Precooling energy and carbon emission reduction technology investment model in a fresh food cold chain based on a differential game

•When considering only the impact of price p on the overall supply chain revenue, the centralized supply chain model has the greatest overall supply chain benefit in three cases.•The impact of parameters K and M on the overall revenue of the supply chain in the three cases is that the overall revenue of the supply chain is reduced first and then gradually stabilized with the increase of the parameter value, and the overall revenue of the supply chain in the three cases is the highest overall income of the centralized supply chain.•When only the impact of price p on the R&D investment level of pre-cooling technology and refrigerated transport technology in three cases is considered, the centralized supply chain model has the highest level of R&D investment in pre-cooling technology and refrigerated transport technology in three cases.