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Strategic service investment by retailers confronted by manufacturer encroachment

  • *Corresponding author: Junwu Chai

    *Corresponding author: Junwu Chai

The authors thank the National Natural Science Foundation of China (71872028) and the Digital Culture and Media Research Fund of Philosophy and Social Sciences Research Base in Sichuan Province (19CDCM03)

Abstract Full Text(HTML) Figure(11) / Table(13) Related Papers Cited by
  • This study investigates the service strategies of retailers confronted by manufacturer encroachment and explores the influences of retail services on profitability under different channel structures. In contrast to previous studies, this paper differentiates between channel costs and considers retail service. First, it is demonstrated that retail services are profitable for supply chain members under certain circumstances, regardless of whether the retail service effort is endogenous or exogenous. In particular, when the service effort is endogenous, the retailer can optimize its service effort to influence sales and profit outcomes. Second, this study finds that a service strategy can cause harm to manufacturers while benefiting retailers, which can help retailers regain market dominance and make manufacturers less competitive. The findings also suggest that there can be a "lose-lose" outcome due to service inefficiencies and intense competition. Third, the results indicate that a retailer would prefer to improve their service effort if market competition is less intense or the retail channel has obvious cost advantages. As the service effort increases, a manufacturer has little incentive to encroach on the market. Finally, consumer surplus and service spillovers are discussed.

    Mathematics Subject Classification: Primary: 91A10, 91B42; Secondary: 90B50, 91A35.

    Citation:

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  • Figure 1.  The supply chain structure

    Figure 2.  The game theory flowchart

    Figure 3.  Impact of encroachment without service ($ d = 0.5 $)

    Figure 4.  Impact of encroachment with retail services ($ d = 0.5 $ $ s = 1 $ $ n = 1 $)

    Figure 5.  The retailer's service strategy ($ d = 0.8 $ $ n = 1 $ $ c = 0.4 $)

    Figure 6.  The impact of service on the manufacturer encroachment threshold ($ n = 1 $)

    Figure 7.  Regions with the introduction of service ($ d = 0.8 $ $ n = 1 $ $ c = 0.4 $)

    Figure 8.  Optimal service effort under different channel structure with variations in $ k $, $ d $, $ c $, $ n $

    Figure 9.  The impact of endogenous service on retailer and total supply chain. ($ d = 0.8 $ $ n = 2 $)

    Figure 10.  The impact of exogenous service on retailer and total supply chain. ($ b = 0.8 $ $ n = 1 $ $ c = 0.4 $)

    Figure 11.  The impact of endogenous service on retailer and total supply chain. ($ b = 0.8 $ $ n = 2 $)

    Table 1.  Recently published works

    Literature Channel preference Retail cost Service cost Direct cost Situations Research issues
    Chen et al. [32] No Yes No Yes Market share, pricing strategy Impact of power structure
    Pei et al. [42] Yes No Yes No Product compatibility Impact of service
    Xia et al. [43] Yes No Yes Yes Dominant power structure Impact of encroachment
    Zhang et al. [13] Yes No Yes Yes Effect of information Impact of service
    Cao et al. [44] No No Yes Yes Different decision sequences Encroachment and service
    Wang et al. [39] No No No Yes Consumer surplus and profit Dual-purpose retailer on encroachment
    Guo et al. [36] Yes No Yes No Degree of free riding Impact of free riding
    Zhao et al. [31] Yes Yes Yes No Cost-sharing proportion resource-utilization and service impact
    This study Yes Yes Yes Yes Extra channel and service cost Endogenous and exogenous service strategy
     | Show Table
    DownLoad: CSV

    Table 2.  Description of notations

    Indices Description
    $ m, r $ Subscript, represents the manufacturer and the retailer.
    $ i $ Superscript, represents Model N, S, E respectively.
    Parameters
    $ k $ Unit marginal cost to open the direct channel.
    $ c $ Unit marginal cost to off-line retailing activity.
    $ d $ The degree of consumer acceptance of direct channel.
    $ n $ The cost-effectiveness of the retail service.
    $ v $ The consumer utility on product.
    $ U_m/U_r $ The consumer's willingness-to-pay through direct/retail channel.
    Independent Variables
    $ q_m^i /q_r^i $ Sales volume via the direct/tradition channel in Model $ i $.
    $ s $ The service effort offered by the retailer.
    $ w^i $ Manufacturer's unit wholesale price in Model $ i $.
    Dependent Variables
    $ p_m^i /p_r^i $ Unit market price from the direct/tradition channel in Model $ i $.
    $ \pi _m^i /\pi _r^i $ Profit for the manufacturer/retailer in Model $ i $.
     | Show Table
    DownLoad: CSV

