A game theoretic approach identifies conditions that foster vaccine-rich to vaccine-poor country donation of surplus vaccines

Background Scarcity in supply of COVID-19 vaccines and severe international inequality in their allocation present formidable challenges. These circumstances stress the importance of identifying the conditions under which self-interested vaccine-rich countries will voluntarily donate their surplus vaccines to vaccine-poor countries. Methods We develop a game-theoretical approach to identify the vaccine donation strategy that is optimal for the vaccine-rich countries as a whole; and to determine whether the optimal strategy is stable (Nash equilibrium or self-enforcing agreement). We examine how the results depend on the following parameters: the fraction of the global unvaccinated population potentially covered if all vaccine-rich countries donate their entire surpluses; the expected emergence rate of variants of concern (VOC); and the relative cost of a new VOC outbreak that is unavoidable despite having surplus doses. Results We show that full or partial donations of the surplus stock are optimal in certain parameter ranges. Notably, full surplus donation is optimal if the global amount of surplus vaccines is sufficiently large. Within a more restrictive parameter region, these optimal strategies are also stable. Conclusions Our results imply that, under certain conditions, coordination between vaccine-rich countries can lead to significant surplus donations even by strictly self-interested countries. However, if the global amount that countries can donate is small, we expect no contribution from self-interested countries. The results provide guidance to policy makers in identifying the circumstances in which coordination efforts for vaccine donation are likely to be most effective. Plain language summary In an unequal world with open economies, pandemics do not stop at national borders. Higher-income countries may then benefit from helping lower-income countries. In particular, since new variants of a virus may emerge in vaccine-poor countries, vaccine-rich countries may have a strong incentive to donate their surplus vaccine doses rather than stocking these domestically. But under which conditions will such self-interested donations occur? We develop a game-theoretic model, used to analyze the strategies of rational decision makers and how they depend on strategies of other decision-makers. We show that, if vaccine-rich countries can vaccinate a large share of the vaccine-poor world, it is optimal for them to donate their surplus vaccines. In certain c