of the Inconvenience Cost on the Profits in the Four Cases
The Effects of the Network Externality on the Profits in the Four Cases
The Bricks-and-Clicks Operation
 The Online Channel Pure component Pure Bundling The Physical Channel Pure component Ⅰ Ⅲ Pure Bundling Ⅳ Ⅱ
 The Online Channel Pure component Pure Bundling The Physical Channel Pure component Ⅰ Ⅲ Pure Bundling Ⅳ Ⅱ
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
 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
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 $p_{d1} ={\rm 29.785}$ $\pi _{4}^{M} {\rm =25.8073}$
 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 $p_{d1} ={\rm 29.785}$ $\pi _{4}^{M} {\rm =25.8073}$
 [1] 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, 2021  doi: 10.3934/jimo.2021056 [2] Feng Wei, Hong Chen. Independent sales or bundling? Decisions under different market-dominant powers. Journal of Industrial & Management Optimization, 2021, 17 (4) : 1593-1612. doi: 10.3934/jimo.2020036 [3] Roberto Civino, Riccardo Longo. Formal security proof for a scheme on a topological network. Advances in Mathematics of Communications, 2021  doi: 10.3934/amc.2021009 [4] Mikhail Dokuchaev, Guanglu Zhou, Song Wang. A modification of Galerkin's method for option pricing. Journal of Industrial & Management Optimization, 2021  doi: 10.3934/jimo.2021077 [5] Joe Gildea, Adrian Korban, Abidin Kaya, Bahattin Yildiz. Constructing self-dual codes from group rings and reverse circulant matrices. Advances in Mathematics of Communications, 2021, 15 (3) : 471-485. doi: 10.3934/amc.2020077 [6] Qing Liu, Bingo Wing-Kuen Ling, Qingyun Dai, Qing Miao, Caixia Liu. Optimal maximally decimated M-channel mirrored paraunitary linear phase FIR filter bank design via norm relaxed sequential quadratic programming. Journal of Industrial & Management Optimization, 2021, 17 (4) : 1993-2011. doi: 10.3934/jimo.2020055 [7] Rui Hu, Yuan Yuan. Stability, bifurcation analysis in a neural network model with delay and diffusion. Conference Publications, 2009, 2009 (Special) : 367-376. doi: 10.3934/proc.2009.2009.367 [8] Jingni Guo, Junxiang Xu, Zhenggang He, Wei Liao. Research on cascading failure modes and attack strategies of multimodal transport network. Journal of Industrial & Management Optimization, 2021  doi: 10.3934/jimo.2020159 [9] Andrey Kovtanyuk, Alexander Chebotarev, Nikolai Botkin, Varvara Turova, Irina Sidorenko, Renée Lampe. Modeling the pressure distribution in a spatially averaged cerebral capillary network. Mathematical Control & Related Fields, 2021  doi: 10.3934/mcrf.2021016 [10] Kai Li, Tao Zhou, Bohai Liu. Pricing new and remanufactured products based on customer purchasing behavior. Journal of Industrial & Management Optimization, 2021  doi: 10.3934/jimo.2021043 [11] Cheng-Kai Hu, Fung-Bao Liu, Hong-Ming Chen, Cheng-Feng Hu. Network data envelopment analysis with fuzzy non-discretionary factors. Journal of Industrial & Management Optimization, 2021, 17 (4) : 1795-1807. doi: 10.3934/jimo.2020046 [12] Benrong Zheng, Xianpei Hong. Effects of take-back legislation on pricing and coordination in a closed-loop supply chain. Journal of Industrial & Management Optimization, 2021  doi: 10.3934/jimo.2021035 [13] Reza Lotfi, Yahia Zare Mehrjerdi, Mir Saman Pishvaee, Ahmad Sadeghieh, Gerhard-Wilhelm Weber. A robust optimization model for sustainable and resilient closed-loop supply chain network design considering conditional value at risk. Numerical Algebra, Control & Optimization, 2021, 11 (2) : 221-253. doi: 10.3934/naco.2020023 [14] Saeed Assani, Muhammad Salman Mansoor, Faisal Asghar, Yongjun Li, Feng Yang. Efficiency, RTS, and marginal returns from salary on the performance of the NBA players: A parallel DEA network with shared inputs. Journal of Industrial & Management Optimization, 2021  doi: 10.3934/jimo.2021053 [15] Haodong Chen, Hongchun Sun, Yiju Wang. A complementarity model and algorithm for direct multi-commodity flow supply chain network equilibrium problem. Journal of Industrial & Management Optimization, 2021, 17 (4) : 2217-2242. doi: 10.3934/jimo.2020066 [16] Ru Li, Guolin Yu. Strict efficiency of a multi-product supply-demand network equilibrium model. Journal of Industrial & Management Optimization, 2021, 17 (4) : 2203-2215. doi: 10.3934/jimo.2020065 [17] Wan-Hua He, Chufang Wu, Jia-Wen Gu, Wai-Ki Ching, Chi-Wing Wong. Pricing vulnerable options under a jump-diffusion model with fast mean-reverting stochastic volatility. Journal of Industrial & Management Optimization, 2021  doi: 10.3934/jimo.2021057 [18] Guiyang Zhu. Optimal pricing and ordering policy for defective items under temporary price reduction with inspection errors and price sensitive demand. Journal of Industrial & Management Optimization, 2021  doi: 10.3934/jimo.2021060 [19] Xue Qiao, Zheng Wang, Haoxun Chen. Joint optimal pricing and inventory management policy and its sensitivity analysis for perishable products: Lost sale case. Journal of Industrial & Management Optimization, 2021  doi: 10.3934/jimo.2021079 [20] Patrick Beißner, Emanuela Rosazza Gianin. The term structure of sharpe ratios and arbitrage-free asset pricing in continuous time. Probability, Uncertainty and Quantitative Risk, 2021, 6 (1) : 23-52. doi: 10.3934/puqr.2021002

2019 Impact Factor: 1.366