Trade credit and information leakage in a supply chain with competing retailers

Man Yu; Erbao Cao

doi:10.3934/jimo.2022042

Article Contents

2023, Volume 19, Issue 4: 2268-2302. Doi: 10.3934/jimo.2022042

This issue Previous Article Next Article Online channel design in the presence of price self-matching: Self-operating or e-marketplace?

Trade credit and information leakage in a supply chain with competing retailers

Man Yu^, and
Erbao Cao

College of Economics and Trade, Hunan University, Changsha, 410079, China

^*Corresponding author: Man Yu
^*Corresponding author: Man Yu

"World Bank urged to lift trade credit finance", Financial Times, November 11, 2008.

Received: June 2021

Revised: November 2021

Published: April 2023

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Abstract

This paper investigates the issue of information leakage in a supply consisting of one manufacturer, one incumbent retailer endowed with superior demand information, and a capital-constrained entrant retailer financed by the manufacturer's trade credit. The incumbent retailer faces the situation that the manufacturer may leak the incumbent retailer's order information to the uninformed entrant retailer. We first examine whether trade credit can prevent information leakage. It shows that the manufacturer always leaks information in the non-bankruptcy scenario where the capital-constrained retailer does not go bankrupt in the low-demand state. In contrast, in the bankruptcy scenario, the manufacturer does not leak information since it could get more transfer revenue from the bankrupt entrant retailer than the revenue obtained from the incumbent retailer. We also explore the impacts of information leakage on each member's optimal decision and profit. Interestingly, the findings show that the informed incumbent retailer, taking the advantage of being the first-mover, is able to actively place a larger order to induce the manufacturer to leak information and benefits from information leakage under certain conditions.

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

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Figure 1. Sequence of events

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Figure 2. The manufacturer's non-leakage region in the bankruptcy scenario

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Figure 3. The manufacturer's non-leakage region in the non-bankruptcy scenario

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Figure 4. Wholesale price w with respect to $ R $ and $ r $

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Figure 5. Impacts of $ r $ on retailers

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Figure 6. Impacts of $ r $ on the manufacturer and the supply chain

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Table 1. Optimal order quantities given different wholesale prices

Non-leakage equilibrium without bankruptcy	$ q_{i L}^{E N 1^{*}}=\dfrac{3 A_{L}-u+2 w_{e}(1+R)-4 w_{i}}{6} $
	$ q_{i H}^{E N 1^{*}}=\dfrac{3 A_{H}-u+2 w_{e}(1+R)-4 w_{i}}{6} $
	$ q_{e}^{E N 1^{*}}=\dfrac{u+w_{i}-2 w_{e}(1+R)}{3} $
Non-leakage equilibrium with bankruptcy	$ q_{i L}^{E N 2^{*}}=\dfrac{3 A_{L}-A_{H}+2 w_{e}(1+R)-4 w_{i}}{6} $
	$ q_{i H}^{E N 2^{*}}=\dfrac{A_{H}+w_{e}(1+R)-2 w_{i}}{3} $
	$ q_{e}^{E N 2^{*}}=\dfrac{A_{H}-2 w_{e}(1+R)+w_{i}}{3} $
Separating equilibrium $ \phi^{\prime} \geq 3 $	$q_{i L}^{E S 1^{*}}=\dfrac{A_{L}-2 w_{i}+w_{e}(1+R)}{2}$
	$q_{e L}^{E S 1^{*}}=\dfrac{A_{L}-3 w_{e}(1+R)+2 w_{i}}{4}$
	$q_{i H}^{E S 1^{*}}=\dfrac{A_{H}-2 w_{i}+w_{e}(1+R)}{2}$
	$q_{e H}^{E S 1^{*}}=\dfrac{A_{H}-3 w_{e}(1+R)+2 w_{i}}{4}$
Separating equilibrium $\phi^{\prime}<3$	$\begin{array}{c} q_{i L}^{E S 2^{*}}=\dfrac{1}{2}\left[2 A_{H}-A_{L}+w_{e}(1+R)-2 w_{i}\right]-\\\dfrac{1}{2} \sqrt{\left(A_{H}-A_{L}\right)\left[3 A_{H}-A_{L}-2 w_{e}(1+R)+4 w_{i}\right]} \end{array}$
Separating equilibrium $\phi^{\prime}<3$	$\begin{array}{c} q_{e L}^{E S 2^{*}}=\dfrac{1}{4}\left[3 A_{L}-2 A_{H}-3 w_{e}(1+R)+2 w_{i}\right]+\\ \dfrac{1}{4} \sqrt{\left(A_{H}-A_{L}\right)\left[3 A_{H}-A_{L}-2 w_{e}(1+R)+4 w_{i}\right]} \end{array}$
Pooling equilibrium	$q_{i}^{E P^{*}}=\dfrac{2 A_{L}-u+w_{e}(1+R)-2 w_{i}}{2}$
Pooling equilibrium	$q_{e}^{E P^{*}}=\dfrac{3 u-2 A_{L}-3 w_{e}(1+R)+2 w_{i}}{4}$

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Table 2. Optimal order decisions

Non-leakage equilibrium without bankruptcy	$q_{i L}^{I N 1^{*}}=\dfrac{3 A_{L}-u-2 w(1+R)}{6}$
	$q_{i H}^{I N 1^{*}}=\dfrac{3 A_{H}-u-2 w(1+R)}{6}$
	$q_{e}^{I N 1^{*}}=\dfrac{u-w(1+R)}{3}$
Non-leakage equilibrium with bankruptcy	$q_{i L}^{I N 2^{*}}=\dfrac{3 A_{L}-A_{H}-2 w(1+R)}{6}$
	$q_{i H}^{I N 2^{*}}=\dfrac{A_{H}-w(1+R)}{3}$
	$q_{e}^{I N 2^{*}}=\dfrac{A_{H}-w(1+R)}{3}$
Separating equilibrium $\phi^{I} \geq 3$	$q_{i L}^{I S 1^{*}}=\dfrac{A_{L}-w(1+R)}{2}$
	$q_{e L}^{I S 1^{*}}=\dfrac{A_{L}-w(1+R)}{4}$
	$q_{i H}^{I S 1^{*}}=\dfrac{A_{H}-w(1+R)}{2}$
	$q_{e L}^{I S 1^{*}}=\dfrac{A_{H}-w(1+R)}{4}$
Separating equilibrium $\phi^{I}<3$	$\begin{array}{c} q_{i L}^{I S 2^{*}}=\dfrac{1}{2}\left(2 A_{H}-A_{L}-w-w R\right)\\ -\dfrac{1}{2} \sqrt{\left(A_{H}-A_{L}\right)\left(3 A_{H}-A_{L}-2 w-2 w R\right)} \end{array}$
Separating equilibrium $\phi^{I}<3$	$\begin{array}{c} q_{e L}^{I S 2^{*}}=\dfrac{1}{4}\left(3 A_{L}-2 A_{H}-w-R w\right)\\ +\dfrac{1}{4} \sqrt{\left(A_{H}-A_{L}\right)\left(3 A_{H}-A_{L}-2 w-2 w R\right)} \end{array}$

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