Independent sales or bundling? Decisions under different market-dominant powers

Feng Wei; Hong Chen

doi:10.3934/jimo.2020036

Article Contents

2021, Volume 17, Issue 4: 1593-1612. Doi: 10.3934/jimo.2020036

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Independent sales or bundling? Decisions under different market-dominant powers

Feng Wei^, and
Hong Chen

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

^* Corresponding author: Feng Wei
^* Corresponding author: Feng Wei

Received: June 2019

Revised: September 2019

Early access: February 2020

Published: July 2021

This research is supported by the National Natural Science Foundation of China(71472026)

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Abstract

Enterprises are aware that bundling strategies can improve profitability in the highly competitive marketplace. This study evaluates an online to offline (O2O) supply chain system made up of a supplier and an e-retailer who can sell two products independently or bundled through online and offline channels, and discuss the influence of pricing strategy and channel choice on profit under different market-dominant powers. Based on a game theory model, we derive an optimal wholesale price for the supplier, an optimal sale price for the e-retailer, and their respective profit. We demonstrate that a Stackelberg leader is more profitable, irrespective of whether independent sales or bundling are chosen. Regardless of who the leader is, the whole supply chain receive equal profit. For a market leader, independent sales or bundling decisions should be made according to market size. Sensitivity analysis show that as the self-price sensitivity coefficient increases, the profit monotonically decreases for both independent sales and bundling; this occur for both the market dominated by the supplier and that dominated by the e-retailer. For independent sales, as the cross-price sensitivity coefficient increases, the profit monotonically increases; for bundled sales, the profit of the game players is not affected.

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Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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Figure 1. Different sales strategies

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Figure 2. Game order dominated by supplier in independent sales

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Figure 3. Game order dominated by the e-retailer in independent sales

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Figure 4. Effect of $ \beta $ in a supplier-dominated market

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Figure 5. Effect of $ \beta $ in an e-retailer-dominated market

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Figure 6. Effect of $ \gamma $ in a supplier-dominated market

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Figure 7. Effect of $ \gamma $ in an e-retailer-dominated market

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Table 1. Recently published works on bundling

Literature	Selling price	Strategy	Situation
Gurler et al. [7]	Independent and bundled sales price	Bundle pricing and inventory levels	Inventory constraints and stochastic model
Prasad et al. [9]	Mixed bundling	Different bundling and network externality	Technological products and network externality
Sheikhzadeh et al. [17]	Bundled sales price	Pure bundling and independent policy	Product heterogeneity and risk considerations
Jiang et al. [19]	Online pricing with bundling	Online pricing strategy Coupon discounts	Customer’s purchase preference and coupon
Prasad et al. [29]	Inter-temporal pricing	Pure components, pure bundling, and mixed bundling	Myopic and strategic consumers
This study	Independent and bundled sales price	Channel selection, Online and offline sales	E-commerce and differentmarket-dominant powers

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Table 2. Notation and explanation

Notation	Explanation
$ w_i $	The supplier's unit wholesale price, where $ i=1,2 $
$ p_1 $	Unit sale price through e-retailer's offline channel
$ p_2 $	Unit sale price through e-retailer's online channel
$ c_1 $	Unit sale cost through e-retailer's offline channel
$ c_2 $	Unit sale cost through e-retailer's online channel
$ a $	Maximum market size
$ \mu $	The proportion of offline demand
$ \beta $	The self-price sensitivity coefficient
$ \gamma $	The cross-price sensitivity coefficient
$ w_{12} $	The wholesale price of two bundled products
$ p_{12} $	The sale price of two bundled products
$ c_{12} $	The sale cost of two bundled products

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