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Introduction Early constraints on vaccine supply during the COVID-19 pandemic prompted many public health leaders to recommend taking the first vaccine available, though many individuals chose to wait for a ‘more effective’ vaccine. This indicates a potential tension between the vaccination strategy that individuals find in their own best interest and the one that maximises population well-being.Methods We integrate a mathematical epidemiological model and an economic decision-making model to determine the conditions under which rational and self-interested individuals opt to wait for a more effective vaccine instead of taking the one readily available and whether their choices align with what is optimal from a population-level perspective. We consider different assumptions about the characteristics of the available vaccines and the severity of the pandemic, and we investigate the population health consequences if individuals stray from the vaccination strategy that best promotes population well-being.Results Taking the first vaccine available is not always optimal from a population-level perspective, but uncertainty about the characteristics of a subsequent vaccine increases the likelihood that this is indeed in the best interest of the population as a whole. However, protection offered by the vaccination of others may induce a greater proportion of rational and self-interested individuals to wait for the more effective vaccine than what would be optimal from a population-level perspective. If individuals decide to follow their own best interests, more people will end up waiting for the more effective vaccine, resulting in more infections and deaths during the waiting period.Conclusions Our results will help policymakers facing future pandemics to craft recommendations that reduce disease transmission and save lives when early vaccines may be less effective than future vaccines.