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Assignment Maximization

29 Pages Posted: 15 Sep 2017  

Mustafa Oguz Afacan

Sabanci University

Inácio Bó

WZB Berlin Social Science Center

Bertan Turhan

Instituto Technologico Autonomo de Mexico (ITAM)

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

Afacan, Mustafa Oguz and Bó, Inácio and Turhan, Bertan, Assignment Maximization (September 2017). Available at SSRN:

Mustafa Afacan

Sabanci University ( email )

Faculty of Art and Social Sciences
Orhanli Tuzla
İstanbul, 34956

Inácio Bó (Contact Author)

WZB Berlin Social Science Center ( email )

Reichpietschufer 50
D-10785 Berlin, 10785


Bertan Turhan

Instituto Technologico Autonomo de Mexico (ITAM) ( email )

Av Camino a Santa Teresa 930, Magdalena Contreras
Col. Héroes de Padierna
Mexico City, Federal District 10700

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