Selling by clicks or leasing by bricks? A dynamic game for pricing durable products in a dual-channel supply chain

Solaleh Sadat Kalantari; Maryam Esmaeili; Ata Allah Taleizadeh

doi:10.3934/jimo.2021221

Article Contents

2023, Volume 19, Issue 2: 1107-1138. Doi: 10.3934/jimo.2021221

This issue Previous Article Analysis on the influence of retailer's introduction of store brand under manufacturer's product line strategy Next Article On convergence properties of the modified trust region method under Hölderian error bound condition

Selling by clicks or leasing by bricks? A dynamic game for pricing durable products in a dual-channel supply chain

1.
Department of Industrial Engineering, Faculty of Engineering, Alzahra University, Tehran, Iran
2.
School of Industrial Engineering, College of Engineering, University of Tehran, Tehran, Iran

^* Corresponding author: Maryam Esmaeili
^* Corresponding author: Maryam Esmaeili

Received: April 30, 2021

Revised: September 30, 2021

Published: February 2023

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Abstract

In this paper, we discuss if and which pricing policies by a manufacturer who sells its products online motivate a retailer as an independent part to enter the market to provide selling and leasing options through a brick store. Moreover, the impact of online shopping preferences and brand image on end-user behavior is examined, and different consumption patterns are considered. For this purpose, a dynamic game is applied to model a supply chain consisting of one manufacturer and one retailer. The model aims to specify the optimal pricing policies in the second-hand market and according to physical utility associated with depreciation, brand image, and online shopping preferences for different end-users in an infinite time horizon. Markov perfect equilibria are considered as the solution concept to predict the behavior of end-users in the long term. The results revealed that enriching brand image always benefits the manufacturer and the retailer, while it does not mean there is the same optimal brand image level for both manufacturer and retailer. Besides, the improvement of physical utility makes more demand for leasing products and motivates the retailer to be active in the market. Notably, online shopping preferences play a prominent role in market segmentation and retailer decision as a result. Also, growing production costs have a significant reverse effect on the profitability of both manufacturer and retailer. Therefore, the manufacturer must focus on economic production.

Keywords:

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

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Figure 1. The outline of the proposed model

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Figure 2. Consumption pattern of each classification under various levels of brand image

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Figure 3. The amounts of selling and leasing prices under various levels of brand image

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Figure 4. The amounts of marginal profit for the manufacturer and retailer under various levels of brand image

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Figure 5. Consumption pattern of in each classification under various physical utilities

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Figure 6. The amounts of selling and leasing prices under various physical utilities

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Figure 7. The amounts of marginal profit for the manufacturer and the retailer under various physical utilities

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Figure 8. Consumption pattern of each classification under various production costs

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Figure 9. The amounts of selling and leasing prices under various production costs

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Figure 10. The amounts of marginal profit for the manufacturer and the retailer under various production costs

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Figure 11. Consumption pattern in each classification under various dealing costs

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Figure 12. The amounts of selling and leasing prices under various dealing costs

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Figure 13. The amounts of marginal profit for the manufacturer and retailer under various dealing costs

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Figure 14. Consumption pattern of each classification under various response levels

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Figure 15. The amounts of selling and leasing prices under various response levels

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Figure 16. The amounts of marginal profit per product for the manufacture under various response levels

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Figure 17. The amounts of marginal profit per product for the manufacturer and retailer based on various alpha

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Table 1. of dual-channel studies and transaction ways for durable products studies in the literature with the present study

