Information sharing when competing manufacturers adopt asymmetric channel in an e-tailer

Guoqiang Shi; Yong Wang; Dejian Xia; Yanfei Zhao

doi:10.3934/jimo.2021207

Article Contents

2023, Volume 19, Issue 2: 792-822. Doi: 10.3934/jimo.2021207

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Information sharing when competing manufacturers adopt asymmetric channel in an e-tailer

1.
School of Economics and Business Administration, Chongqing University, Chongqing, China
2.
School of Economics and Management, Chongqing University of Arts and Sciences, Chongqing, China

^*Corresponding author: Yong Wang
^*Corresponding author: Yong Wang

Received: September 30, 2020

Revised: June 30, 2021

Early access: December 2021

Published: February 2023

This work was supported by the National Natural Science Foundation of China (grant number 71672015)

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Abstract

This paper investigates the incentive for information sharing when competing manufacturers sell substitute products through the marketplace channel and the reseller channel respectively. Our analysis shows that the e-tailer's incentive to share information strongly depends on the platform fee, competition intensity, and different information sharing scenarios. If competition intensity is small, or competition intensity is large and the platform fee is enough large, the e-tailer has incentive to alone share information with the manufacturer who is from the marketplace channel; if competition intensity is moderate and the platform fee is small, or competition intensity is large but the platform fee is moderate, it has incentive to share information with both manufacturers; if competition intensity is large but the platform fee is small, it has no incentive to share information. The results also indicate that the double marginalization effect of information sharing is a promoting factor to share information under linear cost, which is different from previous literature. Additionally, we find that the main qualitative insights from the base model are robust even if one monopolist manufacturer employs both channels. And we also compare the incentive of information sharing under asymmetric channel with that under symmetric channel.

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Mathematics Subject Classification: Primary: 90B06, 91B44; Secondary: 90B50.

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Figure 1. Supply chain structure. Note: The dashed line indicates that the retailing quantity in the marketplace channel is decided by manufacturer 2

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Figure 2. The impacts of information sharing with only manufacturer 2 on the e-tailer

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Figure 3. The impacts of information sharing on the supply chain payoffs. (a) Comparing $ \left( N, I \right) $ with $ \left( N, N \right) $; (b) Comparing $ \left( I, I \right) $ with $ \left( N, N \right) $; (c) Comparing $ \left( I, I \right) $ with $ \left( N, I \right) $

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Figure 4. Equilibrium information sharing decisions. Note: The solid lines indicate the thresholds of Equilibrium information sharing decisions. The dashed line in $ \left( N, I \right) $ area represents the threshold in which $ \pi _{e}^{NN} = \pi _{e}^{NI} $ and the dashed line in $ \left( I, I \right) $ area represents the threshold in which $ {{V}^{NI}} = {{V}^{NN}} $

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Figure 5. Information sharing in a monopolist model. (a) Information sharing voluntarily; (b) Equilibrium information sharing decisions

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Figure A1. $ {{f}_{1}}\left( \beta , \gamma \right)>0 $ when $ \beta \in \left( 0, 1 \right) $ and $ \gamma \in \left( 0, 1 \right) $

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Figure A2. Thresholds $ \beta ^{\left( 3 \right)} $ and $ \beta ^{\left( 4 \right)} $

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Figure A3. Threshold $ \beta ^{\left( 5 \right)} $

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Figure A4. Threshold $ \beta ^{\left( 6 \right)} $

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Table 1. Operation equilibrium

