Efficient Market Design with Distributional Objectives

TL;DR

This paper explores the design of market mechanisms that optimize distributional objectives while satisfying efficiency, individual rationality, and strategy-proofness, introducing a new mathematical concept to achieve this.

Contribution

The paper introduces pseudo M-natural concavity, a new discrete concavity notion, and constructs mechanisms that satisfy key properties under this condition.

Findings

Mechanisms may not always exist for certain distributional objectives.

Pseudo M-natural concavity enables the construction of desirable mechanisms.

Several practical distributional objectives are shown to be pseudo M-natural concave.

Abstract

Given an initial matching and a policy objective on the distribution of agent types to institutions, we study the existence of a mechanism that weakly improves the distributional objective and satisfies constrained efficiency, individual rationality, and strategy-proofness. We show that such a mechanism need not exist in general. We introduce a new notion of discrete concavity, which we call pseudo M$^{\natural}$-concavity, and construct a mechanism with the desirable properties when the distributional objective satisfies this notion. We provide several practically relevant distributional objectives that are pseudo M$^{\natural}$-concave.