## 4 Closed-Loop Supply-Chain Decision Making and Model Analysis
### Incentive Mechanism Design  
#### 4.2.1 Information Screening Contract Model  
In the practice of closed-loop operation of the new energy vehicle power battery industry, since the power battery recycling and disassembly process has market licensing, complex process requirements, and intellectual property protection of power batteries, in the process of remanufacturing power batteries, companies usually first consider recycling and dismantling outsourcing, and find suitable agents through bidding. Under the principal-agent framework, the information asymmetry of the closed-loop supply chain of the power battery includes the \"reverse selection problem\" hidden by the recycling capacity of the recycler before an agreement is made, and the \"moral hazard problem\" of the recycler's retention of their efforts after an agreement is made. The timing of supply chain decision-making is shown in Table 2. Before the agreement, the recycler's ability to recycle and disassemble is its private information, which cannot be observed by the battery manufacturer. At this time, the information asymmetry is reflected in the typical \"reverse selection\" problem. After the agreement is made, the recycling business chooses the optimal level of effort according to the principle of maximizing its own revenue. At this time, the information asymmetry is reflected in the typical \"moral hazard\" problem. It is therefore crucial in supply-chain systems to design incentives to induce third-party recyclers to report their true recycling and dismantling capabilities and improve their efforts after agreements have been made. The information screening contract established in this paper will provide corresponding contracts for recyclers of different capability types. The contract will induce recyclers to improve their efforts while having the characteristics of \"self-selection\" to achieve the goal of information screening. The contract process essentially involves the Stackelberg game model, as follows. First, we consider the \"reverse selection\" problem, where the recycler conceals its true recycling and dismantling ability before \begin{table}
\begin{tabular}{c l} \hline \hline
**Stage One** & \\ \hline i & Recyclers are aware of their own dismantling capabilities \(\epsilon_{ij}\) \\ ii & Remanufactures offer a compensation contract \(\{(T_{j},\beta_{j})\}\) \\ iii & Recyclers choose the appropriate contract based on their own dismantling ability \(\{(T_{j},\beta_{j})\}\) \\ \hline \hline
**Stage Two** & \\ \hline iv & The manufacturer pays the recycler a certain amount of fixed compensation \(T_{j}\) \\ v & Recyclers choose the best effort based on maximizing their own earnings \(\epsilon_{ij}\) \\ \hline
**Stage Three** & \\ \hline vi & The manufacturer uses the raw materials to remanufacture and sell according to the returned dismantling \\ vii & Manufacturers give recyclers revenue share sharing based on sales performance \(\hat{\beta_{j}}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Time series of closed-loop supply chain information screening contract. signing. The principal first designs the contract \(\{(T_{j},\beta_{j})\}\), for recyclers with a reporting capability of \(r_{j}\), the recycler signs a contract based on its true ability type \(r_{i}\), presenting a \"self-selected\" feature. Second, we consider the recycler's efforts after an agreement as a \"moral hazard\" problem of retaining the response. After the agreement is made, the recycler chooses its own recycling effort level of \(e_{ij}\) to maximize the benefits. Finally, the battery manufacturer remanufactures and sells the purchased remanufactured raw materials. The number of products sold has given the recycler a certain revenue share, denoted by \(\beta_{j}\).