$ \left( {{x}_{m1}}, {{x}_{m2}} \right) $	Equilibrium outcome	Ex-ante profit
$ \left( N, N \right) $	$ {{w}^{NN}}=A\alpha $	$ \pi _{e}^{NN}={{\bar{\pi }}_{e}}+\frac{1}{4}\delta $
	$ q_{1}^{NN}=B\alpha +\frac{1}{2}E\left[ \theta \|Y \right] $	$ \pi _{m1}^{NN}={{\bar{\pi }}_{m1}} $
	$ q_{2}^{NN}=C\alpha $	$ \pi _{m2}^{NN}={{\bar{\pi }}_{m2}} $
$ \left( I, N \right) $	$ {{w}^{IN}}=A\alpha +\frac{4-\left( 1+\beta \right){{\gamma }^{2}}}{4-\left( 2+2\beta \right)\gamma }AE\left[ \theta \|Y \right] $	$ \pi _{e}^{IN}={{\bar{\pi }}_{e}}+\frac{4-\left( {{\gamma }^{2}}-8\gamma \right)\beta }{64}\delta $
	$ q_{1}^{IN}=B\alpha +\frac{1}{4}E\left[ \theta \|Y \right] $	$ \pi _{m1}^{IN}={{\bar{\pi }}_{m1}}+\frac{4-\left( 1+\beta \right){{\gamma }^{2}}}{32}\delta $
	$ q_{2}^{IN}=C\alpha $	$ \pi _{m2}^{IN}={{\bar{\pi }}_{m2}} $
$ \left( N, I \right) $	$ {{w}^{NI}}=A\alpha $	$ \pi _{e}^{NI}={{\bar{\pi }}_{e}}+\frac{\left( \beta +{{\beta }^{2}} \right){{\gamma }^{3}}+\left( 1-{{\beta }^{2}}-\beta \right){{\gamma }^{2}}-4\left( 1+\beta \right)\gamma +4\beta +4}{{{\left[ 4-\left( 1+\beta \right){{\gamma }^{2}} \right]}^{2}}}\delta $
	$ q_{1}^{NI}=B\alpha +2BE\left[ \theta \|Y \right] $	$ \pi _{m1}^{NI}={{\bar{\pi }}_{m1}} $
	$ q_{2}^{NI}=C\alpha +\frac{\left( 8-4\gamma \right)E\left[ \theta \|Y \right]}{16-\left( 4+4\beta \right){{\gamma }^{2}}} $	$ \pi _{m2}^{NI}={{\bar{\pi }}_{m2}}+\frac{{{\left( 2-\gamma \right)}^{2}}\left( 1-\beta \right)}{{{\left[ 4-\left( 1+\beta \right){{\gamma }^{2}} \right]}^{2}}}\delta $
$ \left( I, I \right) $	$ {{w}^{II}}=A\alpha +AE\left[ \theta \|Y \right] $	$ \pi _{e}^{II}={{\bar{\pi }}_{e}}\left( 1+\frac{\delta }{{{\alpha }^{2}}} \right) $
	$ q_{1}^{II}=B\alpha +BE\left[ \theta \|Y \right] $	$ \pi _{m1}^{II}={{\bar{\pi }}_{m1}}\left( 1+\frac{\delta }{{{\alpha }^{2}}} \right) $
	$ q_{2}^{II}=C\alpha +CE\left[ \theta \|Y \right] $	$ \pi _{m2}^{II}={{\bar{\pi }}_{m2}}\left( 1+\frac{\delta }{{{\alpha }^{2}}} \right) $
Note: $A=\frac{2-\gamma -\beta \gamma }{4}$, $B=\frac{2-\left( 1+\beta \right)\gamma }{8-\left( 2+2\beta \right){{\gamma }^{2}}}$, $C=\frac{8-\left( 1+\beta \right){{\gamma }^{2}}-2\gamma }{2\left[ 8-\left( 2+2\beta \right){{\gamma }^{2}} \right]}$, ${{\bar{\pi }}_{e}}=\frac{3\beta \left( 1+{{\beta }^{2}} \right){{\gamma }^{4}}+4\beta \left( 1+\beta \right){{\gamma }^{3}}+\left( 4-28{{\beta }^{2}}-28\beta \right){{\gamma }^{2}}-16\left( 1+\beta \right)\gamma +64\beta +16}{16{{\left[ 4-\left( 1+\beta \right){{\gamma }^{2}} \right]}^{2}}}{{\alpha }^{2}}$, ${{\bar{\pi }}_{m1}}=\frac{{{\left[ 2-\left( 1+\beta \right)\gamma \right]}^{2}}{{\alpha }^{2}}}{32-\left( 8+8\beta \right){{\gamma }^{2}}}$, and ${{\bar{\pi }}_{m2}}=\frac{\left( 1-\beta \right){{\left[ 8-\left( 1+\beta \right){{\gamma }^{2}}-2\gamma \right]}^{2}}}{16{{\left[ 4-\left( 1+\beta \right){{\gamma }^{2}} \right]}^{2}}}{{\alpha }^{2}}$. We let ${{\bar{\pi }}_{e}}$, ${{\bar{\pi }}_{m1}}$ and ${{\bar{\pi }}_{m2}}$ be the deterministic payoffs (in the absence of uncertainty). Let $\delta =E\left[ {{\left( E\left[ \theta \|Y \right] \right)}^{2}} \right]$ for simplicity.

