This study presents a game theory-based model to analyze the decision-making processes of key stakeholders in the exploration of natural hydrogen. The model incorporates uncertain parameters such as revenue from hydrogen businesses, government subsidies, and technological risks to provide a comprehensive framework for understanding the stakeholder decisions between governments and energy firms. Numerical experiments reveal that the probability of different Nash equilibria is significantly influenced by the levels of risk compensation and subsidies. Higher subsidies increase the likelihood of passive supervision and market entry by energy firms, while lower subsidies favor active supervision and market entry. These findings highlight key economic and regulatory considerations.