Fair allocations for cooperation problems in vaccination

Vaccination is a very effective measure to fight an outbreak of an infectious disease, but it often suffers from delayed deliveries and limited stockpiles. To use these limited amounts of vaccines effectively, health agencies can decide to cooperate and share their vaccines. In this paper, we analyze this type of cooperation. Typically cooperation leads to an increased total return, but cooperation is only plausible when this total return can be distributed among the agents in a fair way. Using cooperative game theory, we derive theoretical sufficient conditions under which cooperation is plausible and we show that the resources can be traded for a market price in those cases. We perform numerical analyses to generalize these findings and we derive analytical expressions for market prices that can be used in general for distributing the total return in a fair way. Our results demonstrate that cooperation is a delicate matter. Cooperation is most likely to be plausible when the total amount of resources is limited or very large. In those cases, trading resources for a market price often results in a fair allocation of the total return. We confirm these findings with a case study on the redistribution of influenza vaccines.