Renewable portfolio standard (RPS) is a legislative requirement for regulating the utility to increase the output of renewable energy, however, it’s not easy for the government to optimally design the target. To address this problem, this study investigates solar investing problems by theoretically investigating a novel game model. To meet the RPS requirement, the utility has to procure not only traditional energy but also solar energy. This paper aims to capture all the frictions among the stakeholders including the regulator, the utility and also a photovoltaic (PV) developer. The results show that the regulator can benefit from the strategy with higher RPS requirements if there is less resistance to regulation and a high penalty rate. Besides, the development of solar technology will increase the optimal PV panel price and investment in solar. Given a high requirement of renewable output, it’s better off to increase the solar investment for more green output. This study also finds the developer enjoys a high requirement because it promotes the PV adoption and increases the panel price as well. Additionally, a dynamic system was developed to study the players’ long-term behavior as well. The stable region and optimal strategy of behavior have been figured out. Interestingly, for the developer and the utility, a salutation of profit regarding the raising of the regulator’s adjusting speed of decision is observed.

Bibliometric techniques and social network analysis are employed in this study to evaluate 14,955 papers on air pollution and health that were published from 2001 to 2021. To track the research hotspots, the principle of machine learning is applied in this study to divide 10,212 records of keywords into 96 clusters through OmniViz software. Our findings highlight strong research interests and the practical need to control air pollution to improve human health, as evidenced by an annual growth rate of over 15.8% in the related publications. The cluster analysis showed that clusters C22 (exposure, model, mortality) and C8 (health, environment, risk) are the most popular topics in this field of research. Furthermore, we develop co-occurrence networks based on the cluster analysis results in which a more specific keyword classification was obtained. These key areas include: “Air pollutant source”, “Exposure-Response relationship”, “Public & Occupational Health”, and so on. Future research hotspots are analyzed through characteristics of the cluster groups, including the advancement of health risk assessment techniques, an interdisciplinary approach to quantifying human exposure to air pollution, and strategies in health risk assessment.