The previous studies	Transaction Ways		Dynamic nature	More than one channel	Game theory approach	Second hand Market	Durable Products	Deprecia tion	Brand Image
The previous studies	Leasing	selling	Dynamic nature	More than one channel	Game theory approach	Second hand Market	Durable Products	Deprecia tion	Brand Image
Cao et al., 2018 [10]		$\star$		$\star$	$\star$
Wang et al., 2018 [43]		$\star$		$\star$	$\star$
Wang et al., 2019 [44]		$\star$		$\star$	$\star$
Lai et al., 2018 [21]		$\star$		$\star$	$\star$
Soleimani, 2016 [40]		$\star$		$\star$	$\star$
Yu et al., 2020[52]		$\star$		$\star$	$\star$
Zhu et al., 2020 [57]		$\star$		$\star$	$\star$
Sun et al., 2021 [41]		$\star$		$\star$	$\star$
Zhang and Xiao, 2013 [54]		$\star$		$\star$	$\star$
Yang et al., 2018 [49]		$\star$		$\star$	$\star$
Guo et al., 2021 [16]		$\star$		$\star$	$\star$
Hsieh et al., 2014 [19]		$\star$		$\star$	$\star$
Yoo and Lee, 2011[50]		$\star$		$\star$	$\star$
Xiong et al., 2012 [47]	$\star$	$\star$		$\star$	$\star$		$\star$
Xiao and Shi, 2016 [46]		$\star$		$\star$	$\star$
Zhao et al., 2017 [56]		$\star$		$\star$	$\star$
Chen et al., 20171 [11]		$\star$		$\star$	$\star$
Nasiri et al., 2021 [29]				$\star$	$\star$
Agarwal et al., 2011 [1]	$\star$						$\star$	$\star$
Rogers and Rodrigues, 2015 [37]	$\star$					$\star$	$\star$
Agrawal et al., 2012 [2]	$\star$	$\star$					$\star$
Andriko poulos and Markellos, 2015 [3]	$\star$	$\star$	$\star$				$\star$
Li et al., 2021 [24]	$\star$	$\star$			$\star$		$\star$
Barbulescu and Enache, 2016 [36]	$\star$						$\star$
Yan et al., 2016 [48]	$\star$	$\star$		$\star$		$\star$	$\star$	$\star$
hamidi et al., 2016 [17]	$\star$						$\star$	$\star$
This paper	$\star$	$\star$	$\star$	$\star$	$\star$	$\star$	$\star$	$\star$	$\star$

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Table 2. The payoff matrix for end-user $ \theta $ with $ N = 2 $

	$ N^{t}(\theta) $	$ S^{t}(\theta) $	$ L^{t}(\theta) $	$ W^{t}(\theta) $
$ N^{t-1}(\theta) $	$ \Delta_{1}\theta+\lambda_{1}\varphi^{t}-p_{0}^{t}+p_{1}^{t}-d_{2} $	$ \Delta_{2}\theta+\lambda_{3}\varphi^{t} $	$ \Delta_{1}\theta+\lambda_{2}\varphi^{t}-r^{t}+p_{1}^{t}-d_{2} $	$ p_{1}^{t}-d_{2} $
$ S^{t-1}(\theta) $	$ \Delta_{1}\theta+\lambda_{1}\varphi^{t}-p_{0}^{t} $	$ \Delta_{2}\theta+\lambda_{3}\varphi^{t}-p_{1}^{t} $	$ \Delta_{1}\theta+\lambda_{2}\varphi^{t}-r^{t} $	$ 0 $
$ L^{t-1}(\theta) $	$ \Delta_{1}\theta+\lambda_{1}\varphi^{t}-p_{0}^{t} $	$ \Delta_{2}\theta+\lambda_{3}\varphi^{t}-p_{1}^{t} $	$ \Delta_{1}\theta+\lambda_{2}\varphi^{t}-r^{t} $	$ 0 $
$ W^{t-1}(\theta) $	$ \Delta_{1}\theta+\lambda_{1}\varphi^{t}-p_{0}^{t} $	$ \Delta_{2}\theta+\lambda_{3}\varphi^{t}-p_{1}^{t} $	$ \Delta_{1}\theta+\lambda_{2}\varphi^{t}-r^{t} $	$ 0 $

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Table 3. End-users policy in various classification

Policy	Interval
$ LL $	$ (\theta_{1},1) $
$ NS $	$ (\theta_{2},\theta_{1}) $
$ SS $	$ (\theta_{3},\theta_{2}) $
$ WW $	$ (0,\theta_{3}) $

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