Assignment Maximization

TL;DR

This paper investigates the challenges of maximizing individual matchings in assignment problems, revealing inherent impossibilities, and proposes two classes of mechanisms that optimize assignments while addressing fairness and efficiency.

Contribution

It introduces two novel classes of mechanisms that maximize assignments, balancing efficiency and fairness despite theoretical limitations.

Findings

Pareto efficient, undominated mechanisms in equilibrium.

Mechanisms that are fair for unassigned students and assign more students than stable mechanisms.

Demonstrates the inherent impossibilities in achieving all goals simultaneously.

Abstract

We evaluate the goal of maximizing the number of individuals matched to acceptable outcomes. We show that it implies incentive, fairness, and implementation impossibilities. Despite that, we present two classes of mechanisms that maximize assignments. The first are Pareto efficient, and undominated -- in terms of number of assignments -- in equilibrium. The second are fair for unassigned students and assign weakly more students than stable mechanisms in equilibrium.