# 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:

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##### 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 $p_{d1} ={\rm 29.785}$ $\pi _{4}^{M} {\rm =25.8073}$
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