Dynamic Reserves in Matching Markets
57 Pages Posted: 7 Mar 2016 Last revised: 9 Nov 2018
Date Written: October 30, 2018
We study a school choice problem under affirmative action policies where authorities reserve certain fractions of the seats at each school to specific student groups, and students have preferences not only over the schools they are matched to but also what type of seats they receive. Such reservation policies might cause waste when there is low demand from some student groups. To propose a solution to this issue we construct a family of choice functions, dynamic reserves choice functions, for schools that respect within-group fairness and allow transferring otherwise vacant seats from low-demand groups to high demand-groups. We analyze the properties of the choice functions in this family. We propose the cumulative offer mechanism as an allocation function where each school uses a dynamic reserves choice function and show that it is stable with respect to schools' choice functions, is strategy-proof, and respects improvements in school priorities. Furthermore, we provide comparative statics results on capacity transfer schemes one of which is that transferring more of otherwise vacant slots leads to strategy proof Pareto improvement under the cumulative offer mechanism.
Keywords: Affirmative Action, Dynamic Reserves, Market Design, Matching with Contracts, Strategy-Proofness, School Choice
JEL Classification: C78, D63, D78, J15
Suggested Citation: Suggested Citation