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A novel hierarchical graph model, called hierarchical graph model with sequential moves (SHGM), is developed to investigate interrelated conflicts in which common decision-makers (CDMs), participating in all interrelated conflicts, unilaterally move in one subconflict at a time. The preferences of decision-makers are described by a scoring system. Equilibria under different solution concepts are calculated as the indication of possible outcomes or strategic resolutions for decision-makers. This novel methodology is applied to subsidy disputes between the national government in China and two provincial governments, typical hierarchical conflicts containing sequential moves of the national government who wishes to strategically allocate the limited subsidies to encourage the compliance of carbon mitigation policies by the provinces. In-depth analysis is carried out to determine the equilibria that can be evolved from the starting state, called the status quo. Among these equilibria, the most preferred one for the national government, called the optimal equilibrium, suggests meaningful resolutions for each decision-maker. In particular, the national government in China is advised to subsidize the more industrialized province so that both provinces would comply with its carbon mitigation policies.