Implementing Maximum Matchings

34 Pages Posted: 12 Dec 2019

See all articles by Mustafa Oguz Afacan

Mustafa Oguz Afacan

Sabanci University

Inácio Bó

University of York - Department of Economics and Related Studies

Date Written: November 1, 2019


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. We provide comparisons with well-known mechanisms through computer simulations. Those show that the difference in number of matched agents between the proposed mechanisms and others 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, Implementing Maximum Matchings (November 1, 2019). Available at SSRN: or

Mustafa Oguz Afacan

Sabanci University ( email )

Faculty of Art and Social Sciences
Orhanli Tuzla
İstanbul, 34956

Inácio Bó (Contact Author)

University of York - Department of Economics and Related Studies ( email )

York, YO1 5DD
United Kingdom


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