Strategic Immunization and Group Structure
We consider the spread of a harmful state through a population that is divided into two groups. The groups interact with each other to an extent that is parameterized, capturing the full spectrum from perfectly positive to perfectly negative assortativity. We first consider a central planner who can immunize a fraction of the population to eradicate the harmful state. The optimal policy either divides equally the resources across groups, or concentrates entirely on one group, depending on whether there is positive or negative assortative matching, respectively. Furthermore, the value of the social planner learning the exact level of assortativity is zero when interactions are positively assortative, and is increasing in the intensity of negative assortativity. We then study a game in which agents can, at a cost, achieve immunity. Inter-group interactions generate large asymmetries across groups in many outcomes of interest, such as welfare and prevalence, even when groups are, ex-ante, very similar. Hence, a failing to account for the impact of inter-group interactions may lead to over-estimating underlying differences across groups, and to suboptimal immunization plans.
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