Multiple Equilibria in the Vaccination Game: Nash Equilibrium and Socially Optimal Policy Choices

In recent years, global infectious disease pandemics have emerged as one of the most pressing environmental issues, posing a major threat to public health and social stability worldwide. According to previous research, the rational decisions of individuals often lead to lower vaccination rates than the optimal level of society. In this paper, we investigate the difference between Nash equilibrium and socially optimal solution of individual vaccination decisions in the context of a global pandemic. The aim is to establish a theoretical model, analyze the gap between the two, and then propose suggestions for optimizing public health policies to improve vaccination rates, achieve herd immunity, and maximize social welfare. This paper uses the game theory method to set up the basic hypothesis, construct the game model, and the social welfare function, analyze the Nash equilibrium, the social optimal solution and the dynamic model, and make a comparative analysis. Studies have found that individual rational decision-making leads to a lower vaccination rate than the socially optimal level, and it is difficult to achieve herd immunity. On this basis, it is suggested that the government should adopt policy intervention measures such as subsidies, publicity and education, long-term incentives, and improving information transparency. The conclusion shows that policy intervention can effectively improve the current situation, but the model has limitations. Further studies can be conducted from the aspects of parameter sensitivity analysis, incomplete information and individual heterogeneity.