    Table 3.  Equilibrium outcomes under no services

    Strategy N
    Direct channel
    (NM) $k < k_m$
    Dual channel
    (ND) $k_m < k < k_r$
    Retail channel
    (NR) $k>k_r$
    $ N/A $ $ w^{ND} = \frac{{8c + 4d - 4cd + dk - d^2 - 8}}{{6d - 16}} $ $ w^{NR} = \frac{1}{2} - \frac{c}{2} $
    $ N/A $ $ q_r^{ND} = \frac{{2c + 2d - 2k - 2}}{{3d - 8}} $ $ q_r^{NR} = \frac{1}{4} - \frac{c}{4} $
    $ q_m^{NM} = \frac{{d - k}}{{2d}} $ $ q_m^{ND} = \frac{{ - (6d - 8k + 2cd + dk - d^2 )}}{{2d(3d - 8)}} $ $ N/A $
    $ \pi _m^{NM} = \frac{{(d - k)^2 }}{{4d}} $ $ \pi _m^{ND} = \frac{{4c^2 d + 8cd^2 - 8cdk - 8cd + d^3 - 2d^2 k + dk^2 - 8dk + 4d + 8k^2 }}{{ - 4d(3d - 8)}} $ $ \pi _m^{NR} = \frac{{(c - 1)^2 }}{8} $
    $ N/A $ $ \pi _r^{ND} = \frac{{4(c + d - k - 1)^2 }}{{(3d - 8)^2 }} $ $ \pi _r^{NR} = \frac{{(c - 1)^2 }}{{16}} $
     | Show Table
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    Table 4.  Equilibrium outcomes under retail services

    Strategy S
    Direct channel
    (NM) $k < k_m$
    Dual channel
    (ND) $k_m < k < k_r$
    Retail channel
    (NR) $k>k_r$
    $ N/A $ $ w^{SD} = \frac{{8c + 4d - 8s - 4cd + dk + 8cn + 4ds - d^2 - 4cdn - 8}}{{6d - 16}} $ $ w^{SR} = \frac{{1 + s}}{2} - \frac{{c(n + 1)}}{2} $
    $ N/A $ $ q_r^{SD} = \frac{{2c + 2d - 2k - 2s + 2cn - 2}}{{3d - 8}} $ $ q_r^{SR} = \frac{{1 - c + s - cn}}{4} $
    $ q_m^{SM} = \frac{{d - k}}{{2d}} $ $ q_m^{SD} = \frac{{2(3d - 4k + cd - ds + cdn) + dk - d^2 }}{{ - 2d(3d - 8)}} $ $ N/A $
    $ \pi _m^{SM} = \frac{{(d - k)^2 }}{{4d}} $ $ \begin{array}{l} \pi _m^{SD} =\\ \frac{{\left[ \begin{array}{l} 4c^2 dn^2 + 8c^2 dn + 4c^2 d + 8cd^2 n + 8cd^2 \;\;\;\\ - 8cdkn - 8cdk - 8cdns - 8cdn - 8cds\;\;\;\\ - 8cd + d^3 - 2d^2 k - 8d^2 s + dk^2 + 8dks\;\;\;\\ - 8dk + 4ds^2 + 8ds + 4d + 8k^2\\ \end{array} \right]}}{{ - 4d(3d - 8)}}\\ \end{array} $ $ \pi _m^{SR} = \frac{{(c - s + cn - 1)^2 }}{8} $
    $ N/A $ $ \pi _r^{SD} = \frac{{4(c + d - k - s + cn - 1)^2 }}{{(3d - 8)^2 }} $ $ \pi _r^{SR} = \frac{{(c - s + cn - 1)^2 }}{{16}} $
     | Show Table
    DownLoad: CSV

