## 3 Problems and Symbols  
A three-tier low-carbon fresh agricultural product supply chain system consisting of a manufacturer (represented by M), a TPLSP service provider (represented by T) and a retailer (represented by R) are studied in this paper. In the three-level supply chain system, the manufacturer, TPLSP and retailer have a Stackberg game relationship. The specific decision-making process is shown in Figure 1: First, TPLSP provides fresh-keeping services, and the fresh-keeping service price per unit product is positively related to the fresh-keeping degree of the product, that is \(p_{t}=a_{1}\eta\), and the fresh-keeping cost per unit product is \(c_{t}=a_{2}\eta^{2}\); Second, the manufacturer shall decide the level of fresh-keeping service to purchase according to the price of fresh-keeping services provided by TPLSP. At the same time, the manufacturer shall decide the low carbon level of products, the \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Authors** & **Supply Chain System** & **Carbon Emission Reduction** & **Advertising** \\ \hline Ma [21] & Two-echelon cold chain system & Y & N \\ Cai [23] & Three-level green supply & N & N \\  & chain system & & \\ Ji [35] & Retail-/dual-channel & Y & N \\  & supply chain & & \\ Pan [42] & Multi-stage sustainable & N & Y \\  & supply chain & Y & Y \\ This paper & Three-level cold chain system & Y & Y \\ \hline \hline \end{tabular} N indicates not available. Y indicates available.  
\end{table} 
Table 1: Summary of the scenarios in the related literature. advertising and marketing level of low carbon products, and the wholesale price \(\omega\), in which the low carbon cost per unit product is \(a_{3}\sigma^{2}\) and the advertising expense [43] is \(a_{4}\mu^{2}\); Third, the retailer decides the sales price of the product according to the market demand function and the wholesale price. Some assumptions are made for the proposed model. **Assumption 1**. : _The manufacturer launched a low-carbon product against the background of consumers' awareness of low-carbon preference and increased the sales of low-carbon fresh agricultural products through advertising._  
**Assumption 2**. : _TPLSP provided fresh-keeping services, and the price of fresh-keeping services was in direct proportion to the fresh-keeping level._  
**Assumption 3**. : _In this paper, inspired by reference [23], we used the market demand function in the form of a multiplier, with the market demand \(D\) being affected by freshness \(\eta\), advertising level \(\mu\), product low carbon level \(\sigma\), and product sales price \(P_{r}\) at the same time, thus, the market demand function of fresh agricultural products is:_  
\[D(p,\eta\Big{(}\tau))= y_{0}\eta(\tau)\mu\sigma p_{r}^{-k} \tag{1}\]  
Equation (1) means that the market demand mainly depends on the freshness of the product when it reaches the market, the level of advertising, the low carbon level of the product and the sales price set by the retailer. The higher the selling price, the less demand there will be in the market. The higher the freshness, the higher the market demand. This is in line with market demand for fresh produce. The relevant parameters and symbols in this paper are shown in Table 2. \begin{table}
\begin{tabular}{c c} \hline \hline
**Symbols** & **Illustrate** \\ \hline \(y_{0}\) & Potential market size \\ \(\eta\) & Product freshness \\ \(p_{t}\) & Fresh keeping service price per unit product \\ \(c_{t}\) & Fresh keeping cost per unit product \\ \(w\) & Wholesale price set by manufacturer \\ \(c_{m}\) & Manufacturer’s unit manufacturing cost \\ \(\sigma\) & Low carbon level of products \\ \(\mu\) & Advertising level \\ \(p_{r}\) & Product sales price \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Description of relevant parameters and symbols. Figure 1: Game sequence of fresh agricultural product supply chain. We research a three-echelon supply chain system, including three types of agents: manufacturer, TPLSP and retailer.