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Today, the editor brings the "
Platform financing or bank financing in agricultural supply chains: Theimpact of platform digital empowerment".
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1 内容摘要（Content summary）
Today, the editor will interpret and share the BD model analysis part under PDE from the three sections of "Mind Map, Intensive Reading Content, and Knowledge Supplement".
Today, I will share the part of BD model analysis with PDE in the article “Platform financing or bank financing in agricultural supply chain: the impact of platform digital empowerment” from the three sections of “Thinking Guide, Intensive Reading, and Knowledge Supplementation”.
2 思维导图（Mind mapping）
3 精读内容（Intensive reading content）
This section discusses the BD model with PDE, i.e., in the BD model, the farmer uses the PDE to obtain a loan from the bank. In this case, the platform helps farmers by selling agricultural products and providing digital authorization. The expected profit for the farmer and the platform is:
This section discusses the BD model with PDE, i.e., in model BD, the farmer uses PDE to get a loan from the bank. In this case, the platform helps the farmer by selling agricultural products and providing digital licenses. The expected profit for the farmer and the platform is:
where the value of Q is:
where the value of Q is:
Input the profit functions of the above banks and platforms into the calculation software:
Enter the profit function for the above banks and platforms into the calculator:
By finding the partial derivatives of eF and eP respectively and making them zero, the equations for eF and eP with respect to w are obtained as follows:
The following equations for eF and eP with respect to w are obtained by taking the partial derivatives of eF and eP respectively and making them zero:
Then bring the equations of eF and eP about w back into the profit function, get the equation about w, and find the partial derivative of w to make it zero, and get the value of w as follows:
The equation for eF and eP with respect to w is then brought back to the profit function to obtain the equation with respect to w. The value of w is obtained as follows by taking the partial derivation of w to make it zero:
Bringing the values of w back into the equation of eF and eP with respect to w, we get the relevant values of eF and eP, respectively, as follows:
Bringing the value of w back into the equation for eF and eP with respect to w yields the following values associated with eF and eP, respectively:
Bringing the values of eF and eP back into the profit function, respectively, the profits of the platform and the farmer can be obtained as follows:
Bringing the values of eF and eP back into the profit function respectively one can find the profits of the platform and the farmer as follows:
4 知识补充（Knowledge supplement）
什么是逆向归纳法？（What is reverse induction?）
Backward Induction is a strategy method used in game theory to analyze and solve dynamic games with a sequential order of action. This approach starts from the last stage of the game, where participants decide on the optimal strategy based on rational choices and maximizing their own interests, and then applies this logic backwards to the penultimate stage, and so on, until the initial stage of the game. In this way, inverse induction is able to reveal how rational actors should act in order to achieve a perfect equilibrium (SPE) of a subgame under conditions of complete and perfect information. In short, reverse induction is a "look forward, reason backward" strategy that helps us understand how the best choice for the present can be guided by foreseeing future outcomes in a multi-stage decision-making process.
Backward Induction is a strategy method used in game theory to analyze and solve dynamic games with sequential actions. This approach starts from the last stage of the game, where participants decide on the optimal strategy based on the principle of rational choice and maximizing their own interests, and then apply this logic in reverse to the penultimate stage, and so on, until the initial stage of the game. In this way, backward induction is able to reveal how rational participants should act to achieve subgame perfect equilibrium (SPE) under conditions of complete and perfect information. In short, backward induction is a “forward-looking, backward-reasoning” strategy that helps us understand how to anticipate future outcomes to guide the best current choices in a multi-stage decision-making process.
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Reference: ChatGPT
Bibliography:
Qihui Lu, Changhua Liao, Meilan Chen, et al. Platform financing or bank financing in agricultural supply chains: The impact of platform digital empowerment[J]. European Journal of Operational Research, 2024, 315(1): 952-964.
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