    Table 5.  The retailer's service strategy

    Strategy Service effectiveness Direct selling cost Region
    No service $ 0<s<s_1 $ $ k_m(s)<k<k_{rs}(s) $ N
    Services $ 0<s $ $ \max \{ 0, k_{ms} (s), k_{rs} (s)\}< k $ S
    No retailer (direct channel) $ 0<s $ $ 0< k< \min \{ k_m (s), k_{ms} (s)\} $ M
     | Show Table
    DownLoad: CSV

    Table 6.  Impact of service on the retailer and manufacturer

    Service effort Direct selling cost $ (\Delta \pi _r /\Delta \pi _m) $ Region
    $ 0<s<s_1 $ $ k_m(s)<k<k_5(s) $ (-, -)(lose, lose) ND
    $ 0<s<s_1 $ $ k_5(s)<k<k_r(s) $ (-, -)(lose, lose) NR
    $ 0<s<s_1 $ $ k_r(s)<k<k_{rs}(s) $ (-, +)(lose, win) ND
    $ s>s_1 $ $ \max \{ 0, k_{ms} (s)\}<k<k_{rs}(s) $ (+, +)(win, win) SD
    $ s>0 $ $ k>k_{rs}(s) $ (+, +)(win, win) SR
    $ 0<s<s_1 $ $ 0< k< \min \{ k_m (s), k_{ms} (s)\} $ N/A M
     | Show Table
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    Table 7.  Equilibrium outcomes when service effort is endogenous

    Strategy E
    Direct channel
    (NM) $k < k_m$
    Dual channel
    (ND) $k_m < k < k_r$
    Retail channel
    (NR) $k>k_r$
    $ N/A $ $ w^{ED} = \frac{{8c + 4d - 8s - 4cd + dk + 8cn + 4ds - d^2 - 4cdn - 8}}{{6d - 16}} $ $ w^{ER} = \frac{{4n(c + cn - 1)}}{{1 - 8n}} $
    $ N/A $ $ s_d^{ED} = \frac{{8 - 8c - 8d + 8k - 8cn}}{{9nd^2 - 48nd + 64n - 8}} $ $ s_r^{ER} = \frac{{c + cn - 1}}{{1 - 8n}} $
    $ N/A $ $ q_r^{ED} = \frac{{2n(3d - 8)(c + d - k + cn - 1)}}{{9nd^2 - 48nd + 64n - 8}} $ $ q_r^{ER} = \frac{{2n(c + cn - 1)}}{{1 - 8n}} $
    $ q_m^{EM} = \frac{{d - k}}{{2d}} $ $ q_m^{ED} = \frac{{\left[ \begin{array}{l} 8d - 8k - 48dn + 64kn + 26d^2 n \\ - 3d^3 n + 6cd^2 n^2 - 16cdn - 32dkn \;\; \\ - 16cdn^2 + 6cd^2 n + 3d^2 kn \\ \end{array} \right]}}{{ - 2d(9nd^2 - 48nd + 64n - 8)}} $ $ N/A $
    $ \pi _m^{EM} = \frac{{(d - k)^2 }}{{4d}} $ $ \pi _m^{ED} = $ shown in appendix proof $ \pi _m^{ER} = \frac{{8n^2 (c + cn - 1)^2 }}{{(8n - 1)^2 }} $
    $ N/A $ $ \pi _r^{ED} = \frac{{4n(c + d - k + cn - 1)^2 }}{{9nd^2 - 48nd + 64n - 8}} $ $ \pi _r^{ER} = \frac{{n(c + cn - 1)^2 }}{{2(8n - 1)}} $
     | Show Table
    DownLoad: CSV

