Multi-Criteria Allocation Mechanisms: Constraints and Comparative Statics

Abstract

We study the structure of Pareto optimal mechanisms in settings where the planner considers more than one objective criterion. Specifically, we (i) characterize mechanisms that implement the entire Pareto frontier (which cannot be done by maximizing weighted sums of the criteria) and (ii) study how these mechanisms change along the Pareto frontier (comparative statics). We apply these findings to common problems, such as allocation of a public resource according to allocative efficiency and consumer surplus. We show that selecting a point to implement on the Pareto frontier is equivalent to determining the {\em extent of pooling}. Implementing points with higher allocative efficiency requires pooling smaller subsets of agents in the set-inclusion order. Thus, consumer surplus can be seen as a proxy for distributional equality on the Pareto frontier. We also apply the findings to auction design, and provide comparative statics about the structure and the reserve price of optimal auctions.