Vaccination with partial knowledge of external effectiveness

Economists studying public policy have generally assumed that the relevant planner knows how policy affects population behavior. Planners typically do not possess all of this knowledge, so there is reason to consider policy formation with partial knowledge of policy impacts. Here I consider choice of a vaccination policy when a planner has partial knowledge of the effect of vaccination on illness rates. To begin, I pose a planning problem whose objective is to minimize the utilitarian social cost of illness and vaccination. The consequences of candidate vaccination rates depend on the extent to which vaccination prevents illness. I study the planning problem when the planner has partial knowledge of the external-response function, which expresses how the illness rate of unvaccinated persons varies with the vaccination rate. I suppose that the planner observes the illness rate of a study population whose vaccination rate has been chosen previously. He knows that the illness rate of unvaccinated persons weakly decreases as the vaccination rate increases, but he does not know the magnitude of the preventive effect of vaccination. In this setting, I first show how the planner can eliminate dominated vaccination rates and then how he can use the minimax or minimax-regret criterion to choose an undominated vaccination rate.