Market Design Under Distributional Constraints: Diversity in School Choice and Other Applications

Author(s):  
Daniel Fragiadakis ◽  
Peter Troyan

2016 ◽  
Vol 166 ◽  
pp. 186-211 ◽  
Author(s):  
John William Hatfield ◽  
Fuhito Kojima ◽  
Yusuke Narita


Author(s):  
Zhaohong Sun

In recent years, a number of new challenges have been observed in the application of matching theory. One of the most pressing problems concerns how to allocate refugees to hosts safely and in a timely manner. Currently, this placement is implemented on an ad hoc basis where the preferences of both refugees and hosts are not taken into account. Another important realization is that real-life matching markets are often subject to various distributional constraints. For example, there has been increased attention to school choice models that take account of affirmative action and diversity concerns. The objective of this research is to design efficient algorithms while satisfying desirable properties for these new emerging problems.



2017 ◽  
Vol 58 ◽  
pp. 153-184 ◽  
Author(s):  
Ryoji Kurata ◽  
Naoto Hamada ◽  
Atsushi Iwasaki ◽  
Makoto Yokoo

School choice programs are implemented to give students/parents an opportunity to choose the public school the students attend. Controlled school choice programs need to provide choices for students/parents while maintaining distributional constraints on the composition of students, typically in terms of socioeconomic status. Previous works show that setting soft-bounds, which flexibly change the priorities of students based on their types, is more appropriate than setting hard-bounds, which strictly limit the number of accepted students for each type. We consider a case where soft-bounds are imposed and one student can belong to multiple types, e.g., “financially-distressed” and “minority” types. We first show that when we apply a model that is a straightforward extension of an existing model for disjoint types, there is a chance that no stable matching exists. Thus we propose an alternative model and an alternative stability definition, where a school has reserved seats for each type. We show that a stable matching is guaranteed to exist in this model and develop a mechanism called Deferred Acceptance for Overlapping Types (DA-OT). The DA-OT mechanism is strategy-proof and obtains the student-optimal matching within all stable matchings. Furthermore, we introduce an extended model that can handle both type-specific ceilings and floors and propose a extended mechanism DA-OT* to handle the extended model. Computer simulation results illustrate that DA-OT outperforms an artificial cap mechanism where we set a hard-bound for each type in each school. DA-OT* can achieve stability in the extended model without sacrificing students’ welfare.



2017 ◽  
Vol 33 (4) ◽  
pp. 613-634 ◽  
Author(s):  
Estelle Cantillon


Author(s):  
John William Hatfield ◽  
Fuhito Kojima ◽  
Yusuke Narita




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