Assigning a Treatment under Hidden Spillovers

This paper studies the assignment of a treatment by a social planner when the valuations of the treatment are interdependent across individuals in the population. Specifically, an individual’s valuation of the treatment is influenced by the treatment status of some group of individuals and is positive if and only if any member of the group is treated. The identities of those who have positive spillovers on an individual is his private type, and the social planner assigns the treatment based on their reported types aiming to maximize the number of treated individuals less subsidies. We study the property of an assignment mechanism that offers a subsidy to a single individual and provides the treatment to everyone over whom this individual has positive spillovers either directly or indirectly. We use the percolation theorem of McDiarmid (1981) to show that the number of treated individuals under such a mechanism is independent of the reciprocal property of the spillover relationship, and is asymptotically optimal when the population grows large.