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Rare metal minerals are important strategic resources. Promoting the sustainable development of their mining process is not only related to energy and environmental issues, but also directly affects the sustainable development of the entire supply chain. Considering the influence of intergenerational externalities on the equilibrium in the rare metal mineral exploitation process is of critical significance to maintaining the sustainable development of rare metal minerals and securing a sustainable resource exploitation process. This paper develops a sustainability analysis model based on an intergenerational externalities influence and examines the influence of the shift in comprehensive production cost burden through the whole supply chain, which aims at the sustainable development of the exploitation process of rare metal minerals. The results indicate that in a vertically linked industrial chain, the upstream and downstream structure of the supply chain and the type of production cost are the factors that determine sustainable development. Upstream suppliers or countries should design their production systems based on their own circumstances. Specifically, when an upstream country has a low technological level for mineral exploitation processes and high development costs, a resource tax would be more effective in mediating sustainable development.

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In rare metal mineral market, as a complex system, multiple decision-making among the stakeholders increases the complexity in its market structure and dynamic process. The unreasonable compensation pricing mechanism for the development of the rare metal mineral resources in China requires to be studied. Drawing on the methods of game theory model and chaos control analysis, this paper builds theoretical model of rare metal mineral market structure, corporating related parameters of rare metal in the game theory model, to conduct the chaotic nature and path analysis, expecting to solve the bottleneck problems that restrict the rare metal pricing and resource security and enhance the waste valorization for the sustainability. Specificly, a Cournot-Nash Equilibrium model is built to analyze the Cournot-equilibrium point, the stability of the Cournot Equilibrium point, the chaotic status, as well as the pattern to chaos of the game system in the rare metal mineral resource market, numerical simulation is used to verify the model. The conclusions facilitate the formulation of industrial economic policies and further improvement of managerial strategies to solve market problems.