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

  • * Corresponding author: Maryam Esmaeili

    * Corresponding author: Maryam Esmaeili 
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  • 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.

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


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  • Figure 1.  The outline of the proposed model

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

    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
    Leasing selling
    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 $
     | Show Table
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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}) $
     | Show Table
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