In order to realize the sustainable development of the communication industry, many banks have developed some new projects to provide loan to the mobile phone brand companies (MPBCs). This paper studies a perfect information game among three parties: telecom operator (TO), MPBC, and bank. In the first stage, the bank decides an interest rate and shows it to the TO and the competitive MPBC. In the second stage, the TO and MPBC are engaged in Cournot games: a simultaneous subgame, a TO-as-leader sequential subgame, and an MPBC-as-leader sequential subgame. The TO’s and the MPBC’s decisions and the production/sale quantities are investigated. The impacts of the interest rate and the substitute factor on the TO’s and the MPBC’s optimal decisions are analyzed. When the substitute factor is high, at a low interest rate, the total sales in the simultaneous subgame is higher than those in the other two subgames; at a high interest rate, the total sales in the MPBC-as-leader subgame is higher than those in the other two subgames. However, when the substitute factor is low, at a low enough interest rate, the total sales in the simultaneous subgame is higher than those in the other two subgames; at a high enough interest rate, the total sales in the MPBC-as-leader subgame is higher than those in the other two subgames; at a moderate interest rate, the total sales in the TO-as-leader subgame is higher than those in the other two subgames. Besides, the optimal interest rate of the bank is investigated and the impact of the substitute factor on the optimal interest rate is analyzed. The bank sets a higher interest rate in the MPBC-as-leader subgame than those in the other two subgames. Besides, when the substitute factor is low, the bank sets a lower interest rate in the TO-as-leader subgame than that in the simultaneous subgame; however, when the substitute factor is high, the bank sets a higher interest rate in the TO-as-leader subgame than that in the simultaneous subgame.

中文翻译：

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财务受限供应链中的双渠道销售系统

为了实现通信行业的可持续发展，许多银行开发了一些新的项目，为手机品牌公司（MPBCs）提供贷款。本文研究了电信运营商(TO)、MPBC和银行三方之间的完美信息博弈。在第一阶段，银行决定利率并将其显示给 TO 和竞争性 MPBC。在第二阶段，TO 和 MPBC 进行古诺博弈：同时子博弈、TO 作为领导者的序列子博弈和 MPBC 作为领导者的序列子博弈。对 TO 和 MPBC 的决定以及生产/销售数量进行了调查。分析了利率和替代因子对TO和MPBC最优决策的影响。当替代因子高时，在低利率下，同时子博弈的总销售额高于其他两个子博弈的总销售额；在高利率下，MPBC-as-leader 子博弈的总销售额高于其他两个子博弈。然而，当替代因子较低时，在足够低的利率下，同时子博弈的总销售额高于其他两个子博弈的总销售额；在足够高的利率下，MPBC-as-leader 子博弈的总销售额高于其他两个子博弈；在中等利率下，TO-as-leader 子博弈的总销售额高于其他两个子博弈。此外，考察了银行的最优利率，分析了替代因素对最优利率的影响。银行在 MPBC-as-leader 子博弈中设定的利率高于其他两个子博弈中的利率。此外，当替代因子较低时，银行在TO-as-leader子博弈中设置的利率低于同时子博弈中的利率；然而，当替代因子较高时，银行在 TO-as-leader 子博弈中设置的利率高于同时子博弈中的利率。