Increasing customer apprehensions regarding the security and nutritional value of agricultural goods are compelling governments and industries to implement traceable, transparent, and reputable logistics management systems. Blockchain-based agricultural logistics management systems guarantee the permanence of data once it is uploaded but cannot cope with the risk of data being falsified before uploading to the blockchain. In this work, we developed a collaborative game model between government bodies and agricultural enterprises based on the evolutionary game theory and explored the influencing factors of enterprises following the rules to share the real traceability information through numerical simulation using MATLAB. The findings show that government incentives and penalties promote positive behavior, and consumer and media supervision contribute to supply chain transparency, but firms tend to share truthful information only when it benefits them. This study builds upon existing research on the impact of social variables on both members' decision-making behavior. It highlights the positive roles of consumers and the media in the supervision of agricultural product traceability, which can help to raise public awareness of social responsibility and thus promote positive interaction in the market.