**8. Conclusions**

Three basic decision models involving the decision-making behavior on the quality improvement of agri-foods in the supply chain, namely, the decentralized decision model dominated by producers, the decentralized decision model dominated by sellers, and the centralized decision model, were constructed using game theory. The market demand of agri-foods depends on their sales price and supply quality is considered, and two decision variables of "quality safety" and "price compensation factor" are introduced into the linear inverse demand function for the first time. A cost-sharing contract is designed to study the relationship between product price, quality, and market demand in the supply chain. The results show that the centralized model is better than the two other models from the perspective of quality improvement. However, how to make decisions to achieve quality and price of agri-foods varies. Given that the study only analyzed the decisions within the supply chain, that is, the quality improvement action is voluntary and endogenous, future research can further discuss the influence of quality improvement on the behavior of other stakeholders and make clear how quality works in the market. Moreover, the participants in the agricultural supply chain are assumed to be risk-neutral. To validate the findings further, studies can be conducted with risk-appetitive and risk-averse participants.

**Author Contributions:** Writing—original draft preparation, J.X.; writing—review and editing, J.C.; validation, P.D.; funding acquisition, G.Y. All authors have read and agreed to the published version of the manuscript.

**Funding:** National Natural Science Foundation of China: 72103178; Strategic Research and Consulting Project of Chinese Academy of Engineering: 2021-XZ-30; Postdoctoral Research Foundation of China: 2019M661960.

**Data Availability Statement:** Data is contained within the article.

**Acknowledgments:** This research was supported by the National Natural Science Foundation of China (72103178) and Strategic Research and Consulting Project of Chinese Academy of Engineering (2021-XZ-30).

**Conflicts of Interest:** The authors declare no conflict of interest.
