Core 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 doses of vaccine effectively, health agencies can decide to cooperate and share their doses. In this study, 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 in a stable way. This makes cooperation a delicate matter. Using cooperative game theory, we derive theoretical sufficient conditions under which cooperation is plausible (i.e., the core is non-empty) and we show that the doses of vaccine 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. Our results demonstrate that cooperation is most likely to be plausible in case of severe shortages and in case of sufficient supply, with possible mismatches between supply and demand. In those cases, trading doses of vaccine for a market price often results in a core allocation of the total return. We confirm these findings with a case study on the redistribution of influenza vaccines.

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