    Table A1.  results of comparison when $ c<c_1 $

    Comparison of retailer's profit Comparison of manufacturer's profit
    $ k<k_m $ $ N/A(only direct channel) $ $ N/A(only direct channel) $
    $ k_m<k<k_{me} $ $ \pi _r^{EM} - \pi _r^{ND}< 0 $ $ \pi _m^{EM} - \pi _m^{ND}< 0 $
    $ k_{me}<k<k_{re} $ $ \pi _r^{ED} - \pi _r^{ND}> 0 $ $ \pi _m^{ED} - \pi _m^{ND}> 0 $
    $ k_{re}<k<k_{r} $ $ \pi _r^{ER} - \pi _r^{ND}< 0 $ $ \pi _m^{ER} - \pi _m^{ND}> 0 $
    $ k>k_{r} $ if $c <c_3$, $\pi _r^{ER} - \pi _r^{NR} > 0$
    if $c>c_3$, $\pi _r^{ER} - \pi _r^{NR} < 0$
    $ \pi _m^{ER} - \pi _m^{NR}< 0 $
     | Show Table
    DownLoad: CSV

    Table A2.  results of comparison when $ c_1<c<c_2 $

    Comparison of retailer's profit Comparison of manufacturer's profit
    $ k<k_m $ $ N/A(only direct channel) $ $ N/A(only direct channel) $
    $ k_m<k<k_{me} $ $ \pi _r^{EM} - \pi _r^{ND}< 0 $ $ \pi _m^{EM} - \pi _m^{ND}< 0 $
    $ k_{me}<k<k_{r} $ $ \pi _r^{ED} - \pi _r^{ND}< 0 $ $ \pi _m^{ED} - \pi _m^{ND}< 0 $
    $ k_{r}<k<k_{re} $ if $k <k_6$, $\pi _r^{ED} - \pi _r^{NR} <0$
    if $k>k_6$, $\pi _r^{ED} - \pi _r^{NR} > 0$
    $ \pi _m^{ED} - \pi _m^{NR}> 0 $
    $ k>k_{re} $ $ \pi _r^{ER} - \pi _r^{NR}< 0 $ $ \pi _m^{ER} - \pi _m^{NR}< 0 $
     | Show Table
    DownLoad: CSV

    Table A3.  results of comparison when $ c>c_2 $

    Comparison of retailer's profit Comparison of manufacturer's profit
    $ k<k_m $ $ N/A(only direct channel) $ $ N/A(only direct channel) $
    $ k_m<k<k_{r} $ $ \pi _r^{EM} - \pi _r^{ND}< 0 $ $ \pi _m^{EM} - \pi _m^{ND}< 0 $
    $ k_{r}<k<k_{me} $ $ \pi _r^{EM} - \pi _r^{NR}< 0 $ $ \pi _m^{EM} - \pi _m^{NR}< 0 $
    $ k_{me}<k<k_{re} $ $ \pi _r^{ED} - \pi _r^{NR}< 0 $ $ \pi _m^{ED} - \pi _m^{NR}< 0 $
    $ k>k_{re} $ $ \pi _r^{ER} - \pi _r^{NR}< 0 $ $ \pi _m^{ER} - \pi _m^{NR}< 0 $
     | Show Table
    DownLoad: CSV

    Table A4.  Equilibrium outcomes when no service effort

    Strategy N
    Direct channel
    (NM) $k<\frac{{c-1+b}}{{b}}$
    Dual channel
    (ND) $\frac{{c-1+b}}{{b}}<k <\frac{{2b-8-2cb+b^2}}{{b^2-8}}$
    Retail channel
    (NR) $k>\frac{{2b-8-2cb+b^2}}{{b^2-8}}$
    $ N/A $ $ w^{ND} = \frac{{ - 8 + 8c + 4b^2 - 4cb^2 - b^3 + b^3 k}}{{2( - 8 + 3b^2 )}} $ $ w^{NR} = \frac{{1-c}}{{2}} $
    $ N/A $ $ q_r^{ND} = \frac{{2n(3b - 8)(c + b - k + cn - 1)}}{{9nb^2 - 48nb + 64n - 8}} $ $ q_r^{NR} = \frac{{1-c}}{{4}} $
    $ q_m^{NM} = \frac{{1 - k}}{{2}} $ $ q_m^{ND} = \frac{{8 - 2b + 2cb - b^2 - 8k + b^2 k}}{{2(8 - 3b^2 )}} $ $ N/A $
    $ \pi _m^{NM} = \frac{{(k - 1)^2 }}{{4}} $ $ \pi _m^{ND} = \frac{{\left[ \begin{array}{l} 12 - 8c + 4c^2 - 8b + 8cd + b^2 - 16k \;\;\\ + 8bk - 8cbk - 2b^2 k + 8k^2 + b^2 k^2 \;\;\end{array} \right]}}{{4(8 - 3b^2 )}} $ $ \pi _m^{NR} = \frac{{(c - 1)^2 }}{{8}} $
    $ N/A $ $ \pi _r^{ND} = \frac{{4(1 - c - b + bk)^2 }}{{( - 8 + 3b^2 )^2 }} $ $ \pi _r^{NR} = \frac{{(c - 1)^2}}{{16}} $
     | Show Table
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    Table A5.  Equilibrium outcomes when service effort is exogenous

