Equilibrium strategy for deep-sea mineral investments amid protester actions: Balancing terrestrial benefits and marine preservation

Deep-sea mining (DSM) supplies resources to produce new energy materials, which offers benefits for terrestrial environments while causing significant risks to marine ecosystems. To mitigate marine pollution, it is essential to assess the behavior interactions among three parties: new energy materials suppliers (NEMSs), protesters, and governmental bodies. This study develops a game-theoretic framework incorporating stochastic disturbances via stochastic differential equations. The results indicate that: (1) Incomplete information about the government stance distorts the investment range for NEMSs. By strengthening social welfare initiatives, NEMSs can expect clearer government support, optimizing the investment environment. Intriguingly, the analysis suggests that ambiguous governmental attitudes may inadvertently incentivize NEMSs to enhance their social responsibilities. In our simulation experiments, the government's ambiguous approach to DSM has the potential to increase the social welfare provided by NEMSs from the original 10 %–20 %. (2) The consistency and efficacy of governmental policies moderate the impact of protesters on NEMSs' decision-making processes. In contrast to the ambiguity of external policies, the government's internal stance on DSM should maintain clarity and consistency. The divergent policy approaches applied by relevant authorities to various stakeholder groups can effectively channel social forces to facilitate the responsible development of DSM. (3) Environmental protests are not always entirely eco-friendly. Some protest activities have devolved into mere symbolic exercises, lacking substantive impact. Avoiding formism is the primary task to maintain the effectiveness and compliance of public supervision. (4) Finally, the core results of the main model are extended by designing three types of regulations: subsidies, penalties, and mixed framework. Based on this, we give an effective penalty elasticity based on the regulation intensity and provide an optimal form of subsidy.