29 Pages Posted: 15 Sep 2017
Date Written: September 2017
In this paper we evaluate the policy goal of maximizing the number of individuals matched to individually rational assignments in matching markets. We show that assignment maximization is incompatible with both strategy-proofness and fairness, and impossible in equilibrium. We introduce two classes of mechanisms that maximize the number of assigned agents: the Efficient Assignment Maximizing mechanisms (EAM) and the Fair Assignment Maximizing mechanisms (FAM). EAMs maximize assignments and are Pareto efficient. We characterize the unique equilibrium of EAMs, which is Pareto efficient, and show that no mechanism can dominate – in terms of number of assignments – EAMs in equilibrium. FAMs maximize assignments and are fair for unassigned students (a weaker notion of fairness). We show that in equilibrium FAMs assign to schools weakly more than the number of students matched in any stable mechanism. We also provide some comparison of well-known mechanisms in terms of number of assignments and test our theoretical results by conducting computer simulations. Those show that the difference between the number of matched agents by EAM/FAM and other mechanisms in the literature is large and significant.
Keywords: Market Design, Matching, Maximal Matching, Fairness, Object Allocation, School Choice
JEL Classification: D47, C78, D63
Suggested Citation: Suggested Citation