# American Institute of Mathematical Sciences

July  2021, 17(4): 1593-1612. doi: 10.3934/jimo.2020036

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

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

* Corresponding author: Feng Wei

Received  June 2019 Revised  September 2019 Published  February 2020

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

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.

Citation: 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
##### References:

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##### References:
Different sales strategies
Game order dominated by supplier in independent sales
Game order dominated by the e-retailer in independent sales
Effect of $\beta$ in a supplier-dominated market
Effect of $\beta$ in an e-retailer-dominated market
Effect of $\gamma$ in a supplier-dominated market
Effect of $\gamma$ in an e-retailer-dominated market
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
 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
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
 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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