Optimal allocation design without transfers PRELIMINARY DRAFT

This paper studies the allocation of goods to agents without monetary transfers and incomplete information. Agents’ have private, multi-dimensional utilities over goods, drawn from commonly known priors, possibly asymmetric across agents’ types. Both cardinal and ordinal mechanisms are studied. For tractability, a large market approximation is considered with a continuum of agents for each type. We characterize incentive compatible mechanisms that are Pareto-optimal with respect to each type. For general objective functions, this allows reducing the mechanism design problem to a well-defined optimization problem with a few continuous variables. We apply this framework to real data from Boston 2012-2013 school choice reform. The goal is to design an optimal ordinal mechanism to assign students to public schools to maximize a linear combination of utilitarian and max-min welfare, subject to capacity and transportation constraints. We show how to optimally solve a large market model with over 868 types of students and 77 schools, translate the solution into the finite market setup and yield a feasible solution, which significantly outperforms the baseline plan chosen by the city in terms of efficiency, equity, and predictability.