This paper focuses on the economics of vaccination and, more specifically, analyzes the vaccination decision of individuals using a game-theoretic model combined with an epidemiological SIR model that reproduces the infection dynamics of a generic disease. We characterize the equilibrium individual vaccination rate, and we show that it is below the rate compatible with herd immunity due to the existence of externalities that individuals do not internalize when they decide on vaccination. In addition, we analyze three public policies consisting of informational campaigns to reduce the disutility of vaccination, monetary payments to vaccinated individuals and measures to increase the disutility of non-vaccination. If the public authority uses only one type of policy, herd immunity is not necessarily achieved unless monetary incentives are used. When the public authority is not limited to use only one policy, we find that the optimal public policy should consist only of informational campaigns if they are sufficiently effective, or a combination of informational campaigns and monetary incentives otherwise. Surprisingly, the requirement of vaccine passports or other restrictions on the non-vaccinated are not desirable.