The German government attributes a crucial role to green hydrogen in the energy transition, as it has the potential to reduce greenhouse gas emissions when used as an energy carrier. However, currently, green hydrogen is not yet competitive. On the one hand, its production is costly, and on the other, current electrolysis capacities are insufficient to meet the potential demand. Therefore, at least during a transitional period, green hydrogen must compete with gray hydrogen produced from fossil energy sources. In this paper, we examine three government instruments aimed at increasing the market share of green hydrogen: taxes on gray hydrogen, subsidies for the green retailer, and financial support for expanding green hydrogen production capacities. In a bi-criteria, game-theoretic model, in which the government acts as the Stackelberg leader, we observe that all three measures can improve the position of green hydrogen on the market. Notably, the state’s sole intervention can significantly increase the sales volume of green hydrogen. However, if the state’s main focus is on balancing its net gain from hydrogen market interventions, it should concentrate on taxes. If finances and the sales volume of green hydrogen are equally important, the state will increasingly focus on positive measures and support capacity expansions. In contrast, if the state’s expenditures do not matter, the additional use of subsidies leads to maximizing the market share of green hydrogen.