This paper examines how two countries would allocate resources at the onset of an epidemic when they seek to protect their own populations by minimizing the total number of infectives over the entire time horizon. We model this situation as a game between selfish countries, where players strategically allocate their resources in order to minimize the total number of infected individuals in their respective populations during the epidemic. We study this problem when the initial number of infectives is very small, which greatly simplifies the analysis. We show in this framework that selfish countries always allocate their resources so as to bring the effective reproduction ratio below one and avoid a major outbreak. When a major outbreak is avoidable, we further identify the necessary and sufficient conditions under which the individual allocation decisions of selfish countries match the decision that a central planner would make in order to minimize the total number of infectives in the whole population (without distinguishing between countries).