Investigating the types of investment and its consequences has always been of interest to researchers and activists in the economic arena. One of the most common types of investment that today has significant volumes is foreign direct investment. Foreign direct investment is a kind of investment that is the country of the investor or its subsidiaries, invest in another country and have direct involvement in its management. In this research for the first time, the foreign direct investment with respect to different dimensions of sustainability and the use of game theory as an effective tool in multi-agent decision-making have been studied. For this purpose, a mathematical model has been developed. In the developed model, it has been tried to consider the most impressible and impressive factors in foreign direct investment. In this study, the host country and foreign direct investor as the decision-makers of the problem are looking for the most benefit. After the model is worked out, it is solved. The problem is modeled under three state. Also, for each problem state, different scenarios are defined and all scenarios are solved. To solve the model, the Stackelberg game is used. The host country is chosen as a leader and a foreign direct investor as a follower. The tax rate, the degree to which the foreign direct investor participates in the investment, the production capacity, and the green output of the production technology are the decisions that are made after the model is resolved. After the model is solved, the analysis of the results and the sensitivity analysis are discussed. The purpose of the analysis of the results and sensitivity analysis in the first stage is validation of the proposed model and then the extraction of research management points. The reasonableness of the results from the solution of the model, considering the structure of the problem and the assumptions considered, indicates the validity of the model. In order to extract managerial points, several analyzes have been done for the problem. The change in the tax and environmental policies of the host country and its effects on foreign direct investment has been examined. The results will help the host country to choose the right combination of tax and environmental policies to achieve the most desirable. The role of the risk and severity of foreign direct investment in the host country, the importance of the arrival of foreign capital in the host country, and the importance of investment for the host country have also been analyzed. The analysis shows the impact of each of these parameters on the decisions of the host country and foreign direct investor.