Abstract

The paper to be presented is:

Title: First-Choice Maximal and First-Choice Stable School Choice Mechanisms
Authors: Umut Dur, Timo Mennle, Sven Seuken

Paper Abstract: We investigate the class of school choice mechanisms that are first-choice maximal (FCM)(i.e., they match a maximal number of students to their reported first choices) and first-choice stable (FCS) (i.e., no students form blocking pairs with their reported first choices). FCM is a ubiquitous desideratum in school choice,and we show that FCS is the only rank-based relaxation of stability that is compatible with FCM. The class of FCM and FCS mechanisms includes variants of the well-known Boston mechanism as well as certain Asymmetric Chinese Parallel mechanisms. Regarding incentives, we show that while no mechanism in this class is strategy proof, the Pareto efficient ones are least susceptible to manipulation. Regarding student welfare,we show that the Nash equilibrium outcomes of these mechanisms correspond precisely to the set of stable matchings. By contrast, when some students are sincere, we show that more students may be matched to their true first choices in equilibrium than under any stable matching. Finally, we show how our results can be used to obtain a new characterization of the Boston mechanism (i.e., the most widely used FCM and FCS mechanism). On a technical level, this paper provides new insights about an influential class of school choice mechanisms. For practical market design, our results yield a potential rationale for the popularity of FCM and FCS mechanisms in practice.

Link to paper.

This week's presenter is: Vishnu Narayan, McGill University.

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