**2. Literature Review**

### *2.1. The Improvement Strategy of Product Quality*

A review of the literature revealed that how to improve product quality to enhance market competitiveness has been a hot research topic in business operation management. For example, Li et al. studied the supplier's product upgrade strategies considering consumers' strategic behavior [9]. Chen et al. studied the joint pricing and quality decision problems in a dual-channel supply chain [10]. Li et al. studied pricing and quality competition issues under brand differentiation [11]. These studies focus on consumer reactions to product quality upgrades in a highly competitive context. Unlike general products, the problem of structural imbalance on the supply side of agricultural produce has existed for many years. In other words, the oversupply of general mass agri-foods and the undersupply of high-quality agri-foods coexist. In addition, agricultural producers are mostly in a disadvantaged position, operating at low profit. Under the urgen<sup>t</sup> call of consumers for high-quality and safe agri-foods, even if they make quality improvement behaviors, they need the supply chain to bear the cost of quality improvement inputs and put produce into the market with high quality and competitive price. Otherwise, the agricultural supply chain lacks the incentive for quality improvement. Although scholars also pay attention to the quality improvement of agricultural products, they mainly focus on the quality grading [12,13], quality and safety regulation [14], and related behaviors affecting the quality and safety of agricultural produce [15]. Moreover, data surveys and empirical tests are mainly used [16,17], which cannot effectively predict the long-term impact of agri-foods quality upgrading.

### *2.2. Game Study on Product Price and Demand*

In terms of supply chain games considering price and demand, Abad [18] constructed a demand–price-sensitive supply chain coordination model and finally obtained a method to achieve the optimal strategy when buyers and sellers cooperate. Sajadi et al. discussed the issue of supply chain coordination when market demand is influenced by factors such as the size of the retailer's effort to develop the market and the retail price [19]. Chan and Dai et al. discussed the problems of optimal order lot size and optimal order lead time for achieving maximum profit in the supply chain in a cooperative game, respectively [20,21]. Mir Mehdi et al. constructed non-cooperative game models, such as the Nash game and the Stackelberg game, as well as a cooperative game model to study a two-level supply chain game problem in which demand is influenced by advertising and price [22]. Zhao et al. constructed an option contract model to solve the conflict of interest in the supply chain [23]. Leng et al. used the Nash and Stackelberg game model to study the multi-supplier but single-retailer supply chain coordination problem for short life-cycle products [24]. Esmaeili et al. studied the supply chain game problem when demand is dependent on price and marketing costs [25]. In general, the means and game methods of supply chain coordination under different conditions have been studied extensively and thoroughly, but not much

research has been conducted on quality and safety levels of agri-foods and corresponding price compensation mechanisms. For instance, Ren et al. studied the performance of food safety managemen<sup>t</sup> systems of Chinese food business operators [26]. Jacques et al. [27] discussed the quality and safety standards in the food industry. Though the quality of agrifoods is noticed, there is no mention of subsidies for the implementors of the agricultural produce improvement initiative, making it difficult to provide targeted guidance for quality improvement and cost–price compensation in agricultural supply chains. Therefore, we conducted the present study based on our previous research on the quality [2] and price compensation [28] mechanisms of agricultural produce.

### *2.3. Influences after the Improvement of the Agri-Food Quality*

Some other researchers discussed the influence of the foods label that reflects the quality of produce. Messer et al. proposed that labeling produce can have both good and ugly effects [5]. The good effects include that the labeling of quality can reduce information asymmetry, and the ugly effects includes that the labeling and certifying process may be costly, which leads to reduced demand for high-quality agricultural produces. Aftab et al. analyzed the impact of rising food prices on consumer welfare in the most populous countries of South Asia and found that consumer welfare declines in all countries mainly for cereals and milk, as these food items are relatively less elastic to price fluctuations [29]. The labeling process and price increases associated with improved quality of agricultural produce will undoubtedly have an impact on social welfare and other stakeholders. However, this is not the focus of this paper. Different from these articles, we only focused on the quality improvement action though it is a key part of the produce before it is labeled. In addition, the quality improvement studied in this article is voluntary and endogenous, proposed by the participants of the agricultural supply chain. As a result, in order to focus more on the research topic, we will not discuss at grea<sup>t</sup> length the social impact of quality improvement actions.

Above all, compared to existing research, the novelty of our work is as follows: The "quality safety factor" and "price compensation factor" are introduced into the linear inverse demand function of agricultural produce for the first time. By constructing three different game models under decentralized and centralized decision-making situations, the optimal strategy for upgrading the quality of agricultural produce is analyzed, and a cost-sharing contract is designed to coordinate the supply chain. In this way, some theoretical reference is provided for the participants in the agricultural supply chain when making decisions about the quality improvement input and price compensation.

### **3. Materials and Methods**
