Climate change mitigation can be achieved through the large-scale deployment of different carbon management technologies in industry. Governments will also play an important role in creating regulatory environments that incentivize low-carbon investments by self-interested private firms. In game theory, a class of problems known as Stackelberg (or leader-follower) games can be used to model such government-industry interactions. In a Stackelberg game, government is represented as an upper-level decision-maker (leader) and industry acts as the lower-level decision-maker (follower). The government’s problem is to set regulations and incentives so that industry’s rational profit-maximizing reaction aligns closely with the government objectives; the latter is assumed to be directed towards environmental protection on behalf of the general public. In this work, a P-graph based approach to solving a special class of Stackelberg game is developed. The leader is assumed to have binary variables for technology options, while the follower controls binary and continuous variables within the process networks formed by the available options (i.e., determined by the leader). The algorithm is illustrated on a case study involving the deployment of different negative emissions technologies (NETs). The combined use of biochar (BC) and direct air capture (DAC) is found to give near-optimal land and water footprints for the leader when the follower optimizes for cost.