*6.2. Sensitivity Analysis*

According to the assumptions above, *b* is the sensitivity of consumers to the price of agri-foods, while *k* is the sensitivity of consumers to the quality of agri-foods. By analyzing the sensitivity of *b* and *k*, the trend of the decision variables in the game model can be explored when the key parameters change.

### 6.2.1. Sensitivity Analysis on Consumer Price Sensitivity Factors

Based on the parameters above, the variation of each variable in the three models regarding the consumer price sensitivity factor *b* is explored. From Figure 1, it can be seen that the price compensation factor *α* and the quality of agri-foods *g* decrease with the increase of consumer price sensitivity factor *b*. The trend indicates that when consumers become more and more sensitive to the price of agri-foods, the selling price of agri-foods will decrease with the increase of consumer price elasticity in order to increase sales, and at the same time, agricultural producers will choose to reduce quality improvement inputs to reduce costs. However, in general, the centralized decision with the goal of maximizing the overall benefit of the supply chain is still the optimal strategy to realize the quality and price of agri-foods.

From Figure 2, it can be seen that the profit of the participants in the agricultural supply chain decreases as the price elasticity of demand *b* increases, and the overall profit of the supply chain under the centralized decision is the largest. Since the profit of sellers is relatively small under this set of parameters, the overall profit distribution of sellers in the supply chain is slightly lower than that of producers. When the quality of agri-foods is promoted by the seller, the seller gains more profit compared with the producer; i.e., the profit is inclined to the dominant players in the supply chain.

**Figure 1.** Variation of quality safety factor *g* and price compensation factor *α* with consumer price sensitivity factor *b*. (Variables with \* are the optimal variable values.)

**Figure 2.** Variation of profits of agricultural supply chain participants with consumer price sensitivity factor *b*. (Variables with \* are the optimal variable values).

6.2.2. Sensitivity Analysis on Consumer Quality Sensitivity Factors

Using the above parameters, the variation of each variable in the three models with respect to the consumer quality sensitivity factor *k* is analyzed. From Figure 3, it can be seen that with the increase of *k*, the price compensation factor *α* and quality safety *g* in the producer-driven Stackelberg game model are at the lowest level and do not change. However, the price compensation factor *α* and quality safety degree *g* in the seller-dominated Stackelberg game model and the centralized decision model are both on the rise. In the producer-dominated Stackelberg game model, producers dominate the quality safety degree *g,* and sellers dominate the price compensation factor *α*. The trend shows that with consumers' increasing care about the quality of agri-foods, producers are concerned that sellers will not compensate them for the cost of their efforts to improve quality. Therefore, in order to ensure their own maximum gain, producers will be stingy to increase the quality improvement input, which ultimately indicates that the producer is insensitive to the consumer's quality demand elasticity. In Model 2 and 3, when consumers pay more and more attention on the quality of agri-foods, sellers will incentivize producers to improve the quality of agri-foods by increasing the price compensation factor.

**Figure 3.** Variation of quality safety factor *g* and price compensation factor α with consumer quality sensitivity factor *k*. (Variables with \* are the optimal variable values).

As can be seen in Figure 4, the producer is insensitive to the quality elasticity of demand because the producer does not actually make quality improvements in Model 1. The maximum profit of the seller in model 2 and the total profit of the supply chain in model 3 increase with the increase of the quality elasticity of demand, and the profit of the producer decreases with the increase of the quality elasticity of demand. When the quality elasticity of demand reaches a certain threshold, if the price increase is not large, the producers of agri-foods will be unprofitable due to the high quality input cost.

From Figure 5, it can be seen that the actual market demand for agri-foods in models 2 and 3 decreases with the increase of consumer price sensitivity and diverges into two stages with the increase of quality sensitivity.

**Figure 4.** Variation of profit of agricultural supply chain participants with consumer quality sensitivity factor *k*. (Variables with \* are the optimal variable values).

**Figure 5.** Variation of real market demand *d* with consumer price sensitivity factor *b* (**A**) and quality sensitivity factor *k* (**B**) (Variables with \* are the optimal variable values).

In the first stage, when the price sensitivity of consumers is very low, the actual market demand in the centralized decision model is the lowest, followed by the game model dominated by producers, and finally the game model dominated by sellers. The second stage is when the quality sensitivity of consumers reaches a certain value, the actual market demand in the centralized decision model starts to exceed the actual market demand in the decentralized decision model with the increase of quality sensitivity.

This indicates that when consumers are not sensitive to the quality of agri-foods, low-quality agri-foods sell better. When consumers are more and more concerned about the quality of agri-foods, the "high-quality and high-priced" produce sells better.

### *6.3. Analysis of Other Parameters*

### 6.3.1. The Impact of Agricultural Selling Prices on Profits

The above parameters were also used to analyze the profit changes of supply chain participants when the retail price gradually increases from 5 to 10, and the results are shown in Figure 6A. As can be seen from the figure, the profit of sellers increases with the increase of selling price of agri-foods, while producers' profit increases first and then decreases with the increase of selling price. With the increase of unit value of agri-foods, supply chain profit gradually inclines to sellers.

**Figure 6.** Variation of profits of supply chain participants with agricultural sales price *p*0 (**A**) and wholesale price *w*0 (**B**). (Variables with \* are the optimal variable values).

Considering that the profit of sellers in the original parameters is low, in order to observe the change of profit of supply chain participants with the wholesale price of agrifoods, the retail price is assumed to be 10. When the wholesale price increases from 3 to 8, the change of profit of supply chain participants is shown in Figure 6B. From the figure, it can be seen that with the increase of wholesale price, the profit of sellers gradually decreases, and the profit of producers first increases and then decreases. The total profit of the centralized decision supply chain is the largest, mainly related to parameters such as total regional sales volume rather than prices.

### 6.3.2. The Impact of Cost-Sharing Factor

According to Proposition 8, the parameters *k* = 1 and *b* = 0.375 are reset to observe the changes of some variables, such as the quality of agri-foods, the level of price subsidy, and the profit of supply chain participants with the sharing coefficient *β*, under the costsharing contract. The results are shown in Figure 7. It is easy to find from Figure 7A that the adoption of cost-sharing contracts can significantly improve the quality of agri-foods, and also the price subsidy level is lower than that before the introduction of cost-sharing contracts, which means that the price of agri-foods is more "high-quality and low-price" at this time. From Figure 7B, it can be seen that as the cost-sharing coefficient of sellers increases, the supply chain profit keeps shifting to producers. The producer and seller can achieve the same profit at a specific moment.

**Figure 7.** Variation of the main parameters (**A**,**B**) of the supply chain with the sharing ratio *β* after the introduction of the cost-sharing contract. (Variables with \* are the optimal variable values).
