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doi: 10.3934/jimo.2022042
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## Trade credit and information leakage in a supply chain with competing retailers

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

*Corresponding author: Man Yu

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

Received  June 2021 Revised  November 2021 Early access March 2022

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.

Citation: Man Yu, Erbao Cao. Trade credit and information leakage in a supply chain with competing retailers. Journal of Industrial and Management Optimization, doi: 10.3934/jimo.2022042
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##### References:
Sequence of events
The manufacturer's non-leakage region in the bankruptcy scenario
The manufacturer's non-leakage region in the non-bankruptcy scenario
Wholesale price w with respect to $R$ and $r$
Impacts of $r$ on retailers
Impacts of $r$ on the manufacturer and the supply chain
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 $\phi^{\prime}<3$ $\begin{array}{c} q_{i L}^{E S 2^{*}}=\dfrac{1}{2}\left[2 A_{H}-A_{L}+w_{e}(1+R)-2 w_{i}\right]-\\\dfrac{1}{2} \sqrt{\left(A_{H}-A_{L}\right)\left[3 A_{H}-A_{L}-2 w_{e}(1+R)+4 w_{i}\right]} \end{array}$ $\begin{array}{c} q_{e L}^{E S 2^{*}}=\dfrac{1}{4}\left[3 A_{L}-2 A_{H}-3 w_{e}(1+R)+2 w_{i}\right]+\\ \dfrac{1}{4} \sqrt{\left(A_{H}-A_{L}\right)\left[3 A_{H}-A_{L}-2 w_{e}(1+R)+4 w_{i}\right]} \end{array}$ Pooling equilibrium $q_{i}^{E P^{*}}=\dfrac{2 A_{L}-u+w_{e}(1+R)-2 w_{i}}{2}$ $q_{e}^{E P^{*}}=\dfrac{3 u-2 A_{L}-3 w_{e}(1+R)+2 w_{i}}{4}$
 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 $\phi^{\prime}<3$ $\begin{array}{c} q_{i L}^{E S 2^{*}}=\dfrac{1}{2}\left[2 A_{H}-A_{L}+w_{e}(1+R)-2 w_{i}\right]-\\\dfrac{1}{2} \sqrt{\left(A_{H}-A_{L}\right)\left[3 A_{H}-A_{L}-2 w_{e}(1+R)+4 w_{i}\right]} \end{array}$ $\begin{array}{c} q_{e L}^{E S 2^{*}}=\dfrac{1}{4}\left[3 A_{L}-2 A_{H}-3 w_{e}(1+R)+2 w_{i}\right]+\\ \dfrac{1}{4} \sqrt{\left(A_{H}-A_{L}\right)\left[3 A_{H}-A_{L}-2 w_{e}(1+R)+4 w_{i}\right]} \end{array}$ Pooling equilibrium $q_{i}^{E P^{*}}=\dfrac{2 A_{L}-u+w_{e}(1+R)-2 w_{i}}{2}$ $q_{e}^{E P^{*}}=\dfrac{3 u-2 A_{L}-3 w_{e}(1+R)+2 w_{i}}{4}$
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 $\phi^{I}<3$ $\begin{array}{c} q_{i L}^{I S 2^{*}}=\dfrac{1}{2}\left(2 A_{H}-A_{L}-w-w R\right)\\ -\dfrac{1}{2} \sqrt{\left(A_{H}-A_{L}\right)\left(3 A_{H}-A_{L}-2 w-2 w R\right)} \end{array}$ $\begin{array}{c} q_{e L}^{I S 2^{*}}=\dfrac{1}{4}\left(3 A_{L}-2 A_{H}-w-R w\right)\\ +\dfrac{1}{4} \sqrt{\left(A_{H}-A_{L}\right)\left(3 A_{H}-A_{L}-2 w-2 w R\right)} \end{array}$
 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 $\phi^{I}<3$ $\begin{array}{c} q_{i L}^{I S 2^{*}}=\dfrac{1}{2}\left(2 A_{H}-A_{L}-w-w R\right)\\ -\dfrac{1}{2} \sqrt{\left(A_{H}-A_{L}\right)\left(3 A_{H}-A_{L}-2 w-2 w R\right)} \end{array}$ $\begin{array}{c} q_{e L}^{I S 2^{*}}=\dfrac{1}{4}\left(3 A_{L}-2 A_{H}-w-R w\right)\\ +\dfrac{1}{4} \sqrt{\left(A_{H}-A_{L}\right)\left(3 A_{H}-A_{L}-2 w-2 w R\right)} \end{array}$

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