    Strategy S
    Direct channel
    (SM) $k<k_1^S$
    Dual channel
    (SD) $k_1^S <k<k_2^S$
    Retail channel
    (SR) $k>k_2^S$
    $ N/A $ $ w^{SD} = \frac{{ - 8 + 8c + 4b^2 - 4cb^2 - b^3 + b^3 k + 8cn - 4cb^2 n - 8s + 4b^2 s}}{{2(3b^2 - 8)}} $ $ w^{SR} = \frac{{1-c-cn+s}}{{2}} $
    $ N/A $ $ q_r^{SD} = \frac{{2(1 - c - b + bk - cn + s)}}{{8 - 3b^2 }} $ $ q_r^{SR} = \frac{{1-c-cn+s}}{{4}} $
    $ q_m^{SM} = \frac{{1 - k}}{{2}} $ $ q_m^{SD} = \frac{{8 - 2b + 2cb - b^2 - 8k + b^2 k + 2cbn - 2bs}}{{2(8 - 3b^2 )}} $ $ N/A $
    $ \pi _m^{SM} = \frac{{(k - 1)^2 }}{{4}} $ $ \pi _m^{SD} = \frac{{\left[ \begin{array}{l} 12 - 8c + 4c^2 - 8b + 8cb + b^2 - 16k \\ + 8bk - 8cbk - 2b^2 k + 8k^2 + b^2 k^2 - \\ 8cn + 8c^2 n + 8cbn - 8cbkn + 4c^2 n^2 + \;\;\\ 8s - 8cs - 8bs + 8bks - 8cns + 4s^2 \end{array} \right]}}{{4(3b^2 - 8)}} $ $ \pi _m^{SR} = \frac{{(c + cn - s - 1)^2 }}{{8}} $
    $ N/A $ $ \pi _r^{SD} = \frac{{4(1 - c - b + bk - cn +s)^2 }}{{( - 8 + 3b^2 )^2 }} $ $ \pi _r^{SR} = \frac{{(c + cn - s - 1)^2}}{{16}} $
     | Show Table
    DownLoad: CSV

    Table A6.  Equilibrium outcomes when service effort is endogenous

    Strategy E
    Direct channel
    (EM) $k <k_1^E$
    Dual channel
    (ED) $k_1^E<k<k_2^E$
    Retail channel
    (ER) $k>k_2^E$
    $ N/A $ $ w^{ED} = $ shown in below $ w^{ER} = \frac{{1-c-cn+s}}{{2}} $
    $ N/A $ $ q_r^{ED} = \frac{{2n(3b^2 - 8)(c + b - bk + cn - 1)}}{{9nb^4 - 48nb^2 + 64n - 8}} $ $ q_r^{ER} = \frac{{1-c-cn+s}}{{4}} $
    $ q_m^{EM} = \frac{{1 - k}}{{2}} $ $ q_m^{ED} = $ shown in below $ N/A $
    $ \pi _m^{EM} = \frac{{(k - 1)^2 }}{{4}} $ $ \pi _m^{ED} = $ shown in below $ \pi _m^{ER} = \frac{{(c + cn - s - 1)^2 }}{{8}} $
    $ N/A $ $ \pi _r^{ED} = \frac{{4n(c + b - bk + cn -1)^2 }}{{(9nb^4 - 48nb^2 + 64n - 8)}} $ $ \pi _r^{ER} = \frac{{(c + cn - s - 1)^2}}{{16}} $
     | Show Table
    DownLoad: CSV
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