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Table A1. Operation equilibrium

$ {{x}_{m}} $	Equilibrium outcome	Ex-ante profit
$ N $	$ {{w}^{N}}=D\alpha $	$ \pi _{e}^{N}={{\bar{\pi }}_{e}}+\frac{1}{4}\delta $
	$ q_{1}^{N}=F\alpha +\frac{1}{2}E\left[ \theta \|Y \right] $	$ \pi _{m}^{N}={{\bar{\pi }}_{m}} $
	$ q_{2}^{N}=G\alpha $
$ I $	$ {{w}^{I}}=D\alpha +DE\left[ \theta \|Y \right] $	$ \pi _{e}^{I}={{\bar{\pi }}_{e}}\left( 1+\frac{\delta }{{{\alpha }^{2}}} \right) $
	$ q_{1}^{I}=F\alpha +FE\left[ \theta \|Y \right] $	$ \pi _{m}^{I}={{\bar{\pi }}_{m}}\left( 1+\frac{\delta }{{{\alpha }^{2}}} \right) $
	$ q_{2}^{I}=G\alpha +GE\left[ \theta \|Y \right] $
Note: $D \ = \ \frac{8+{{\left( 1+\beta \right)}^{2}}{{\gamma }^{3}}-4{{\gamma }^{2}}-8\beta \gamma }{16-\left( 6+2\beta \right){{\gamma }^{2}}}$, $F=\frac{2\left( 1-\gamma \right)}{8-\left( 3+\beta \right){{\gamma }^{2}}}$, $G=\frac{8-\left( 1+\beta \right){{\gamma }^{2}}-2\gamma }{2\left[ 8-\left( 3+\beta \right){{\gamma }^{2}} \right]}$, ${{\bar{\pi }}_{e}}= {\small \frac{\left( 5\beta +6{{\beta }^{2}}+{{\beta }^{3}} \right){{\gamma }^{4}}+8\beta {{\gamma }^{3}}+\left( 16-16{{\beta }^{2}}-52\beta \right){{\gamma }^{2}}-32\gamma +64\beta +16}{4{{\left[ 8-\left( 3+\beta \right){{\gamma }^{2}} \right]}^{2}}}{{\alpha }^{2}}}$, and {\small ${{\bar{\pi }}_{m}}=\frac{{{\left( 1+\beta \right)}^{2}}{{\gamma }^{2}}-8\gamma -8\beta +12}{32-\left( 12+4\beta \right){{\gamma }^{2}}}{{\alpha }^{2}}$. We let ${{\bar{\pi }}_{e}}$ and ${{\bar{\pi }}_{m}}$ be the deterministic payoffs (in the absence of uncertainty). Let $\delta =E\left[ {{\left( E\left[ \theta \|Y \right] \right)}^{2}} \right]$ for simplicity.

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Table A2. Operation equilibrium under the pure reseller channel

