The COVAX program aims to provide global equitable access to life-saving vaccines. Despite calls for increased sharing, vaccine protectionism has limited progress towards vaccine sharing goals. For example, as of April 2022 only ~20% of the population in Africa had received at least one COVID-19 vaccine dose. Here we use a two-nation coupled epidemic model to evaluate optimal vaccine-sharing policies given a selfish objective: in which countries with vaccine stockpiles aim to minimize fatalities in their own population. Computational analysis of a suite of simulated epidemics reveal that it is often optimal for a donor country to share a significant fraction of its vaccine stockpile with a recipient country that has no vaccine stockpile. Sharing a vaccine stockpile reduces the intensity of outbreaks in the recipient, in turn reducing travel-associated incidence in the donor. This effect is intensified as vaccination rates in a donor country decrease and epidemic coupling between countries increases. Critically, vaccine sharing by a donor significantly reduces transmission and fatalities in the recipient. Moreover, the same computational framework reveals the potential use of hybrid sharing policies that have a negligible effect on fatalities in the donor compared to the optimal policy while significantly reducing fatalities in the recipient. Altogether, these findings provide a self-interested rationale for countries to consider sharing part of their vaccine stockpiles.