June 8, 2017, 11:00–12:15
Toulouse
Room MS 001
MAD-Stat. Seminar
Abstract
We consider a planner's problem of splitting a continuum of agents (e.g., students) with one-dimensional heterogeneous characteristic (e.g., ability) to finitely many groups (e.g., schools) to maximize the planner's objective (e.g., total attainment). Certain constraints may be imposed on the number of groups, each group's size, and monotonicity of assignment. An agent in a group enjoys externality from the other agents in the group (e.g., peer effects) summarized by the average characteristics, and in this sense, splitting is a nontrivial problem. First, the optimal splitting is characterized in the ``linear'' environment, that is, in the environment where the planner's objective is affine in the agents' characteristics. Second, the optimal splitting is characterized in some ``nonlinear'' cases under additional assumptions of convexity-in-differences.