$ \left( {{x}_{m1}}, {{x}_{m2}} \right) $	Equilibrium outcome	Ex-ante profit
$ \left( N, N \right) $	$ w_{1}^{NN}=H\alpha $	$ \pi _{e}^{NN}={{\bar{\pi }}_{e}}+\frac{1}{2\left( 1+\gamma \right)}\delta $
	$ w_{2}^{NN}=H\alpha $	$ \pi _{m1}^{NN}={{\bar{\pi }}_{m1}} $
	$ q_{1}^{NN}=J\alpha +\frac{E\left[ \theta \|Y \right]}{2\left( 1+\gamma \right)} $	$ \pi _{m2}^{NN}={{\bar{\pi }}_{m2}} $
	$ q_{2}^{NN}=J\alpha +\frac{E\left[ \theta \|Y \right]}{2\left( 1+\gamma \right)} $
$ \left( N, I \right) $	$ w_{1}^{NI}=H\alpha $	$ \pi _{e}^{NI}={{\bar{\pi }}_{e}}+\frac{5+3\gamma }{16\left( 1+\gamma \right)}\delta $
	$ w_{2}^{NI}=H\alpha +\frac{1-\gamma }{2}E\left[ \theta \|Y \right] $	$ \pi _{m1}^{NI}={{\bar{\pi }}_{m1}} $
	$ q_{1}^{NI}=J\alpha +\frac{\left( 2+\gamma \right)E\left[ \theta \|Y \right]}{4\left( 1+\gamma \right)} $	$ \pi _{m2}^{NI}={{\bar{\pi }}_{m2}}+\frac{1-\gamma }{8\left( 1+\gamma \right)}\delta $
	$ q_{2}^{NI}=J\alpha +\frac{E\left[ \theta \|Y \right]}{4\left( 1+\gamma \right)} $
$ \left( I, I \right) $	$ w_{1}^{II}=H\alpha +HE\left[ \theta \|Y \right] $	$ \pi _{e}^{II}={{\bar{\pi }}_{e}}\left( 1+\frac{\delta }{{{\alpha }^{2}}} \right) $
	$ w_{2}^{II}=H\alpha +HE\left[ \theta \|Y \right] $	$ \pi _{m1}^{II}={{\bar{\pi }}_{m1}}\left( 1+\frac{\delta }{{{\alpha }^{2}}} \right) $
	$ q_{1}^{II}=J\alpha +JE\left[ \theta \|Y \right] $	$ \pi _{m2}^{II}={{\bar{\pi }}_{m2}}\left( 1+\frac{\delta }{{{\alpha }^{2}}} \right) $
	$ q_{2}^{II}=J\alpha +JE\left[ \theta \|Y \right] $
Note: $H=\frac{1-\gamma }{2-\gamma }$, $J=\frac{1}{2\left( 2-\gamma \right)\left( 1+\gamma \right)}$, and ${{\bar{\pi }}_{e}}={{\bar{\pi }}_{m1}}={{\bar{\pi }}_{m2}}=\frac{1-\gamma }{2{{\left( 2-\gamma \right)}^{2}}\left( 1+\gamma \right)}{{\alpha }^{2}}$. We let ${{\bar{\pi }}_{e}}$, ${{\bar{\pi }}_{m1}}$ and ${{\bar{\pi }}_{m2}}$ be the deterministic payoffs (in the absence of uncertainty). Let $\delta =E\left[ {{\left( E\left[ \theta \|Y \right] \right)}^{2}} \right]$ for simplicity.

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Table A3. Operation equilibrium

$ \left( {{x}_{m1}}, {{x}_{m2}} \right) $	Equilibrium outcome	Ex-ante profit
$ \left( N, N \right) $	$ q_{1}^{NN}=K\alpha $	$ \pi _{e}^{NN}={{\bar{\pi }}_{e}} $
	$ q_{2}^{NN}=K\alpha $	$ \pi _{m1}^{NN}={{\bar{\pi }}_{m1}} $
		$ \pi _{m2}^{NN}={{\bar{\pi }}_{m2}} $
$ \left( N, I \right) $	$ q_{1}^{NI}=K\alpha $	$ \pi _{e}^{NI}={{\bar{\pi }}_{e}}+\frac{\beta }{4}\delta $
	$ q_{2}^{NI}=K\alpha +\frac{E\left[ \theta \|Y \right]}{2} $	$ \pi _{m1}^{NI}={{\bar{\pi }}_{m1}} $
		$ \pi _{m2}^{NI}={{\bar{\pi }}_{m2}}+\frac{1-\beta }{4}\delta $
$ \left( I, I \right) $	$ q_{1}^{II}=K\alpha +KE\left[ \theta \|Y \right] $	$ \pi _{e}^{II}={{\bar{\pi }}_{e}}\left( 1+\frac{\delta }{{{\alpha }^{2}}} \right) $
	$ q_{2}^{II}=K\alpha +KE\left[ \theta \|Y \right] $	$ \pi _{m1}^{II}={{\bar{\pi }}_{m1}}\left( 1+\frac{\delta }{{{\alpha }^{2}}} \right) $
		$ \pi _{m2}^{II}={{\bar{\pi }}_{m2}}\left( 1+\frac{\delta }{{{\alpha }^{2}}} \right) $
Note: $K=\frac{1}{2+\gamma }$, ${{\bar{\pi }}_{e}}=\frac{2\beta }{{{\left( 2+\gamma \right)}^{2}}}{{\alpha }^{2}}$, and ${{\bar{\pi }}_{m1}}={{\bar{\pi }}_{m2}}=\frac{\left( 1-\beta \right)}{{{\left( 2+\gamma \right)}^{2}}}{{\alpha }^{2}}$. We let ${{\bar{\pi }}_{e}}$, ${{\bar{\pi }}_{m1}}$ and ${{\bar{\pi }}_{m2}}$ be the deterministic payoffs (in the absence of uncertainty). Let $\delta = E\left[ {{\left( E\left[ \theta \|Y \right] \right)}^{2}} \right]$ for simplicity.

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