The present study aimed to identify and prioritize determinants of the interaction between lean production management stakeholders in the National Iranian Oil Company. The statistical population consisted of all key experts in the field of National Iranian Oil Company and the statistical sample included 25 experts of the National Iranian South Oil Company who were selected using the purposive sampling method. To analyze the data obtained from interviews and questionnaires, the most important criteria and key sub-criteria affecting the supply chain were first localized using Saaty's Delphi method, and then the relationships of the factors were determined using the Fuzzy DEMATEL method and with the help of experts, and the criteria and sub-criteria were ranked. MATLAB software was also utilized for data analysis. In this research, the initial framework of the stakeholder interaction management model was created using the dynamic game theory approach in the lean management process, and their solutions were compared in three game scenarios, namely Nash, Stackelberg, and cooperative scenarios. Based on the research results, the correct layout was the most effective criterion, and up-to-date and efficient equipment was the most affectable sub-criterion. Among the main criteria, logistics ability was the most effective criterion, and financial ability was the most affectable criterion. In terms of interaction, new production items had the highest interaction and correct layout had the lowest interaction. The highest interaction of the main criteria was related to experience and the least was related to production ability. Based on the results, the producer preferred to choose the Stackelberg game with the suppliers and act as a leader and make decisions independently from the suppliers in the present study, thereby, obtaining more profit and production, and then more popularity among people.