The performance of government subsidy schemes in a competitive vaccine market considering consumers' free-riding behavior

Vaccination is acknowledged as the most cost-effective means of combating epidemics. However, the free-riding behavior frequently results in vaccination rates falling below the socially optimal level. To address this issue, governments frequently offer subsidies to either vaccine suppliers or consumers. This paper develops a game theoretic model that incorporates two vaccine suppliers with different efficacy rates and prices. We propose two subsidy schemes, one based on vaccine price and the other based on vaccine efficacy rate, with the aim of improving vaccination rates. Our results demonstrate that the price-based subsidy scheme (PSS) leads to a higher vaccine price compared to the efficacy-based subsidy scheme (ESS). Moreover, the ESS proves more effective in increasing the equilibrium vaccination rate when the efficacy rate is low, while the PSS is more effective when the efficacy rate is high. However, if the government's budget is limited, the ESS is more likely to improve the equilibrium vaccination rate compared to the PSS.