As immunization campaigns are accelerating, understanding how to distribute the scarce doses of vaccines is of paramount importance and a quantitative analysis of the trade-offs involved in domestic-only versus cooperative distribution is still missing. In this study we use a network Susceptible-Infected-Removed (SIR) model to show circumstances under which it is in a country's self-interest to ensure other countries can obtain COVID-19 vaccines rather than focusing only on vaccination of their own residents. In particular, we focus our analysis on the United States and estimate the internal burden of COVID-19 disease under different scenarios about vaccine cooperation. We show that in scenarios in which the US has reached the threshold for domestic herd immunity, the US may find it optimal to donate doses to other countries with lower vaccination coverage, as this would allow for a sharp reduction in the inflow of infected individuals from abroad.