Strategic service investment by retailers confronted by manufacturer encroachment

Hengyu Li; Junwu Chai

doi:10.3934/jimo.2022086

Article Contents

2023, Volume 19, Issue 5: 3255-3286. Doi: 10.3934/jimo.2022086

This issue Previous Article Cooperative and noncooperative R&D in duopoly manufacturers with a common supplier Next Article Retailer's willingness to adopt blockchain technology based on private demand information

Strategic service investment by retailers confronted by manufacturer encroachment

Hengyu Li^1, and
Junwu Chai^2, ,

1.
School of Management and Economics, University of Electronic Science and Technology of China, Chengdu Sichuan 611731, China
2.
School of Management and Economics; Center for Digital Culture and Media Studies, University of Electronic Science and Technology of China, Chengdu Sichuan 611731, China

^*Corresponding author: Junwu Chai
^*Corresponding author: Junwu Chai

Received: July 2021

Revised: April 2022

Early access: June 2022

Published: May 2023

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)

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Abstract

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.

Keywords:

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

Citation:

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Figure 1. The supply chain structure

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Figure 2. The game theory flowchart

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

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

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

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

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

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

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

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

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

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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

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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 $.

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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}} $

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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}} $

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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

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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

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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)}} $

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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 $

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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 $

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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 $

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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}} $

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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}} $

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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}} $

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